Spectral Difference method with a posteriori limiting: II- Application to low Mach number flows
arXiv:2405.11063 · doi:10.1093/mnras/staf133
Abstract
Stellar convection poses two main gargantuan challenges for astrophysical fluid solvers: low-Mach number flows and minuscule perturbations over steeply stratified hydrostatic equilibria. Most methods exhibit excessive numerical diffusion and are unable to capture the correct solution due to large truncation errors. In this paper, we analyze the performance of the Spectral Difference (SD) method under these extreme conditions using an arbitrarily high-order shock capturing scheme with a posteriori limiting. We include both a modification to the HLLC Riemann solver adapted to low Mach number flows (L-HLLC) and a well-balanced scheme to properly evolve perturbations over steep equilibrium solutions. We evaluate the performance of our method using a series of test tailored specifically for stellar convection. We observe that our high-order SD method is capable of dealing with very subsonic flows without necessarily using the modified Riemann solver. We find however that the well-balanced framework is unavoidable if one wants to capture accurately small amplitude convective and acoustic modes. Analyzing the temporal and spatial evolution of the turbulent kinetic energy, we show that our fourth-order SD scheme seems to emerge as an optimal variant to solve this difficult numerical problem.
16 pages, 11 figures, Published in MNRAS
References in corpus (29)
- The Athena++ Adaptive Mesh Refinement Framework: Design and Magnetohydrodynamic Solvers
- A Posteriori Subcell Limiting of the Discontinuous Galerkin Finite Element Method for Hyperbolic Conservation Laws
- Internal Gravity Waves in Massive Stars: Angular Momentum Transport
- An update on the double cascade scenario in two-dimensional turbulence
- Evolution and Yields of Extremely Metal Poor Intermediate Mass Stars
- A provably entropy stable subcell shock capturing approach for high order split form DG for the compressible Euler Equations
- Cholla : A New Massively-Parallel Hydrodynamics Code For Astrophysical Simulation
- New numerical solver for flows at various Mach numbers
- Hydrodynamic simulations of He-shell flash convection
- High-resolution calculations of the solar global convection with the reduced speed of sound technique: I. The structure of the convection and the magnetic field without the rotation
- Towards a new generation of multi-dimensional stellar evolution models: development of an implicit hydrodynamic code
- Astrophysical hydrodynamics with a high-order discontinuous Galerkin scheme and adaptive mesh refinement
- Fully compressible simulations of waves and core convection in main-sequence stars
- High-order Magnetohydrodynamics for Astrophysics with an Adaptive Mesh Refinement Discontinuous Galerkin Scheme
- A study of convective core overshooting as a function of stellar mass based on two-dimensional hydrodynamical simulations
- A 3D Spectral Anelastic Hydrodynamic Code for Shearing, Stratified Flows
- Benchmarking the Multi-dimensional Stellar Implicit Code MUSIC
- MAESTROeX: A Massively Parallel Low Mach Number Astrophysical Solver
- Well-balanced treatment of gravity in astrophysical fluid dynamics simulations at low Mach numbers
- A high performance and portable all-Mach regime flow solver code with well-balanced gravity. Application to compressible convection
- Multidimensional low-Mach number time-implicit hydrodynamic simulations of convective helium shell burning in a massive star
- A finite-volume scheme for modeling compressible magnetohydrodynamic flows at low Mach numbers in stellar interiors
- A spectral solver for solar inertial waves
- APSARA: A multi-dimensional unsplit fourth-order explicit Eulerian hydrodynamics code for arbitrary curvilinear grids
- Planet-disc interactions with Discontinuous Galerkin Methods using GPUs
- Toward fully compressible numerical simulations of stellar magneto-convection with the RAMSES code
- High-order Discontinuous Galerkin hydrodynamics with sub-cell shock capturing on GPUs
- Spectral Difference method with a posteriori limiting: Application to the Euler equations in one and two space dimensions
- WENO-Wombat: Scalable Fifth-Order Constrained-Transport Magnetohydrodynamics for Astrophysical Applications