The Experts below are selected from a list of 16587 Experts worldwide ranked by ideXlab platform
Volker Springel - One of the best experts on this subject based on the ideXlab platform.
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non ideal magnetohydrodynamics on a Moving Mesh
Monthly Notices of the Royal Astronomical Society, 2018Co-Authors: Federico Marinacci, Mark Vogelsberger, Philip Mocz, Rudiger Pakmor, Rahul Kannan, Volker SpringelAbstract:In certain astrophysical systems the commonly employed ideal magnetohydrodynamics (MHD) approximation breaks down. Here, we introduce novel explicit and implicit numerical schemes of ohmic resistivity terms in the Moving-Mesh code AREPO. We include these non-ideal terms for two MHD techniques: the Powell 8-wave formalism and a constrained transport scheme, which evolves the cell-centred magnetic vector potential. We test our implementation against problems of increasing complexity, such as one- and two-dimensional diffusion problems, and the evolution of progressive and stationary Alfven waves. On these test problems, our implementation recovers the analytic solutions to second-order accuracy. As first applications, we investigate the tearing instability in magnetized plasmas and the gravitational collapse of a rotating magnetized gas cloud. In both systems, resistivity plays a key role. In the former case, it allows for the development of the tearing instability through reconnection of the magnetic field lines. In the latter, the adopted (constant) value of ohmic resistivity has an impact on both the gas distribution around the emerging protostar and the mass loading of magnetically driven outflows. Our new non-ideal MHD implementation opens up the possibility to study magneto-hydrodynamical systems on a Moving Mesh beyond the ideal MHD approximation.
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simulating cosmic ray physics on a Moving Mesh
Monthly Notices of the Royal Astronomical Society, 2017Co-Authors: Christoph Pfrommer, Volker Springel, Rudiger Pakmor, Kevin Schaal, Christine M SimpsonAbstract:We discuss new methods to integrate the cosmic ray (CR) evolution equations coupled to magneto-hydrodynamics (MHD) on an unstructured Moving Mesh, as realised in the massively parallel AREPO code for cosmological simulations. We account for diffusive shock acceleration of CRs at resolved shocks and at supernova remnants in the interstellar medium (ISM), and follow the advective CR transport within the magnetised plasma, as well as anisotropic diffusive transport of CRs along the local magnetic field. CR losses are included in terms of Coulomb and hadronic interactions with the thermal plasma. We demonstrate the accuracy of our formalism for CR acceleration at shocks through simulations of plane-parallel shock tubes that are compared to newly derived exact solutions of the Riemann shock tube problem with CR acceleration. We find that the increased compressibility of the post-shock plasma due to the produced CRs decreases the shock speed. However, CR acceleration at spherically expanding blast waves does not significantly break the self-similarity of the Sedov-Taylor solution; the resulting modifications can be approximated by a suitably adjusted, but constant adiabatic index. In first applications of the new CR formalism to simulations of isolated galaxies and cosmic structure formation, we find that CRs add an important pressure component to the ISM that increases the vertical scale height of disk galaxies, and thus reduces the star formation rate. Strong external structure formation shocks inject CRs into the gas, but the relative pressure of this component decreases towards halo centres as adiabatic compression favours the thermal over the CR pressure.
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a Moving Mesh unstaggered constrained transport scheme for magnetohydrodynamics
Monthly Notices of the Royal Astronomical Society, 2016Co-Authors: Philip Mocz, Volker Springel, Mark Vogelsberger, Rudiger Pakmor, Federico Marinacci, Lars HernquistAbstract:We present a constrained transport (CT) algorithm for solving the 3D ideal magnetohydrodynamic (MHD) equations on a Moving Mesh, which maintains the divergence-free condition on the magnetic field to machine-precision. Our CT scheme uses an unstructured representation of the magnetic vector potential, making the numerical method simple and computationally efficient. The scheme is implemented in the Moving Mesh code Arepo. We demonstrate the performance of the approach with simulations of driven MHD turbulence, a magnetized disc galaxy, and a cosmological volume with primordial magnetic field. We compare the outcomes of these experiments to those obtained with a previously implemented Powell divergence-cleaning scheme. While CT and the Powell technique yield similar results in idealized test problems, some differences are seen in situations more representative of astrophysical flows. In the turbulence simulations, the Powell cleaning scheme artificially grows the mean magnetic field, while CT maintains this conserved quantity of ideal MHD. In the disc simulation, CT gives slower magnetic field growth rate and saturates to equipartition between the turbulent kinetic energy and magnetic energy, whereas Powell cleaning produces a dynamically dominant magnetic field. Such difference has been observed in adaptive-Mesh refinement codes with CT and smoothed-particle hydrodynamics codes with divergence-cleaning. In the cosmological simulation, both approaches give similar magnetic amplification, but Powell exhibits more cell-level noise. CT methods in general are more accurate than divergence-cleaning techniques, and, when coupled to a Moving Mesh can exploit the advantages of automatic spatial/temporal adaptivity and reduced advection errors, allowing for improved astrophysical MHD simulations.
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semi implicit anisotropic cosmic ray transport on an unstructured Moving Mesh
Monthly Notices of the Royal Astronomical Society, 2016Co-Authors: Rudiger Pakmor, Volker Springel, Rahul Kannan, Christoph Pfrommer, Christine M SimpsonAbstract:In the interstellar medium of galaxies and the intracluster gas of galaxy clusters, the charged particles making up cosmic rays are Moving almost exclusively along (but not across) magnetic field lines. The resulting anisotropic transport of cosmic rays in the form of diffusion or streaming not only affects the gas dynamics but also rearranges the magnetic fields themselves. The coupled dynamics of magnetic fields and cosmic rays can thus impact the formation and evolution of galaxies and the thermal evolution of galaxy clusters in critical ways. Numerically studying these effects requires solvers for anisotropic diffusion that are accurate, efficient, and robust, requirements that have proven difficult to satisfy in practice. Here, we present an anisotropic diffusion solver on an unstructured Moving Mesh that is conservative, does not violate the entropy condition, allows for semi-implicit time integration with individual timesteps, and only requires solving a single linear system of equations per timestep. We apply our new scheme to a large number of test problems and show that it works as well or better than previous implementations. Finally, we demonstrate for a numerically demanding simulation of the formation of an isolated disk galaxy that our local time-stepping scheme reproduces the results obtained with global time-stepping at a fraction of the computational cost.
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improving the convergence properties of the Moving Mesh code arepo
Monthly Notices of the Royal Astronomical Society, 2016Co-Authors: Rudiger Pakmor, Diego J Munoz, Volker Springel, Philip Mocz, Andreas Bauer, Sebastian T Ohlmann, Kevin SchaalAbstract:Accurate numerical solutions of the equations of hydrodynamics play an ever more important role in many fields of astrophysics. In this work, we reinvestigate the accuracy of the Moving-Mesh code \textsc{Arepo} and show how its convergence order can be improved for general problems. In particular, we clarify that for certain problems \textsc{Arepo} only reaches first-order convergence for its original formulation. This can be rectified by simple modifications we propose to the time integration scheme and the spatial gradient estimates of the code, both improving the accuracy of the code. We demonstrate that the new implementation is indeed second-order accurate under the $L^1$ norm, and in particular substantially improves conservation of angular momentum. Interestingly, whereas these improvements can significantly change the results of smooth test problems, we also find that cosmological simulations of galaxy formation are unaffected, demonstrating that the numerical errors eliminated by the new formulation do not impact these simulations. In contrast, simulations of binary stars followed over a large number of orbital times are strongly affected, as here it is particularly crucial to avoid a long-term build up of errors in angular momentum conservation.
Weizhang Huang - One of the best experts on this subject based on the ideXlab platform.
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a quasi lagrangian Moving Mesh discontinuous galerkin method for hyperbolic conservation laws
Journal of Computational Physics, 2019Co-Authors: Weizhang HuangAbstract:Abstract A Moving Mesh discontinuous Galerkin method is presented for the numerical solution of hyperbolic conservation laws. The method is a combination of the discontinuous Galerkin method and the Mesh movement strategy which is based on the Moving Mesh partial differential equation approach and moves the Mesh continuously in time and orderly in space. It discretizes hyperbolic conservation laws on Moving Meshes in the quasi-Lagrangian fashion with which the Mesh movement is treated continuously and no interpolation is needed for physical variables from the old Mesh to the new one. Two convection terms are induced by the Mesh movement and their discretization is incorporated naturally in the DG formulation. Numerical results for a selection of one- and two-dimensional scalar and system conservation laws are presented. It is shown that the Moving Mesh DG method achieves the second and third order of convergence for P 1 and P 2 elements, respectively, for problems with smooth solutions and is able to capture shocks and concentrate Mesh points in non-smooth regions. Its advantage over uniform Meshes and its insensitiveness to Mesh smoothness are also demonstrated.
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Moving Mesh simulation of contact sets in two dimensional models of elastic electrostatic deflection problems
Journal of Computational Physics, 2018Co-Authors: Kelsey L Dipietro, Weizhang Huang, Ronald D Haynes, Alan E LindsayAbstract:Abstract Numerical and analytical methods are developed for the investigation of contact sets in electrostatic–elastic deflections modeling micro-electro mechanical systems. The model for the membrane deflection is a fourth-order semi-linear partial differential equation and the contact events occur in this system as finite time singularities. Primary research interest is in the dependence of the contact set on model parameters and the geometry of the domain. An adaptive numerical strategy is developed based on a Moving Mesh partial differential equation to dynamically relocate a fixed number of Mesh points to increase density where the solution has fine scale detail, particularly in the vicinity of forming singularities. To complement this computational tool, a singular perturbation analysis is used to develop a geometric theory for predicting the possible contact sets. The validity of these two approaches are demonstrated with a variety of test cases.
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a quasi lagrangian Moving Mesh discontinuous galerkin method for hyperbolic conservation laws
arXiv: Numerical Analysis, 2018Co-Authors: Weizhang HuangAbstract:A Moving Mesh discontinuous Galerkin method is presented for the numerical solution of hyperbolic conservation laws. The method is a combination of the discontinuous Galerkin method and the Mesh movement strategy which is based on the Moving Mesh partial differential equation approach and moves the Mesh continuously in time and orderly in space. It discretizes hyperbolic conservation laws on Moving Meshes in the quasi-Lagrangian fashion with which the Mesh movement is treated continuously and no interpolation is needed for physical variables from the old Mesh to the new one. Two convection terms are induced by the Mesh movement and their discretization is incorporated naturally in the DG formulation. Numerical results for a selection of one- and two-dimensional scalar and system conservation laws are presented. It is shown that the Moving Mesh DG method achieves the theoretically predicted order of convergence for problems with smooth solutions and is able to capture shocks and concentrate Mesh points in non-smooth regions. Its advantage over uniform Meshes and its insensitiveness to Mesh smoothness are also demonstrated.
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Moving Mesh finite element simulation for phase field modeling of brittle fracture and convergence of newton s iteration
Journal of Computational Physics, 2018Co-Authors: Fei Zhang, Weizhang Huang, Shicheng ZhangAbstract:Abstract A Moving Mesh finite element method is studied for the numerical solution of a phase-field model for brittle fracture. The Moving Mesh partial differential equation approach is employed to dynamically track crack propagation. Meanwhile, the decomposition of the strain tensor into tensile and compressive components is essential for the success of the phase-field modeling of brittle fracture but results in a non-smooth elastic energy and stronger nonlinearity in the governing equation. This makes the governing equation much more difficult to solve and, in particular, Newton's iteration often fails to converge. Three regularization methods are proposed to smooth out the decomposition of the strain tensor. Numerical examples of fracture propagation under quasi-static load demonstrate that all of the methods can effectively improve the convergence of Newton's iteration for relatively small values of the regularization parameter but without compromising the accuracy of the numerical solution. They also show that the Moving Mesh finite element method is able to adaptively concentrate the Mesh elements around propagating cracks and handle multiple and complex crack systems.
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an adaptive Moving Mesh finite element solution of the regularized long wave equation
Journal of Scientific Computing, 2018Co-Authors: Weizhang Huang, Jianxian QiuAbstract:An adaptive Moving Mesh finite element method is proposed for the numerical solution of the regularized long wave (RLW) equation. A Moving Mesh strategy based on the so-called Moving Mesh PDE is used to adaptively move the Mesh to improve computational accuracy and efficiency. The RLW equation represents a class of partial differential equations containing spatial-time mixed derivatives. For the numerical solution of those equations, a $$C^0$$ finite element method cannot apply directly on a Moving Mesh since the mixed derivatives of the finite element approximation may not be defined. To avoid this difficulty, a new variable is introduced and the RLW equation is rewritten into a system of two coupled equations. The system is then discretized using linear finite elements in space and the fifth-order Radau IIA scheme in time. A range of numerical examples in one and two dimensions, including the RLW equation with one or two solitary waves and special initial conditions that lead to the undular bore and solitary train solutions, are presented. Numerical results demonstrate that the method has a second order convergence and is able to move and adapt the Mesh to the evolving features in the solution.
Lars Hernquist - One of the best experts on this subject based on the ideXlab platform.
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a Moving Mesh unstaggered constrained transport scheme for magnetohydrodynamics
Monthly Notices of the Royal Astronomical Society, 2016Co-Authors: Philip Mocz, Volker Springel, Mark Vogelsberger, Rudiger Pakmor, Federico Marinacci, Lars HernquistAbstract:We present a constrained transport (CT) algorithm for solving the 3D ideal magnetohydrodynamic (MHD) equations on a Moving Mesh, which maintains the divergence-free condition on the magnetic field to machine-precision. Our CT scheme uses an unstructured representation of the magnetic vector potential, making the numerical method simple and computationally efficient. The scheme is implemented in the Moving Mesh code Arepo. We demonstrate the performance of the approach with simulations of driven MHD turbulence, a magnetized disc galaxy, and a cosmological volume with primordial magnetic field. We compare the outcomes of these experiments to those obtained with a previously implemented Powell divergence-cleaning scheme. While CT and the Powell technique yield similar results in idealized test problems, some differences are seen in situations more representative of astrophysical flows. In the turbulence simulations, the Powell cleaning scheme artificially grows the mean magnetic field, while CT maintains this conserved quantity of ideal MHD. In the disc simulation, CT gives slower magnetic field growth rate and saturates to equipartition between the turbulent kinetic energy and magnetic energy, whereas Powell cleaning produces a dynamically dominant magnetic field. Such difference has been observed in adaptive-Mesh refinement codes with CT and smoothed-particle hydrodynamics codes with divergence-cleaning. In the cosmological simulation, both approaches give similar magnetic amplification, but Powell exhibits more cell-level noise. CT methods in general are more accurate than divergence-cleaning techniques, and, when coupled to a Moving Mesh can exploit the advantages of automatic spatial/temporal adaptivity and reduced advection errors, allowing for improved astrophysical MHD simulations.
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planet disc interaction on a freely Moving Mesh
Monthly Notices of the Royal Astronomical Society, 2014Co-Authors: Diego J Munoz, Kaitlin M Kratter, Volker Springel, Lars HernquistAbstract:General-purpose, Moving-Mesh schemes for hydrodynamics have opened the possibility of combining the accuracy of grid-based numerical methods with the flexibility and automatic resolution adaptivity of particle-based methods. Due to their supersonic nature, Keplerian accretion discs are in principle a very attractive system for applying such freely Moving Mesh techniques. However, the high degree of symmetry of simple accretion disc models can be difficult to capture accurately by these methods, due to the generation of geometric grid noise and associated numerical diffusion, which is absent in polar grids. To explore these and other issues, in this work we study the idealized problem of two-dimensional planet-disc interaction with the Moving-Mesh code AREPO. We explore the hydrodynamic evolution of discs with planets through a series of numerical experiments that vary the planet mass, the disc viscosity and the Mesh resolution, and compare the resulting surface density, vortensity field and tidal torque with results from the literature. We find that the performance of the Moving-Mesh code in this problem is in accordance with published results, showing good consistency with grid codes written in polar coordinates. We also conclude that grid noise and Mesh distortions do not introduce excessive numerical diffusion. Finally, we show how the Moving-Mesh approach can naturally increase resolution in regions of high densityaround planets and planetary wakes, while retaining the background flow at low resolution. This provides an alternative to the difficult task of implementing adaptive Mesh refinement in conventional polar-coordinate codes.
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Moving Mesh cosmology tracing cosmological gas accretion
Monthly Notices of the Royal Astronomical Society, 2013Co-Authors: Dylan Nelson, Volker Springel, Mark Vogelsberger, Debora Sijacki, Dušan Kereš, Shy Genel, Lars HernquistAbstract:We investigate the nature of gas accretion onto haloes and galaxies at z=2 using cosmological hydrodynamic simulations run with the Moving Mesh code AREPO. Implementing a Monte Carlo tracer particle scheme to determine the origin and thermodynamic history of accreting gas, we make quantitative comparisons to an otherwise identical simulation run with the smoothed particle hydrodynamics (SPH) code GADGET-3. Contrasting these two numerical approaches, we find significant physical differences in the thermodynamic history of accreted gas in haloes above 10^10.5 solar masses. In agreement with previous work, GADGET simulations show a cold fraction near unity for galaxies forming in massive haloes, implying that only a small percentage of accreted gas heats to an appreciable fraction of the virial temperature during accretion. The same galaxies in AREPO show a much lower cold fraction, <20% in haloes above 10^11 solar masses. This results from a hot gas accretion rate which, at this same halo mass, is an order of magnitude larger than with GADGET, while the cold accretion rate is also lower. These discrepancies increase for more massive systems, and we explain both as due to numerical inaccuracies in the standard formulation of SPH. We also observe that the relatively sharp transition from cold to hot mode dominated accretion, at a halo mass of ~10^11, is a consequence of comparing past gas temperatures to a constant threshold value independent of virial temperature. Examining the spatial distribution of accreting gas, we find that gas filaments in GADGET tend to remain collimated and flow coherently to small radii, or artificially fragment and form a large number of purely numerical "blobs". Similar gas streams in AREPO show increased heating and disruption at 0.25-0.5 virial radii and contribute to the hot gas accretion rate in a manner distinct from classical cooling flows.
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Moving Mesh cosmology properties of neutral hydrogen in absorption
Monthly Notices of the Royal Astronomical Society, 2013Co-Authors: Simeon Bird, Volker Springel, Mark Vogelsberger, Debora Sijacki, Matias Zaldarriaga, Lars HernquistAbstract:We examine the distribution of neutral hydrogen in cosmological simulations carried out with the new Moving-Mesh code AREPO and compare it with the corresponding GADGET simulations based on the smoothed particle hydrodynamics (SPH) technique. The two codes use identical gravity solvers and baryonic physics implementations, but very different methods for solving the Euler equations, allowing us to assess how numerical effects associated with the hydro-solver impact the results of simulations. Here we focus on an analysis of the neutral gas, as detected in quasar absorption lines. We find that the high column density regime probed by Damped Lyman-alpha (DLA) and Lyman Limit Systems (LLS) exhibits significant differences between the codes. GADGET produces spurious artefacts in large halos in the form of gaseous clumps, boosting the LLS cross-section. Furthermore, it forms halos with denser central baryonic cores than AREPO, which leads to a substantially greater DLA cross-section from smaller halos. AREPO thus produces a significantly lower cumulative abundance of DLAs, which is intriguingly in much closer agreement with observations. The column density function, however, is not altered enough to significantly reduce the discrepancy with the observed value. For the low column density gas probed by the Lyman-alpha forest, the codes differ only at the level of a few percent, suggesting that this regime is quite well described by both methods, a fact that is reassuring for the many Lyman-alpha studies carried out with SPH thus far. While the residual differences are smaller than the errors on current Lyman-alpha forest data, we note that this will likely change for future precision experiments.
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Moving Mesh cosmology properties of gas discs
Monthly Notices of the Royal Astronomical Society, 2012Co-Authors: Paul Torrey, Volker Springel, Mark Vogelsberger, Debora Sijacki, Lars HernquistAbstract:We compare the structural properties of galaxies formed in cosmological simulations using the smoothed particle hydrodynamics (SPH) code GADGET with those using the Moving-Mesh code AREPO. Both codes employ identical gravity solvers and the same subresolution physics but use very different methods to track the hydrodynamic evolution of gas. This permits us to isolate the effects of the hydro solver on the formation and evolution of galactic gas discs in GADGET and AREPO haloes with comparable numerical resolution. In a matching sample of GADGET and AREPO haloes, we fit simulated gas discs with exponential profiles. We find that the cold gas discs formed using the Moving-Mesh approach have systematically larger disc scale lengths and higher specific angular momenta than their GADGET counterparts across a wide range in halo masses. For low-mass galaxies, differences between the properties of the simulated galaxy discs are caused by an insufficient number of resolution elements which lead to the artificial angular momentum transfer in our SPH calculation. We however find that galactic discs formed in massive haloes, resolved with ≥10 6 particles/cells, are still systematically smaller in the GADGET run by a factor of ∼2. The reason for this is twofold: (i) the excessive heating of haloes close to the cooling radius due to spurious dissipation of the subsonic turbulence in GADGET reduces the supply of gas which can cool and settle on to the central disc; (ii) the efficient delivery of low angular momentum gaseous blobs to the bottom of the potential well results in the centrally concentrated gas discs in GADGET simulation. While this large population of gaseous blobs in GADGET originates from the filaments which are pressure confined and fragment due to the SPH surface tension while infalling into hot halo atmospheres, it is essentially absent in the Moving-Mesh calculation, clearly indicating numerical rather than physical origin of the blob material.
Mark Vogelsberger - One of the best experts on this subject based on the ideXlab platform.
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simulating dust grain radiation coupling on a Moving Mesh
Monthly Notices of the Royal Astronomical Society, 2021Co-Authors: R Mckinnon, Rahul Kannan, Mark Vogelsberger, Stephanie Oneil, Paul TorreyAbstract:We present a model for the interaction between dust and radiation fields in the radiation hydrodynamic code AREPO-RT, which solves the moment-based radiative transfer equations on an unstructured Moving Mesh. Dust is directly treated using live simulation particles, each of which represent a population of grains that are coupled to hydrodynamic motion through a drag force. We introduce methods to calculate radiation pressure on and photon absorption by dust grains. By including a direct treatment of dust, we are able to calculate dust opacities and update radiation fields self-consistently based on the local dust distribution. This hybrid scheme coupling dust particles to an unstructured Mesh for radiation is validated using several test problems with known analytic solutions, including dust driven via spherically-symmetric flux from a constant luminosity source and photon absorption from radiation incident on a thin layer of dust. Our methods are compatible with the multifrequency scheme in AREPO-RT, which treats UV and optical photons as single-scattered and IR photons as multi-scattered. At IR wavelengths, we model heating of and thermal emission from dust. Dust and gas are not assumed to be in local thermodynamic equilibrium but transfer energy through collisional exchange. We estimate dust temperatures by balancing these dust-radiation and dust-gas energy exchange rates. This framework for coupling dust and radiation can be applied in future radiation hydrodynamic simulations of galaxy formation.
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arepo mcrt monte carlo radiation hydrodynamics on a Moving Mesh
The Astrophysical Journal, 2020Co-Authors: Aaron Smith, Mark Vogelsberger, Rahul Kannan, Benny T H Tsang, Rudiger PakmorAbstract:We present Arepo-MCRT, a novel Monte Carlo radiative transfer (MCRT) radiation-hydrodynamics (RHD) solver for the unstructured Moving-Mesh code Arepo. Our method is designed for general multiple scattering problems in both optically thin and thick conditions. We incorporate numerous efficiency improvements and noise reduction schemes to help overcome efficiency barriers that typically inhibit convergence. These include continuous absorption and energy deposition, photon weighting and luminosity boosting, local packet merging and splitting, path-based statistical estimators, conservative (face-centered) momentum coupling, adaptive convergence between time steps, implicit Monte Carlo algorithms for thermal emission, and discrete-diffusion Monte Carlo techniques for unresolved scattering, including a novel advection scheme. We primarily focus on the unique aspects of our implementation and discussions of the advantages and drawbacks of our methods in various astrophysical contexts. Finally, we consider several test applications including the levitation of an optically thick layer of gas by trapped infrared radiation. We find that the initial acceleration phase and revitalized second wind are connected via self-regulation of the RHD coupling, such that the RHD method accuracy and simulation resolution each leave important imprints on the long-term behavior of the gas.
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simulating galactic dust grain evolution on a Moving Mesh
Monthly Notices of the Royal Astronomical Society, 2018Co-Authors: R Mckinnon, Paul Torrey, Mark Vogelsberger, Federico Marinacci, Rahul KannanAbstract:Interstellar dust is an important component of the galactic ecosystem, playing a key role in multiple galaxy formation processes. We present a novel numerical framework for the dynamics and size evolution of dust grains implemented in the Moving-Mesh hydrodynamics code AREPO suited for cosmological galaxy formation simulations. We employ a particle-based method for dust subject to dynamical forces including drag and gravity. The drag force is implemented using a second-order semi-implicit integrator and validated using several dust-hydrodynamical test problems. Each dust particle has a grain size distribution, describing the local abundance of grains of different sizes. The grain size distribution is discretised with a second-order piecewise linear method and evolves in time according to various dust physical processes, including accretion, sputtering, shattering, and coagulation. We present a novel scheme for stochastically forming dust during stellar evolution and new methods for sub-cycling of dust physics time-steps. Using this model, we simulate an isolated disc galaxy to study the impact of dust physical processes that shape the interstellar grain size distribution. We demonstrate, for example, how dust shattering shifts the grain size distribution to smaller sizes resulting in a significant rise of radiation extinction from optical to near-ultraviolet wavelengths. Our framework for simulating dust and gas mixtures can readily be extended to account for other dynamical processes relevant in galaxy formation, like magnetohydrodynamics, radiation pressure, and thermo-chemical processes.
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non ideal magnetohydrodynamics on a Moving Mesh
Monthly Notices of the Royal Astronomical Society, 2018Co-Authors: Federico Marinacci, Mark Vogelsberger, Philip Mocz, Rudiger Pakmor, Rahul Kannan, Volker SpringelAbstract:In certain astrophysical systems the commonly employed ideal magnetohydrodynamics (MHD) approximation breaks down. Here, we introduce novel explicit and implicit numerical schemes of ohmic resistivity terms in the Moving-Mesh code AREPO. We include these non-ideal terms for two MHD techniques: the Powell 8-wave formalism and a constrained transport scheme, which evolves the cell-centred magnetic vector potential. We test our implementation against problems of increasing complexity, such as one- and two-dimensional diffusion problems, and the evolution of progressive and stationary Alfven waves. On these test problems, our implementation recovers the analytic solutions to second-order accuracy. As first applications, we investigate the tearing instability in magnetized plasmas and the gravitational collapse of a rotating magnetized gas cloud. In both systems, resistivity plays a key role. In the former case, it allows for the development of the tearing instability through reconnection of the magnetic field lines. In the latter, the adopted (constant) value of ohmic resistivity has an impact on both the gas distribution around the emerging protostar and the mass loading of magnetically driven outflows. Our new non-ideal MHD implementation opens up the possibility to study magneto-hydrodynamical systems on a Moving Mesh beyond the ideal MHD approximation.
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a Moving Mesh unstaggered constrained transport scheme for magnetohydrodynamics
Monthly Notices of the Royal Astronomical Society, 2016Co-Authors: Philip Mocz, Volker Springel, Mark Vogelsberger, Rudiger Pakmor, Federico Marinacci, Lars HernquistAbstract:We present a constrained transport (CT) algorithm for solving the 3D ideal magnetohydrodynamic (MHD) equations on a Moving Mesh, which maintains the divergence-free condition on the magnetic field to machine-precision. Our CT scheme uses an unstructured representation of the magnetic vector potential, making the numerical method simple and computationally efficient. The scheme is implemented in the Moving Mesh code Arepo. We demonstrate the performance of the approach with simulations of driven MHD turbulence, a magnetized disc galaxy, and a cosmological volume with primordial magnetic field. We compare the outcomes of these experiments to those obtained with a previously implemented Powell divergence-cleaning scheme. While CT and the Powell technique yield similar results in idealized test problems, some differences are seen in situations more representative of astrophysical flows. In the turbulence simulations, the Powell cleaning scheme artificially grows the mean magnetic field, while CT maintains this conserved quantity of ideal MHD. In the disc simulation, CT gives slower magnetic field growth rate and saturates to equipartition between the turbulent kinetic energy and magnetic energy, whereas Powell cleaning produces a dynamically dominant magnetic field. Such difference has been observed in adaptive-Mesh refinement codes with CT and smoothed-particle hydrodynamics codes with divergence-cleaning. In the cosmological simulation, both approaches give similar magnetic amplification, but Powell exhibits more cell-level noise. CT methods in general are more accurate than divergence-cleaning techniques, and, when coupled to a Moving Mesh can exploit the advantages of automatic spatial/temporal adaptivity and reduced advection errors, allowing for improved astrophysical MHD simulations.
Rudiger Pakmor - One of the best experts on this subject based on the ideXlab platform.
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arepo mcrt monte carlo radiation hydrodynamics on a Moving Mesh
The Astrophysical Journal, 2020Co-Authors: Aaron Smith, Mark Vogelsberger, Rahul Kannan, Benny T H Tsang, Rudiger PakmorAbstract:We present Arepo-MCRT, a novel Monte Carlo radiative transfer (MCRT) radiation-hydrodynamics (RHD) solver for the unstructured Moving-Mesh code Arepo. Our method is designed for general multiple scattering problems in both optically thin and thick conditions. We incorporate numerous efficiency improvements and noise reduction schemes to help overcome efficiency barriers that typically inhibit convergence. These include continuous absorption and energy deposition, photon weighting and luminosity boosting, local packet merging and splitting, path-based statistical estimators, conservative (face-centered) momentum coupling, adaptive convergence between time steps, implicit Monte Carlo algorithms for thermal emission, and discrete-diffusion Monte Carlo techniques for unresolved scattering, including a novel advection scheme. We primarily focus on the unique aspects of our implementation and discussions of the advantages and drawbacks of our methods in various astrophysical contexts. Finally, we consider several test applications including the levitation of an optically thick layer of gas by trapped infrared radiation. We find that the initial acceleration phase and revitalized second wind are connected via self-regulation of the RHD coupling, such that the RHD method accuracy and simulation resolution each leave important imprints on the long-term behavior of the gas.
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braginskii viscosity on an unstructured Moving Mesh accelerated with super time stepping
Monthly Notices of the Royal Astronomical Society, 2020Co-Authors: Thomas Berlok, Rudiger Pakmor, Christoph PfrommerAbstract:We present a method for efficiently modelling Braginskii viscosity on an unstructured, Moving Mesh. Braginskii viscosity, i.e., anisotropic transport of momentum with respect to the direction of the magnetic field, is thought to be of prime importance for studies of the weakly collisional plasma that comprises the intracluster medium (ICM) of galaxy clusters. Here anisotropic transport of heat and momentum has been shown to have profound consequences for the stability properties of the ICM. Our new method for modelling Braginskii viscosity has been implemented in the Moving Mesh code Arepo. We present a number of examples that serve to test the implementation and illustrate the modified dynamics found when including Braginskii viscosity in simulations. These include (but are not limited to) damping of fast magneto-sonic waves, interruption of linearly polarized Alfven waves by the firehose instability and the inhibition of the Kelvin-Helmholtz instability by Braginskii viscosity. An explicit update of Braginskii viscosity is associated with a severe time step constraint that scales with $(\Delta x)^2$ where $\Delta x$ is the grid size. In our implementation, this restrictive time step constraint is alleviated by employing 2nd order accurate Runge-Kutta-Legendre super-time-stepping. We envision including Braginskii viscosity in future large-scale simulations of Kelvin-Helmholtz unstable cold fronts in cluster mergers and AGN-generated bubbles in central cluster regions.
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non ideal magnetohydrodynamics on a Moving Mesh
Monthly Notices of the Royal Astronomical Society, 2018Co-Authors: Federico Marinacci, Mark Vogelsberger, Philip Mocz, Rudiger Pakmor, Rahul Kannan, Volker SpringelAbstract:In certain astrophysical systems the commonly employed ideal magnetohydrodynamics (MHD) approximation breaks down. Here, we introduce novel explicit and implicit numerical schemes of ohmic resistivity terms in the Moving-Mesh code AREPO. We include these non-ideal terms for two MHD techniques: the Powell 8-wave formalism and a constrained transport scheme, which evolves the cell-centred magnetic vector potential. We test our implementation against problems of increasing complexity, such as one- and two-dimensional diffusion problems, and the evolution of progressive and stationary Alfven waves. On these test problems, our implementation recovers the analytic solutions to second-order accuracy. As first applications, we investigate the tearing instability in magnetized plasmas and the gravitational collapse of a rotating magnetized gas cloud. In both systems, resistivity plays a key role. In the former case, it allows for the development of the tearing instability through reconnection of the magnetic field lines. In the latter, the adopted (constant) value of ohmic resistivity has an impact on both the gas distribution around the emerging protostar and the mass loading of magnetically driven outflows. Our new non-ideal MHD implementation opens up the possibility to study magneto-hydrodynamical systems on a Moving Mesh beyond the ideal MHD approximation.
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simulating cosmic ray physics on a Moving Mesh
Monthly Notices of the Royal Astronomical Society, 2017Co-Authors: Christoph Pfrommer, Volker Springel, Rudiger Pakmor, Kevin Schaal, Christine M SimpsonAbstract:We discuss new methods to integrate the cosmic ray (CR) evolution equations coupled to magneto-hydrodynamics (MHD) on an unstructured Moving Mesh, as realised in the massively parallel AREPO code for cosmological simulations. We account for diffusive shock acceleration of CRs at resolved shocks and at supernova remnants in the interstellar medium (ISM), and follow the advective CR transport within the magnetised plasma, as well as anisotropic diffusive transport of CRs along the local magnetic field. CR losses are included in terms of Coulomb and hadronic interactions with the thermal plasma. We demonstrate the accuracy of our formalism for CR acceleration at shocks through simulations of plane-parallel shock tubes that are compared to newly derived exact solutions of the Riemann shock tube problem with CR acceleration. We find that the increased compressibility of the post-shock plasma due to the produced CRs decreases the shock speed. However, CR acceleration at spherically expanding blast waves does not significantly break the self-similarity of the Sedov-Taylor solution; the resulting modifications can be approximated by a suitably adjusted, but constant adiabatic index. In first applications of the new CR formalism to simulations of isolated galaxies and cosmic structure formation, we find that CRs add an important pressure component to the ISM that increases the vertical scale height of disk galaxies, and thus reduces the star formation rate. Strong external structure formation shocks inject CRs into the gas, but the relative pressure of this component decreases towards halo centres as adiabatic compression favours the thermal over the CR pressure.
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a Moving Mesh unstaggered constrained transport scheme for magnetohydrodynamics
Monthly Notices of the Royal Astronomical Society, 2016Co-Authors: Philip Mocz, Volker Springel, Mark Vogelsberger, Rudiger Pakmor, Federico Marinacci, Lars HernquistAbstract:We present a constrained transport (CT) algorithm for solving the 3D ideal magnetohydrodynamic (MHD) equations on a Moving Mesh, which maintains the divergence-free condition on the magnetic field to machine-precision. Our CT scheme uses an unstructured representation of the magnetic vector potential, making the numerical method simple and computationally efficient. The scheme is implemented in the Moving Mesh code Arepo. We demonstrate the performance of the approach with simulations of driven MHD turbulence, a magnetized disc galaxy, and a cosmological volume with primordial magnetic field. We compare the outcomes of these experiments to those obtained with a previously implemented Powell divergence-cleaning scheme. While CT and the Powell technique yield similar results in idealized test problems, some differences are seen in situations more representative of astrophysical flows. In the turbulence simulations, the Powell cleaning scheme artificially grows the mean magnetic field, while CT maintains this conserved quantity of ideal MHD. In the disc simulation, CT gives slower magnetic field growth rate and saturates to equipartition between the turbulent kinetic energy and magnetic energy, whereas Powell cleaning produces a dynamically dominant magnetic field. Such difference has been observed in adaptive-Mesh refinement codes with CT and smoothed-particle hydrodynamics codes with divergence-cleaning. In the cosmological simulation, both approaches give similar magnetic amplification, but Powell exhibits more cell-level noise. CT methods in general are more accurate than divergence-cleaning techniques, and, when coupled to a Moving Mesh can exploit the advantages of automatic spatial/temporal adaptivity and reduced advection errors, allowing for improved astrophysical MHD simulations.