A well-balanced discontinuous Galerkin method for the first-order Z4 formulation of the Einstein-Euler system
From MaRDI portal
Publication:6497232
DOI10.1016/J.JCP.2024.112875MaRDI QIDQ6497232
Elena Gaburro, I. M. Peshkov, Michael Dumbser, Olindo Zanotti
Publication date: 6 May 2024
Published in: Journal of Computational Physics (Search for Journal in Brave)
Einstein field equationsdiscontinuous Galerkinrelativistic Euler equationswell-balancingnon conservativefirst order hyperbolic formulation of the Z4 formalism
Basic methods in fluid mechanics (76Mxx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) General relativity (83Cxx)
Cites Work
- Hybrid DG/FV schemes for magnetohydrodynamics and relativistic hydrodynamics
- Space-time adaptive ADER-DG finite element method with LST-DG predictor and a posteriori sub-cell WENO finite-volume limiting for simulation of non-stationary compressible multicomponent reactive flows
- A well-balanced semi-implicit IMEX finite volume scheme for ideal magnetohydrodynamics at all Mach numbers
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A high order special relativistic hydrodynamic and magnetohydrodynamic code with space-time adaptive mesh refinement
- ADER-WENO finite volume schemes with space-time adaptive mesh refinement
- Finite volume local evolution Galerkin method for two-dimensional relativistic hydrodynamics
- Well-balanced schemes for the Euler equations with gravitation
- \textit{A posteriori} subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws
- Arbitrary high order \(P_{N}P_{M}\) schemes on unstructured meshes for the compressible Navier-Stokes equations
- A well-balanced scheme for the shallow-water equations with topography
- A simple extension of the Osher Riemann solver to non-conservative hyperbolic systems
- Well balanced finite volume methods for nearly hydrostatic flows
- FORCE schemes on unstructured meshes. II: Non-conservative hyperbolic systems
- A simple robust and accurate \textit{a posteriori} sub-cell finite volume limiter for the discontinuous Galerkin method on unstructured meshes
- Formulation of discontinuous Galerkin methods for relativistic astrophysics
- \(3+1\) formalism in general relativity. Bases of numerical relativity.
- Very high order \(P_NP_M\) schemes on unstructured meshes for the resistive relativistic MHD equations
- On Godunov-type methods near low densities
- A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes
- Efficient, high accuracy ADER-WENO schemes for hydrodynamics and divergence-free magneto\-hydrodynamics
- ADER schemes on unstructured meshes for nonconservative hyperbolic systems: applications to geophysical flows
- Hyperbolicity of the 3+1 system of Einstein equations
- On the hyperbolicity of Einstein's and other gauge field equations
- 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
- Hyperbolic methods for Einstein's equations
- Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method: One-dimensional case.
- Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws.
- Divergence correction techniques for Maxwell solvers based on a hyperbolic model
- On numerical treatment of the source terms in the shallow water equations
- Hyperbolic divergence cleaning for the MHD equations
- ADER: Arbitrary high-order Godunov approach
- A well balanced diffuse interface method for complex nonhydrostatic free surface flows
- Space-time adaptive ADER discontinuous Galerkin finite element schemes with \textit{a posteriori} sub-cell finite volume limiting
- Direct arbitrary-Lagrangian-Eulerian finite volume schemes on moving nonconforming unstructured meshes
- SpECTRE: A task-based discontinuous Galerkin code for relativistic astrophysics
- ADER schemes for three-dimensional non-linear hyperbolic systems
- A posteriori subcell finite volume limiter for general \(P_NP_M\) schemes: applications from gasdynamics to relativistic magnetohydrodynamics
- Aliasing instabilities in the numerical evolution of the Einstein field equations
- Subcell limiting strategies for discontinuous Galerkin spectral element methods
- High order direct arbitrary-Lagrangian-Eulerian schemes on moving Voronoi meshes with topology changes
- High-order accurate entropy stable nodal discontinuous Galerkin schemes for the ideal special relativistic magnetohydrodynamics
- An all speed second order well-balanced IMEX relaxation scheme for the Euler equations with gravity
- In-cell discontinuous reconstruction path-conservative methods for non conservative hyperbolic systems -- second-order extension
- A simple diffuse interface approach for compressible flows around moving solids of arbitrary shape based on a reduced Baer-Nunziato model
- New directional vector limiters for discontinuous Galerkin methods
- 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
- Efficient parallelization of a shock capturing for discontinuous Galerkin methods using finite volume sub-cells
- Numerical solution of non-isothermal non-adiabatic flow of real gases in pipelines
- Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws
- High-order well-balanced finite volume WENO schemes for shallow water equation with moving water
- Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows
- The discontinuous Galerkin method with Lax--Wendroff type time discretizations
- Building blocks for arbitrary high order discontinuous Galerkin schemes
- Derivative Riemann solvers for systems of conservation laws and ader methods
- Relativistic Hydrodynamics
- Shock Capturing for Discontinuous Galerkin Methods using Finite Volume Subcells
- An operator-based local discontinuous Galerkin method compatible with the BSSN formulation of the Einstein equations
- Covariant formulations of Baumgarte, Shapiro, Shibata, and Nakamura and the standard gauge
- Evolution of three-dimensional gravitational waves: Harmonic slicing case
- Numerical integration of Einstein’s field equations
- The Runge-Kutta local projection $P^1$-discontinuous-Galerkin finite element method for scalar conservation laws
- The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
- Well-Balanced High Order Extensions of Godunov's Method for Semilinear Balance Laws
- On Godunov-Type Methods for Gas Dynamics
- TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
- Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics
- Hyperbolic equations for vacuum gravity using special orthonormal frames
- Towards standard testbeds for numerical relativity
- Einstein and Yang-Mills Theories in Hyperbolic Form without Gauge Fixing
- Fixing Einstein's Equations
- 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
- Runge--Kutta Discontinuous Galerkin Method Using WENO Limiters
- A WELL-BALANCED SCHEME USING NON-CONSERVATIVE PRODUCTS DESIGNED FOR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS WITH SOURCE TERMS
- A symmetric hyperbolic formulation of the vacuum Einstein equations in affine-null coordinates
- A Well Balanced Finite Volume Scheme for General Relativity
- Well-Balanced Central Scheme for the System of MHD Equations with Gravitational Source Term
- An All Speed Second Order IMEX Relaxation Scheme for the Euler Equations
- A Second Order Well-Balanced Finite Volume Scheme for Euler Equations with Gravity
- 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
- Constraint damping in the Z4 formulation and harmonic gauge
- On Massive Neutron Cores
- A high-order shock capturing discontinuous Galerkin–finite difference hybrid method for GRMHD
- The new discontinuous Galerkin methods based numerical relativity program Nmesh
- ExaHyPE: an engine for parallel dynamically adaptive simulations of wave problems
- A well-balanced and exactly divergence-free staggered semi-implicit hybrid finite volume / finite element scheme for the incompressible MHD equations
This page was built for publication: A well-balanced discontinuous Galerkin method for the first-order Z4 formulation of the Einstein-Euler system