The Experts below are selected from a list of 327 Experts worldwide ranked by ideXlab platform
Michael Zingale - One of the best experts on this subject based on the ideXlab platform.
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Modelling low Mach Number stellar hydrodynamics with MAESTROeX
Journal of Physics: Conference Series, 2020Co-Authors: Alice Harpole, Andrew Nonaka, D. Fan, M. P. Katz, Donald E. Willcox, Michael ZingaleAbstract:Author(s): Harpole, A; Fan, D; Katz, MP; Nonaka, AJ; Willcox, DE; Zingale, M | Abstract: Modelling long-time convective flows in the interiors of stars is extremely challenging using conventional compressible hydrodynamics codes due to the acoustic timestep limitation. Many of these flows are in the low Mach Number regime, which allows us to exploit the relationship between acoustic and advective time scales to develop a more computationally efficient approach. MAESTROeX is an open source low Mach Number stellar hydrodynamics code that allows much larger timesteps to be taken, therefore enabling systems to be modelled for much longer periods of time. This is particularly important for the problem of convection in the cores of rotating massive stars prior to core collapse. To fully capture the dynamics, it is necessary to model these systems in three dimensions at high resolution over many rotational periods. We present an overview of MAESTROeX's current capabilities, describe ongoing work to incorporate the effects of rotation and discuss how we are optimising the code to run on GPUs.
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Modelling low Mach Number stellar hydrodynamics with MAESTROeX
arXiv: Computational Physics, 2019Co-Authors: Alice Harpole, Andrew Nonaka, D. Fan, M. P. Katz, Donald E. Willcox, Michael ZingaleAbstract:Modelling long-time convective flows in the interiors of stars is extremely challenging using conventional compressible hydrodynamics codes due to the acoustic timestep limitation. Many of these flows are in the low Mach Number regime, which allows us to exploit the relationship between acoustic and advective time scales to develop a more computationally efficient approach. MAESTROeX is an open source low Mach Number stellar hydrodynamics code that allows much larger timesteps to be taken, therefore enabling systems to be modelled for much longer periods of time. This is particularly important for the problem of convection in the cores of rotating massive stars prior to core collapse. To fully capture the dynamics, it is necessary to model these systems in three dimensions at high resolution over many rotational periods. We present an overview of MAESTROeX's current capabilities, describe ongoing work to incorporate the effects of rotation and discuss how we are optimising the code to run on GPUs.
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Low Mach Number Modeling of Stratified Flows
Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects, 2014Co-Authors: Ann S. Almgren, John B. Bell, Andrew Nonaka, Michael ZingaleAbstract:Low Mach Number equation sets approximate the equations of motion of a compressible fluid by filtering out the sound waves, which allows the system to evolve on the advective rather than the acoustic time scale. Depending on the degree of approximation, low Mach Number models retain some subset of possible compressible effects. In this paper we give an overview of low Mach Number methods for modeling stratified flows arising in astrophysics and atmospheric science as well as low Mach Number reacting flows. We discuss how elements from the different fields are combined to form MAESTRO, a code for modeling low Mach Number stratified flows with general equations of state, reactions and time-varying stratification.
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Low Mach Number modeling of type Ia supernovae. I. Hydrodynamics
The Astrophysical Journal, 2006Co-Authors: Ann S. Almgren, John B. Bell, Charles A. Rendleman, Michael ZingaleAbstract:We introduce a low Mach Number equation set for the large-scale numerical simulation of carbon-oxygen white dwarfs experiencing a thermonuclear deflagration. Since most of the interesting physics in a Type Ia supernova transpires at Mach Numbers from 0.01 to 0.1, such an approach enables both a considerable increase in accuracy and a savings in computer time compared with frequently used compressible codes. Our equation set is derived from the fully compressible equations using low Mach Number asymptotics, but without any restriction on the size of perturbations in density or temperature. Comparisons with simulations that use the fully compressible equations validate the low Mach Number model in regimes where both are applicable. Comparisons to simulations based on the more traditional anelastic approximation also demonstrate the agreement of these models in the regime for which the anelastic approximation is valid. For low Mach Number flows with potentially finite amplitude variations in density and temperature, the low Mach Number model overcomes the limitations of each of the more traditional models and can serve as the basis for an accurate and efficient simulation tool.
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Low Mach Number Modeling of Type Ia Supernovae. II. Energy Evolution
The Astrophysical Journal, 2006Co-Authors: Ann S. Almgren, John B. Bell, Charles A. Rendleman, Michael ZingaleAbstract:The convective period leading up to a Type Ia supernova (SNIa) explosion is characterized by very low Mach Number flows, requiringhydrodynamical methods well-suited to long-time integration. We continuethe development of the low Mach Number equation set for stellar scaleflows by incorporating the effects of heat release due to externalsources. Low Mach Number hydrodynamics equations with a time-dependentbackground state are derived, and a numerical method based on theapproximate projection formalism is presented. We demonstrate throughvalidation with a fully compressible hydrodynamics code that this lowMach Number model accurately captures the expansion of the stellaratmosphere as well as the local dynamics due to external heat sources.This algorithm provides the basis for an efficient simulation tool forstudying the ignition of SNe Ia.
John B. Bell - One of the best experts on this subject based on the ideXlab platform.
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A hybrid adaptive low-Mach Number/compressible method: Euler equations
Journal of Computational Physics, 2018Co-Authors: Emmanuel Motheau, Max Duarte, Ann S. Almgren, John B. BellAbstract:Author(s): Motheau, E; Duarte, M; Almgren, A; Bell, JB | Abstract: © 2018 Elsevier Inc. Flows in which the primary features of interest do not rely on high-frequency acoustic effects, but in which long-wavelength acoustics play a nontrivial role, present a computational challenge. Integrating the entire domain with low-Mach-Number methods would remove all acoustic wave propagation, while integrating the entire domain with the fully compressible equations can in some cases be prohibitively expensive due to the CFL time step constraint. For example, simulation of thermoacoustic instabilities might require fine resolution of the fluid/chemistry interaction but not require fine resolution of acoustic effects, yet one does not want to neglect the long-wavelength wave propagation and its interaction with the larger domain. The present paper introduces a new multi-level hybrid algorithm to address these types of phenomena. In this new approach, the fully compressible Euler equations are solved on the entire domain, potentially with local refinement, while their low-Mach-Number counterparts are solved on subregions of the domain with higher spatial resolution. The finest of the compressible levels communicates inhomogeneous divergence constraints to the coarsest of the low-Mach-Number levels, allowing the low-Mach-Number levels to retain the long-wavelength acoustics. The performance of the hybrid method is shown for a series of test cases, including results from a simulation of the aeroacoustic propagation generated from a Kelvin–Helmholtz instability in low-Mach-Number mixing layers. It is demonstrated that compared to a purely compressible approach, the hybrid method allows time-steps two orders of magnitude larger at the finest level, leading to an overall reduction of the computational time by a factor of 8.
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A Low Mach Number Model for Moist Atmospheric Flows
Journal of the Atmospheric Sciences, 2015Co-Authors: Max Duarte, Ann S. Almgren, John B. BellAbstract:AbstractA low Mach Number model for moist atmospheric flows is introduced that accurately incorporates reversible moist processes in flows whose features of interest occur on advective rather than acoustic time scales. Total water is used as a prognostic variable, so that water vapor and liquid water are diagnostically recovered as needed from an exact Clausius–Clapeyron formula for moist thermodynamics. Low Mach Number models can be computationally more efficient than a fully compressible model, but the low Mach Number formulation introduces additional mathematical and computational complexity because of the divergence constraint imposed on the velocity field. Here, latent heat release is accounted for in the source term of the constraint by estimating the rate of phase change based on the time variation of saturated water vapor subject to the thermodynamic equilibrium constraint. The authors numerically assess the validity of the low Mach Number approximation for moist atmospheric flows by contrasting t...
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Low Mach Number fluctuating hydrodynamics of multispecies liquid mixtures
Physics of Fluids, 2015Co-Authors: Aleksandar Donev, Andrew Nonaka, Alejandro L. Garcia, Amit Kumar Bhattacharjee, John B. BellAbstract:We develop a low Mach Number formulation of the hydrodynamic equations describing transport of mass and momentum in a multispecies mixture of incompressible miscible liquids at specified temperature and pressure, which generalizes our prior work on ideal mixtures of ideal gases [Balakrishnan et al., “Fluctuating hydrodynamics of multispecies nonreactive mixtures,” Phys. Rev. E 89 013017 (2014)] and binary liquid mixtures [Donev et al., “Low Mach Number fluctuating hydrodynamics of diffusively mixing fluids,” Commun. Appl. Math. Comput. Sci. 9(1), 47-105 (2014)]. In this formulation, we combine and extend a Number of existing descriptions of multispecies transport available in the literature. The formulation applies to non-ideal mixtures of arbitrary Number of species, without the need to single out a “solvent” species, and includes contributions to the diffusive mass flux due to gradients of composition, temperature, and pressure. Momentum transport and advective mass transport are handled using a low Mach Number approach that eliminates fast sound waves (pressure fluctuations) from the full compressible system of equations and leads to a quasi-incompressible formulation. Thermal fluctuations are included in our fluctuating hydrodynamics description following the principles of nonequilibrium thermodynamics. We extend the semi-implicit staggered-grid finite-volume numerical method developed in our prior work on binary liquid mixtures [Nonaka et al., “Low Mach Number fluctuating hydrodynamics of binary liquid mixtures,” arXiv:1410.2300 (2015)] and use it to study the development of giant nonequilibrium concentration fluctuations in a ternary mixture subjected to a steady concentration gradient. We also numerically study the development of diffusion-driven gravitational instabilities in a ternary mixture and compare our numerical results to recent experimental measurements [Carballido-Landeira et al., “Mixed-mode instability of a miscible interface due to coupling between Rayleigh–Taylor and double-diffusive convective modes,” Phys. Fluids 25, 024107 (2013)] in a Hele-Shaw cell. We find that giant nonequilibrium fluctuations can trigger the instability but are eventually dominated by the deterministic growth of the unstable mode, in both quasi-two-dimensional (Hele-Shaw) and fully three-dimensional geometries used in typical shadowgraph experiments.
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Low Mach Number Modeling of Stratified Flows
Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects, 2014Co-Authors: Ann S. Almgren, John B. Bell, Andrew Nonaka, Michael ZingaleAbstract:Low Mach Number equation sets approximate the equations of motion of a compressible fluid by filtering out the sound waves, which allows the system to evolve on the advective rather than the acoustic time scale. Depending on the degree of approximation, low Mach Number models retain some subset of possible compressible effects. In this paper we give an overview of low Mach Number methods for modeling stratified flows arising in astrophysics and atmospheric science as well as low Mach Number reacting flows. We discuss how elements from the different fields are combined to form MAESTRO, a code for modeling low Mach Number stratified flows with general equations of state, reactions and time-varying stratification.
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LOW Mach Number FLUCTUATING HYDRODYNAMICS OF DIFFUSIVELY MIXING FLUIDS
Communications in Applied Mathematics and Computational Science, 2014Co-Authors: Aleksandar Donev, Andrew Nonaka, Yifei Sun, Thomas G. Fai, Alejandro L. Garcia, John B. BellAbstract:We formulate low Mach Number fluctuating hydrodynamic equations appropriate for modeling diffusive mixing in isothermal mixtures of fluids with different density and transport coefficients. These equations eliminate the fluctuations in pressure associated with the propagation of sound waves by replacing the equation of state with a local thermodynamic constraint. We demonstrate that the low Mach Number model preserves the spatio-temporal spectrum of the slower diffusive fluctuations. We develop a strictly conservative finite-volume spatial discretization of the low Mach Number fluctuating equations in both two and three dimensions and construct several explicit Runge-Kutta temporal integrators that strictly maintain the equation of state constraint. The resulting spatio-temporal discretization is second-order accurate deterministically and maintains fluctuation-dissipation balance in the linearized stochastic equations. We apply our algorithms to model the development of giant concentration fluctuations in the presence of concentration gradients, and investigate the validity of common simplifications such as neglecting the spatial non-homogeneity of density and transport properties. We perform simulations of diffusive mixing of two fluids of different densities in two dimensions and compare the results of low Mach Number continuum simulations to hard-disk molecular dynamics simulations. Excellent agreement is observed between the particle and continuum simulations of giant fluctuations during time-dependent diffusive mixing.
Ann S. Almgren - One of the best experts on this subject based on the ideXlab platform.
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A hybrid adaptive low-Mach Number/compressible method: Euler equations
Journal of Computational Physics, 2018Co-Authors: Emmanuel Motheau, Max Duarte, Ann S. Almgren, John B. BellAbstract:Author(s): Motheau, E; Duarte, M; Almgren, A; Bell, JB | Abstract: © 2018 Elsevier Inc. Flows in which the primary features of interest do not rely on high-frequency acoustic effects, but in which long-wavelength acoustics play a nontrivial role, present a computational challenge. Integrating the entire domain with low-Mach-Number methods would remove all acoustic wave propagation, while integrating the entire domain with the fully compressible equations can in some cases be prohibitively expensive due to the CFL time step constraint. For example, simulation of thermoacoustic instabilities might require fine resolution of the fluid/chemistry interaction but not require fine resolution of acoustic effects, yet one does not want to neglect the long-wavelength wave propagation and its interaction with the larger domain. The present paper introduces a new multi-level hybrid algorithm to address these types of phenomena. In this new approach, the fully compressible Euler equations are solved on the entire domain, potentially with local refinement, while their low-Mach-Number counterparts are solved on subregions of the domain with higher spatial resolution. The finest of the compressible levels communicates inhomogeneous divergence constraints to the coarsest of the low-Mach-Number levels, allowing the low-Mach-Number levels to retain the long-wavelength acoustics. The performance of the hybrid method is shown for a series of test cases, including results from a simulation of the aeroacoustic propagation generated from a Kelvin–Helmholtz instability in low-Mach-Number mixing layers. It is demonstrated that compared to a purely compressible approach, the hybrid method allows time-steps two orders of magnitude larger at the finest level, leading to an overall reduction of the computational time by a factor of 8.
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A Low Mach Number Model for Moist Atmospheric Flows
Journal of the Atmospheric Sciences, 2015Co-Authors: Max Duarte, Ann S. Almgren, John B. BellAbstract:AbstractA low Mach Number model for moist atmospheric flows is introduced that accurately incorporates reversible moist processes in flows whose features of interest occur on advective rather than acoustic time scales. Total water is used as a prognostic variable, so that water vapor and liquid water are diagnostically recovered as needed from an exact Clausius–Clapeyron formula for moist thermodynamics. Low Mach Number models can be computationally more efficient than a fully compressible model, but the low Mach Number formulation introduces additional mathematical and computational complexity because of the divergence constraint imposed on the velocity field. Here, latent heat release is accounted for in the source term of the constraint by estimating the rate of phase change based on the time variation of saturated water vapor subject to the thermodynamic equilibrium constraint. The authors numerically assess the validity of the low Mach Number approximation for moist atmospheric flows by contrasting t...
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A Low Mach Number Model for Moist Atmospheric Flows
Journal of the Atmospheric Sciences, 2015Co-Authors: Max Duarte, Ann S. Almgren, John BellAbstract:We introduce a low Mach Number model for moist atmospheric flows that accurately incorporates reversible moist processes in flows whose features of interest occur on advective rather than acoustic time scales. Total water is used as a prognostic variable, so that water vapor and liquid water are diagnostically recovered as needed from an exact Clausius--Clapeyron formula for moist thermodynamics. Low Mach Number models can be computationally more efficient than a fully compressible model, but the low Mach Number formulation introduces additional mathematical and computational complexity because of the divergence constraint imposed on the velocity field. Here, latent heat release is accounted for in the source term of the constraint by estimating the rate of phase change based on the time variation of saturated water vapor subject to the thermodynamic equilibrium constraint. We numerically assess the validity of the low Mach Number approximation for moist atmospheric flows by contrasting the low Mach Number solution to reference solutions computed with a fully compressible formulation for a variety of test problems.
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Low Mach Number Modeling of Stratified Flows
Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects, 2014Co-Authors: Ann S. Almgren, John B. Bell, Andrew Nonaka, Michael ZingaleAbstract:Low Mach Number equation sets approximate the equations of motion of a compressible fluid by filtering out the sound waves, which allows the system to evolve on the advective rather than the acoustic time scale. Depending on the degree of approximation, low Mach Number models retain some subset of possible compressible effects. In this paper we give an overview of low Mach Number methods for modeling stratified flows arising in astrophysics and atmospheric science as well as low Mach Number reacting flows. We discuss how elements from the different fields are combined to form MAESTRO, a code for modeling low Mach Number stratified flows with general equations of state, reactions and time-varying stratification.
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Low Mach Number modeling of type Ia supernovae. I. Hydrodynamics
The Astrophysical Journal, 2006Co-Authors: Ann S. Almgren, John B. Bell, Charles A. Rendleman, Michael ZingaleAbstract:We introduce a low Mach Number equation set for the large-scale numerical simulation of carbon-oxygen white dwarfs experiencing a thermonuclear deflagration. Since most of the interesting physics in a Type Ia supernova transpires at Mach Numbers from 0.01 to 0.1, such an approach enables both a considerable increase in accuracy and a savings in computer time compared with frequently used compressible codes. Our equation set is derived from the fully compressible equations using low Mach Number asymptotics, but without any restriction on the size of perturbations in density or temperature. Comparisons with simulations that use the fully compressible equations validate the low Mach Number model in regimes where both are applicable. Comparisons to simulations based on the more traditional anelastic approximation also demonstrate the agreement of these models in the regime for which the anelastic approximation is valid. For low Mach Number flows with potentially finite amplitude variations in density and temperature, the low Mach Number model overcomes the limitations of each of the more traditional models and can serve as the basis for an accurate and efficient simulation tool.
Erik Dick - One of the best experts on this subject based on the ideXlab platform.
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Solving low Mach Number Riemann problems by a momentum interpolation method
Journal of Computational Physics, 2015Co-Authors: Yann Moguen, Pascal Bruel, Erik DickAbstract:A momentum interpolation based scheme is proposed, giving satisfactory acoustic solutions in low Mach Number regime.
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Momentum interpolation for quasi one-dimensional unsteady low Mach Number flows with acoustics
2014Co-Authors: Yann Moguen, Pascal Bruel, Stéphane Dellacherie, Erik DickAbstract:A Rhie-Chow based algorithm for quasi 1-D sound propagation in a low Mach Number mean flow is described. It is shown that the proposed Rhie-Chow interpolation method preserves the linear wave equation at first order, giving confidence in its ability to properly simulate flows that feature simultaneously acoustic waves and low Mach Number convection.
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Solving low Mach Number Riemann problems by momentum interpolation
2014Co-Authors: Yann Moguen, Pascal Bruel, Erik DickAbstract:Momentum interpolation methods for unsteady low Mach Number flow calculations are re-examined to allow for solution of low Mach Number Riemann problems. The classic momentum interpolation is modified in order to improve its behavior for problems with rarefaction waves and shock waves in flow of an ideal gas at low Mach Number.
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Boundary conditions for semi-implicit low Mach Number flow calculation
2012Co-Authors: Yann Moguen, Pascal Bruel, Erik DickAbstract:For low Mach Number flow calculation, when acoustic waves have to be captured, semi-implicit methods allow to avoid the time-step limitation that arises when explicit schemes are used. A method is suggested to solve the boundary equations so that the semi-implicitness of the algorithm is maintained, as well as its pressure-velocity coupling. This method is stud- ied theoretically and numerically, in the low Mach Number regime. Partially non-reflective characteristic-based boundary conditions, with the linear relaxation form suggested by Rudy and Strikwerda, [J. Comput. Phys. 36:55-70, 1980], are considered. It is shown that their properties, well known in the framework of explicit schemes, are recovered with the proposed semi-implicit treatment and an acoustic CFL Number significantly larger than unity.
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Pressure-velocity coupling for unsteady low Mach Number flow
2011Co-Authors: Yann Moguen, Erik Dick, Jan Vierendeels, Pascal BruelAbstract:The proper scaling of the pressure-velocity coupling that arises from the momentum interpolation approach for unsteady calculation in low Mach Number flow is identified. It is used to modify the AUSM+-up scheme for acoustic simulations in low Mach Number flows.
Charles A. Rendleman - One of the best experts on this subject based on the ideXlab platform.
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Low Mach Number modeling of type Ia supernovae. I. Hydrodynamics
The Astrophysical Journal, 2006Co-Authors: Ann S. Almgren, John B. Bell, Charles A. Rendleman, Michael ZingaleAbstract:We introduce a low Mach Number equation set for the large-scale numerical simulation of carbon-oxygen white dwarfs experiencing a thermonuclear deflagration. Since most of the interesting physics in a Type Ia supernova transpires at Mach Numbers from 0.01 to 0.1, such an approach enables both a considerable increase in accuracy and a savings in computer time compared with frequently used compressible codes. Our equation set is derived from the fully compressible equations using low Mach Number asymptotics, but without any restriction on the size of perturbations in density or temperature. Comparisons with simulations that use the fully compressible equations validate the low Mach Number model in regimes where both are applicable. Comparisons to simulations based on the more traditional anelastic approximation also demonstrate the agreement of these models in the regime for which the anelastic approximation is valid. For low Mach Number flows with potentially finite amplitude variations in density and temperature, the low Mach Number model overcomes the limitations of each of the more traditional models and can serve as the basis for an accurate and efficient simulation tool.
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Low Mach Number Modeling of Type Ia Supernovae. II. Energy Evolution
The Astrophysical Journal, 2006Co-Authors: Ann S. Almgren, John B. Bell, Charles A. Rendleman, Michael ZingaleAbstract:The convective period leading up to a Type Ia supernova (SNIa) explosion is characterized by very low Mach Number flows, requiringhydrodynamical methods well-suited to long-time integration. We continuethe development of the low Mach Number equation set for stellar scaleflows by incorporating the effects of heat release due to externalsources. Low Mach Number hydrodynamics equations with a time-dependentbackground state are derived, and a numerical method based on theapproximate projection formalism is presented. We demonstrate throughvalidation with a fully compressible hydrodynamics code that this lowMach Number model accurately captures the expansion of the stellaratmosphere as well as the local dynamics due to external heat sources.This algorithm provides the basis for an efficient simulation tool forstudying the ignition of SNe Ia.
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Low Mach Number Modeling of Type Ia Supernovae
The Astrophysical Journal, 2005Co-Authors: Ann S. Almgren, John B. Bell, Charles A. Rendleman, Michael ZingaleAbstract:We introduce a low Mach Number equation set for the large-scale numerical simulation of carbon-oxygen white dwarfs experiencing a thermonuclear deflagration. Since most of the interesting physics in a Type Ia supernova transpires at Mach Numbers from 0.01 to 0.1, such an approach enables both a considerable increase in accuracy and savings in computer time compared with frequently used compressible codes. Our equation set is derived from the fully compressible equations using low Mach Number asymptotics, but without any restriction on the size of perturbations in density or temperature. Comparisons with simulations that use the fully compressible equations validate the low Mach Number model in regimes where both are applicable. Comparisons to simulations based on the more traditional an elastic approximation also demonstrate the agreement of these models in the regime for which the anelastic approximation is valid. For low Mach Number flows with potentially finite amplitude variations in density and temperature, the low Mach Number model overcomes the limitations of each of the more traditional models and can serve as the basis for an accurate and efficient simulation tool.
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Adaptive low Mach Number simulations of nuclear flame microphysics
Journal of Computational Physics, 2004Co-Authors: John B. Bell, Charles A. Rendleman, Marcus S. Day, S. E. Woosley, Michael ZingaleAbstract:We introduce a numerical model for the simulation of nuclear flames in Type Ia supernovae. This model is based on a low Mach Number formulation that analytically removes acoustic wave propagation while retaining the compressibility effects resulting from nuclear burning. The formulation presented here generalizes low Mach Number models used in combustion that are based on an ideal gas approximation to the arbitrary equations of state such as those describing the degenerate matter found in stellar material. The low Mach Number formulation permits time steps that are controlled by the advective time scales resulting in a substantial improvement in computational efficiency compared to a compressible formulation. We briefly discuss the basic discretization methodology for the low Mach Number equations and their implementation in an adaptive projection framework. We present validation computations in which the computational results from the low Mach Number model are compared to a compressible code and present an application of the methodology to the Landau-Darrieus instability of a carbon flame.
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A parallel adaptive projection method for low Mach Number flows
International Journal for Numerical Methods in Fluids, 2002Co-Authors: John B. Bell, Michael J. Lijewski, Ann S. Almgren, Marcus S. Day, Charles A. RendlemanAbstract:We describe an adaptive projection method for numerically simulating low Mach Number flows. The projection method formulation enforces the velocity divergence constraint resulting from the low Mach Number approximation. It is implemented on an adaptive hierarchy of logically rectangular grids, where each finer level is refined in space and in time. The adaptive algorithm has been shown in previous papers to be robust and second-order accurate, and to satisfy the principles of conservation and free-stream preservation as applicable. Here, the parallelization is described in some detail, and the methodology is demonstrated on two examples from premixed, low Mach Number combustion