A well-balanced finite volume scheme for the Euler equations with gravitation
METADATA ONLY
Loading...
Author / Producer
Date
2015-11
Publication Type
Report
ETH Bibliography
yes
Citations
Altmetric
METADATA ONLY
Data
Rights / License
Abstract
Context
Many problems in astrophysics feature flows which are close to hydrostatic equilibrium. However, standard numerical schemes for compressible hydrodynamics may be deficient in approximating this stationary state, in which the pressure gradient is nearly balanced by gravitational forces.
Aims
We aim to develop a second-order well-balanced scheme for the Euler equations. The scheme is designed to mimic a discrete version of the hydrostatic balance. Hence, it can resolve a discrete hydrostatic equilibrium exactly (up to machine precision) and propagate perturbations, on top of this equilibrium, very accurately.
Methods
A local second-order hydrostatic equilibrium preserving pressure reconstruction is developed. Combined with a standard central gravitational source term discretization and numerical fluxes that resolve stationary contact discontinuities exactly, the wellbalanced property is achieved.
Results
The resulting well-balanced scheme is robust and simple enough to be very easily implemented within any existing computer code solving time explicitly/implicitly the compressible hydrodynamics equations. We demonstrate the performance of the wellbalanced scheme for several astrophysically relevant applications: wave propagation in stellar atmospheres, a toy model for corecollapse supernovae, convection in carbon shell burning and a "realistic" proto-neutron star.
Many problems in astrophysics feature flows which are close to hydrostatic equilibrium. However, standard numerical schemes for compressible hydrodynamics may be deficient in approximating this stationary state, in which the pressure gradient is nearly balanced by gravitational forces.
Aims
We aim to develop a second-order well-balanced scheme for the Euler equations. The scheme is designed to mimic a discrete version of the hydrostatic balance. Hence, it can resolve a discrete hydrostatic equilibrium exactly (up to machine precision) and propagate perturbations, on top of this equilibrium, very accurately.
Methods
A local second-order hydrostatic equilibrium preserving pressure reconstruction is developed. Combined with a standard central gravitational source term discretization and numerical fluxes that resolve stationary contact discontinuities exactly, the wellbalanced property is achieved.
Results
The resulting well-balanced scheme is robust and simple enough to be very easily implemented within any existing computer code solving time explicitly/implicitly the compressible hydrodynamics equations. We demonstrate the performance of the wellbalanced scheme for several astrophysically relevant applications: wave propagation in stellar atmospheres, a toy model for corecollapse supernovae, convection in carbon shell burning and a "realistic" proto-neutron star.
Permanent link
Publication status
published
Editor
Book title
Journal / series
Volume
2015-40
Pages / Article No.
Publisher
Seminar for Applied Mathematics, ETH Zurich
Event
Edition / version
Methods
Software
Geographic location
Date collected
Date created
Subject
Hydrodynamics; Methods: numerical; Convection; Stars: interiors; Stars: neutron
Organisational unit
03851 - Mishra, Siddhartha / Mishra, Siddhartha