A well-balanced discontinuous Galerkin method for the first–order Z4 formulation of the Einstein–Euler system

Dumbser, Michael; Zanotti, Olindo; Gaburro, Elena; Peshkov, Ilya

doi:10.1016/j.jcp.2024.112875

Journal of Computational Physics

2024

DOI: 10.1016/j.jcp.2024.112875

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A well-balanced discontinuous Galerkin method for the first–order Z4 formulation of the Einstein–Euler system

Michael Dumbser,

Olindo Zanotti,

Elena Gaburro

et al.

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2024

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Cited by 9 publications

References 132 publications

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Arbitrary High Order ADER-DG Method with Local DG Predictor for Solutions of Initial Value Problems for Systems of First-Order Ordinary Differential Equations

Popov

2024

J Sci Comput

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Arbitrary High Order ADER-DG Method with Local DG Predictor for Solutions of Initial Value Problems for Systems of First-Order Ordinary Differential Equations

Popov

2024

J Sci Comput

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A High-Order Well-Balanced Discontinuous Galerkin Method for Hyperbolic Balance Laws Based on the Gauss-Lobatto Quadrature Rules

Xu,

Shu

2024

J Sci Comput

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In this paper, we develop a high-order well-balanced discontinuous Galerkin method for hyperbolic balance laws based on the Gauss-Lobatto quadrature rules. Important applications of the method include preserving the non-hydrostatic equilibria of shallow water equations with non-flat bottom topography and Euler equations in gravitational fields. The well-balanced property is achieved through two essential components. First, the source term is reformulated in a flux-gradient form in the local reference equilibrium state to mimic the true flux gradient in the balance laws. Consequently, the source term integral is discretized using the same approach as the flux integral at Gauss-Lobatto quadrature points, ensuring that the source term is exactly balanced by the flux in equilibrium states. Our method differs from existing well-balanced DG methods for shallow water equations with non-hydrostatic equilibria, particularly in the aspect that it does not require the decomposition of the source term integral. The effectiveness of our method is demonstrated through ample numerical tests.

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Discontinuous Galerkin schemes for hyperbolic systems in non-conservative variables: Quasi-conservative formulation with subcell finite volume corrections

Gaburro,

Boscheri,

Chiocchetti

et al. 2024

Computer Methods in Applied Mechanics and Engineering

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A well-balanced discontinuous Galerkin method for the first–order Z4 formulation of the Einstein–Euler system

Cited by 9 publications

References 132 publications

Arbitrary High Order ADER-DG Method with Local DG Predictor for Solutions of Initial Value Problems for Systems of First-Order Ordinary Differential Equations

Arbitrary High Order ADER-DG Method with Local DG Predictor for Solutions of Initial Value Problems for Systems of First-Order Ordinary Differential Equations

A High-Order Well-Balanced Discontinuous Galerkin Method for Hyperbolic Balance Laws Based on the Gauss-Lobatto Quadrature Rules

Discontinuous Galerkin schemes for hyperbolic systems in non-conservative variables: Quasi-conservative formulation with subcell finite volume corrections

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