A Well Balanced Finite Volume Scheme for General Relativity
From MaRDI portal
Publication:5021405
DOI10.1137/21M1399154MaRDI QIDQ5021405
Michael Dumbser, Elena Gaburro, Manuel J. Castro
Publication date: 13 January 2022
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2108.02960
finite volume schemesgeneral relativityfirst order hyperbolic systemswell balanced schemesEinstein-Euler systemfirst order conformal and covariant reformulation of the Einstein field equations
Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Equations of motion in general relativity and gravitational theory (83C10) Hydrodynamic and hydromagnetic problems in astronomy and astrophysics (85A30) Computational methods for problems pertaining to astronomy and astrophysics (85-08) First-order hyperbolic systems (35L40) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08) Numerical analysis (65-XX) Mathematical modeling or simulation for problems pertaining to astronomy and astrophysics (85-10)
Related Items (4)
A well-balanced and exactly divergence-free staggered semi-implicit hybrid finite volume / finite element scheme for the incompressible MHD equations ⋮ Structure-preserving discretizations for nonlinear systems of hyperbolic, involution-constrained partial differential equations on manifolds. Abstracts from the workshop held April 10--16, 2022 ⋮ A well-balanced semi-implicit IMEX finite volume scheme for ideal magnetohydrodynamics at all Mach numbers ⋮ Well balanced finite volume schemes for shallow water equations on manifolds
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Exactly well-balanced discontinuous Galerkin methods for the shallow water equations with moving water equilibrium
- Well-balanced schemes for the Euler equations with gravitation
- Well balanced finite volume methods for nearly hydrostatic flows
- A gas-kinetic scheme for shallow-water equations with source terms
- Very high order \(P_NP_M\) schemes on unstructured meshes for the resistive relativistic MHD equations
- Republication of: The dynamics of general relativity
- Numerical hydrodynamics and magnetohydrodynamics in general relativity
- Balancing source terms and flux gradients in high-resolution Godunov methods: The quasi-steady wave-propagation algorithm
- Upwind methods for hyperbolic conservation laws with source terms
- Towards the ultimate conservative difference scheme. II: Monotonicity and conservation combined in a second-order scheme
- A well balanced diffuse interface method for complex nonhydrostatic free surface flows
- Direct arbitrary-Lagrangian-Eulerian finite volume schemes on moving nonconforming unstructured meshes
- A hybrid finite volume -- finite element method for bulk-surface coupled problems
- A kinetic scheme for the Saint-Venant system with a source term
- A family of stable numerical solvers for the shallow water equations with source terms.
- Definition and weak stability of nonconservative products
- On high order ADER discontinuous Galerkin schemes for first order hyperbolic reformulations of nonlinear dispersive systems
- A posteriori subcell finite volume limiter for general \(P_NP_M\) schemes: applications from gasdynamics to relativistic magnetohydrodynamics
- Adaptive deformation of 3D unstructured meshes with curved body fitted boundaries with application to unsteady compressible flows
- High order direct arbitrary-Lagrangian-Eulerian schemes on moving Voronoi meshes with topology changes
- High order ADER schemes and GLM curl cleaning for a first order hyperbolic formulation of compressible flow with surface tension
- On GLM curl cleaning for a first order reduction of the CCZ4 formulation of the Einstein field equations
- Well balanced residual distribution for the ALE spherical shallow water equations on moving adaptive meshes
- High order well-balanced finite volume methods for multi-dimensional systems of hyperbolic balance laws
- Well-balanced high-order finite volume methods for systems of balance laws
- High-order well-balanced finite volume schemes for the Euler equations with gravitation
- Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
- Numerical solution of non-isothermal non-adiabatic flow of real gases in pipelines
- High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms
- A hyperbolic reformulation of the Serre-Green-Naghdi model for general bottom topographies
- Well-balanced schemes to capture non-explicit steady states: Ripa model
- Relativistic Hydrodynamics
- Well-Balanced Schemes and Path-Conservative Numerical Methods
- Evolution of three-dimensional gravitational waves: Harmonic slicing case
- Numerical integration of Einstein’s field equations
- Formation and damping of relativistic strong shocks
- Well-Balanced High Order Extensions of Godunov's Method for Semilinear Balance Laws
- Stability properties of relativistic shock waves: Basic results
- Arbitrary Order Finite Volume Well-Balanced Schemes for the Euler Equations with Gravity
- A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows
- An efficient shock-capturing central-type scheme for multidimensional relativistic flows
- Relativistic Fluids and Magneto-fluids
- A WELL-BALANCED SCHEME USING NON-CONSERVATIVE PRODUCTS DESIGNED FOR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS WITH SOURCE TERMS
- A Second Order Well-Balanced Finite Volume Scheme for Euler Equations with Gravity
- WhiskyMHD: a new numerical code for general relativistic magnetohydrodynamics
- Constraint-preserving boundary conditions in the Z4 numerical relativity formalism
- Introduction to 3+1 Numerical Relativity
- High order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products. Applications to shallow-water systems
- Numerical methods for nonconservative hyperbolic systems: a theoretical framework.
- Hyperbolicity of second order in space systems of evolution equations
- On Massive Neutron Cores
- General Relativity
This page was built for publication: A Well Balanced Finite Volume Scheme for General Relativity
