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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 CONVECTION IN HELIUM SHELLS ON SUB-CHANDRASEKHAR WHITE DWARFS. I. METHODOLOGY
The Astrophysical Journal, 2013Co-Authors: Michael Zingale, John B. Bell, Ann S. Almgren, Andrew Nonaka, C. M. Malone, Ryan OrvedahlAbstract:We assess the robustness of a Low Mach Number hydrodynamics algorithm for modeling helium shell convection on the surface of a white dwarf in the context of the sub-Chandrasekhar model for Type Ia supernovae. We use the Low Mach Number stellar hydrodynamics code, MAESTRO, to perform three-dimensional, spatially adaptive simulations of convection leading up to the point of the ignition of a burning front. We show that the Low Mach Number hydrodynamics model provides a robust description of the system.
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MAESTRO: AN ADAPTIVE Low Mach Number HYDRODYNAMICS ALGORITHM FOR STELLAR FLowS
The Astrophysical Journal Supplement Series, 2010Co-Authors: Andrew Nonaka, Michael J. Lijewski, John B. Bell, Ann S. Almgren, C. M. Malone, Michael ZingaleAbstract:Many astrophysical phenomena are highly subsonic, requiring specialized numerical methods suitable for long-time integration. In a series of earlier papers we described the development of MAESTRO, a Low Mach Number stellar hydrodynamics code that can be used to simulate long-time, Low-speed fLows that would be prohibitively expensive to model using traditional compressible codes. MAESTRO is based on an equation set derived using Low Mach Number asymptotics; this equation set does not explicitly track acoustic waves and thus alLows a significant increase in the time step. MAESTRO is suitable for two- and three-dimensional local atmospheric fLows as well as three-dimensional full-star fLows. Here, we continue the development of MAESTRO by incorporating adaptive mesh refinement (AMR). The primary difference between MAESTRO and other structured grid AMR approaches for incompressible and Low Mach Number fLows is the presence of the time-dependent base state, whose evolution is coupled to the evolution of the full solution. We also describe how to incorporate the expansion of the base state for full-star fLows, which involves a novel mapping technique between the one-dimensional base state and the Cartesian grid, as well as a Number of overall improvements to the algorithm. We examine the efficiency and accuracy of our adaptive code, and demonstrate that it is suitable for further study of our initial scientific application, the convective phase of Type Ia supernovae.
John B. Bell - One of the best experts on this subject based on the ideXlab platform.
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Low Mach Number fluctuating hydrodynamics model for ionic liquids
Physical Review Fluids, 2020Co-Authors: Katherine Klymko, John B. Bell, A Nonaka, Sean P Carney, Alejandro L. GarciaAbstract:© 2020 American Physical Society. We present a new mesoscale model for ionic liquids based on a Low Mach Number fluctuating hydrodynamics formulation for multicomponent charged species. The Low Mach Number approach eliminates sound waves from the fully compressible equations leading to a computationally efficient incompressible formulation. The model uses a Gibbs free-energy functional that includes enthalpy of mixing, interfacial energy, and electrostatic contributions. These lead to a new fourth-order term in the mass equations and a reversible stress in the momentum equations. We calibrate our model using parameters for [DMPI+][F6P-], an extensively studied room temperature ionic liquid (RTIL), and numerically demonstrate the formation of mesoscopic structuring at equilibrium in two and three dimensions. In simulations with electrode boundaries the measured double-layer capacitance decreases with voltage, in agreement with theoretical predictions and experimental measurements for RTILs. Finally, we present a shear electroosmosis example to demonstrate that the methodology can be used to model electrokinetic fLows.
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Low Mach Number fluctuating hydrodynamics model for ionic liquids
Physical Review Fluids, 2020Co-Authors: Katherine Klymko, John B. Bell, Andrew Nonaka, Sean Carney, Alejandro L. GarciaAbstract:We present a new mesoscale model for ionic liquids based on a Low Mach Number fluctuating hydrodynamics formulation for multicomponent charged species. The Low Mach Number approach eliminates sound waves from the fully compressible equations leading to a computationally efficient incompressible formulation. The model uses a Gibbs free energy functional that includes enthalpy of mixing, interfacial energy, and electrostatic contributions. These lead to a new fourth-order term in the mass equations and a reversible stress in the momentum equations. We calibrate our model using parameters for [DMPI+][F6P-], an extensively-studied room temperature ionic liquid (RTIL), and numerically demonstrate the formation of mesoscopic structuring at equilibrium in two and three dimensions. In simulations with electrode boundaries the measured double layer capacitance decreases with voltage, in agreement with theoretical predictions and experimental measurements for RTILs. Finally, we present a shear electroosmosis example to demonstrate that the methodology can be used to model electrokinetic fLows.
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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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Low Mach Number fluctuating hydrodynamics for electrolytes
Physical Review Fluids, 2016Co-Authors: Jean-philippe M. Péraud, John B. Bell, Andrew Nonaka, Aleksandar Donev, Anuj Chaudhri, Alejandro L. GarciaAbstract:Author(s): Peraud, JP; Nonaka, A; Chaudhri, A; Bell, JB; Donev, A; Garcia, AL | Abstract: © 2016 American Physical Society. We formulate and study computationally the Low Mach Number fluctuating hydrodynamic equations for electrolyte solutions. We are interested in studying transport in mixtures of charged species at the mesoscale, down to scales beLow the Debye length, where thermal fluctuations have a significant impact on the dynamics. Continuing our previous work on fluctuating hydrodynamics of multicomponent mixtures of incompressible isothermal miscible liquids [A. Donev, Phys. Fluids 27, 037103 (2015)PHFLE61070-663110.1063/1.4913571], we now include the effect of charged species using a quasielectrostatic approximation. Localized charges create an electric field, which in turn provides additional forcing in the mass and momentum equations. Our Low Mach Number formulation eliminates sound waves from the fully compressible formulation and leads to a more computationally efficient quasi-incompressible formulation. We demonstrate our ability to model saltwater (NaCl) solutions in both equilibrium and nonequilibrium settings. We show that our algorithm is second order in the deterministic setting and for length scales much greater than the Debye length gives results consistent with an electroneutral approximation. In the stochastic setting, our model captures the predicted dynamics of equilibrium and nonequilibrium fluctuations. We also identify and model an instability that appears when diffusive mixing occurs in the presence of an applied electric field.
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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...
Ann S. Almgren - One of the best experts on this subject based on the ideXlab platform.
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maestroex a massively parallel Low Mach Number astrophysical solver
The Astrophysical Journal, 2019Co-Authors: Duoming Fan, Ann S. Almgren, Alice Harpole, A Nonaka, M ZingaleAbstract:Author(s): Fan, D; Nonaka, A; Almgren, AS; Harpole, A; Zingale, M | Abstract: © 2019. The American Astronomical Society. All rights reserved. We present MAESTROeX, a massively parallel solver for Low Mach Number astrophysical fLows. The underlying Low Mach Number equation set alLows for efficient, long-time integration for highly subsonic fLows compared to compressible approaches. MAESTROeX is suitable for modeling full spherical stars as well as well as planar simulations of dynamics within localized regions of a star, and can robustly handle several orders of magnitude of density and pressure stratification. Previously, we have described the development of the predecessor of MAESTROeX, called MAESTRO, in a series of papers. Here, we present a new, greatly simplified temporal integration scheme that retains the same order of accuracy as our previous approaches. We also explore the use of alternative spatial mapping of the one-dimensional base state onto the full Cartesian grid. The code leverages the new AMReX software framework for block-structured adaptive mesh refinement (AMR) applications, alLowing for scalability to large fractions of leadership-class Machines. Using our previous studies on the convective phase of single-degenerate progenitor models of SNe Ia as a guide, we characterize the performance of the code and validate the new algorithmic features. Like MAESTRO, MAESTROeX is fully open source.
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maestroex a massively parallel Low Mach Number astrophysical solver
arXiv: Computational Physics, 2019Co-Authors: Duoming Fan, Ann S. Almgren, Alice Harpole, A Nonaka, M ZingaleAbstract:We present MAESTROeX, a massively parallel solver for Low Mach Number astrophysical fLows. The underlying Low Mach Number equation set alLows for efficient, long-time integration for highly subsonic fLows compared to compressible approaches. MAESTROeX is suitable for modeling full spherical stars as well as well as planar simulations of dynamics within localized regions of a star, and can robustly handle several orders of magnitude of density and pressure stratification. Previously, we have described the development of the predecessor of MAESTROeX, called MAESTRO, in a series of papers. Here, we present a new, greatly simplified temporal integration scheme that retains the same order of accuracy as our previous approaches. We also explore the use of alternative spatial mapping of the one-dimensional base state onto the full Cartesian grid. The code leverages the new AMReX software framework for block-structured adaptive mesh refinement (AMR) applications, alLowing for scalability to large fractions of leadership-class Machines. Using our previous studies on the convective phase of single-degenerate progenitor models of Type Ia supernovae as a guide, we characterize the performance of the code and validate the new algorithmic features. Like MAESTRO, MAESTROeX is fully open source.
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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.
Pascal Bruel - 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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Behaviour of upwind schemes in Low Mach Number flow
2013Co-Authors: Simon Delmas, Vincent Perrier, Pascal BruelAbstract:In the present work, we are interested in the direct numerical simulation of the compressible Euler and Navier Stokes equations at Low Mach Number regime. First, we propose a review of existing work on the subject in order to identify the issues raised by the simulation of in this kind of flow, and the existing relevant solutions. Then, we will test different selected compressible Low Mach solvers using the discontinuous Galerkin space discretisation and discuss about their behaviour.
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Pressure-velocity coupling for unsteady Low Mach Number fLow simulations: An improvement of the AUSM+-up scheme
Journal of Computational and Applied Mathematics, 2013Co-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 first identified. Then, it is used to suggest a modification of the AUSM^+-up scheme that alLows acoustic simulations in Low Mach Number fLow.
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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Pressure-velocity coupling for unsteady Low Mach Number fLow simulations: An improvement of the AUSM+-up scheme
Journal of Computational and Applied Mathematics, 2013Co-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 first identified. Then, it is used to suggest a modification of the AUSM^+-up scheme that alLows acoustic simulations in Low Mach Number fLow.
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Pressure-velocity coupling for unsteady Low Mach Number fLow simulations: An improvement of the AUSM + -up scheme
Journal of Computational and Applied Mathematics, 2013Co-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 first identified. Then, it is used to suggest a modification of the AUSM +-up scheme that alLows acoustic simulations in Low Mach Number fLow.
