[HTML][HTML] A simple and general framework for the construction of thermodynamically compatible schemes for computational fluid and solid mechanics

R Abgrall, S Busto, M Dumbser - Applied Mathematics and Computation, 2023 - Elsevier
We introduce a simple and general framework for the construction of thermodynamically
compatible schemes for the numerical solution of overdetermined hyperbolic PDE systems …

On thermodynamically compatible finite volume schemes for continuum mechanics

S Busto, M Dumbser, I Peshkov, E Romenski - SIAM Journal on Scientific …, 2022 - SIAM
In this paper we present a new family of semidiscrete and fully discrete finite volume
schemes for overdetermined, hyperbolic, and thermodynamically compatible PDE systems …

An efficient lattice Boltzmann method for compressible aerodynamics on D3Q19 lattice

S Guo, Y Feng, J Jacob, F Renard, P Sagaut - Journal of Computational …, 2020 - Elsevier
An efficient lattice Boltzmann (LB) model relying on a hybrid recursive regularization (HRR)
collision operator on D3Q19 stencil is proposed for the simulation of three-dimensional high …

On thermodynamically compatible finite volume methods and path-conservative ADER discontinuous Galerkin schemes for turbulent shallow water flows

S Busto, M Dumbser, S Gavrilyuk, K Ivanova - Journal of Scientific …, 2021 - Springer
In this paper we propose a new reformulation of the first order hyperbolic model for unsteady
turbulent shallow water flows recently proposed in Gavrilyuk et al.(J Comput Phys 366: 252 …

A new thermodynamically compatible finite volume scheme for magnetohydrodynamics

S Busto, M Dumbser - SIAM Journal on Numerical Analysis, 2023 - SIAM
In this paper we propose a novel thermodynamically compatible finite volume scheme for
the numerical solution of the equations of magnetohydrodynamics (MHD) in one and two …

[HTML][HTML] Discontinuous Galerkin schemes for hyperbolic systems in non-conservative variables: quasi-conservative formulation with subcell finite volume corrections

E Gaburro, W Boscheri, S Chiocchetti… - Computer Methods in …, 2024 - Elsevier
We present a novel quasi-conservative arbitrary high order accurate ADER (Arbitrary-
Derivative) discontinuous Galerkin method allowing to efficiently use a non-conservative …

A general framework to construct schemes satisfying additional conservation relations. Application to entropy conservative and entropy dissipative schemes

R Abgrall - Journal of Computational Physics, 2018 - Elsevier
We are interested in the approximation of a steady hyperbolic problem. In some cases, the
solution can satisfy an additional conservation relation, at least when it is smooth. This is the …

Reinterpretation and extension of entropy correction terms for residual distribution and discontinuous Galerkin schemes: application to structure preserving …

R Abgrall, P Öffner, H Ranocha - Journal of Computational Physics, 2022 - Elsevier
For the general class of residual distribution (RD) schemes, including many finite element
(such as continuous/discontinuous Galerkin) and flux reconstruction methods, an approach …

Analysis of the SBP-SAT stabilization for finite element methods part II: entropy stability

R Abgrall, J Nordström, P Öffner, S Tokareva - Communications on Applied …, 2021 - Springer
In the hyperbolic research community, there exists the strong belief that a continuous
Galerkin scheme is notoriously unstable and additional stabilization terms have to be added …

A pressure‐based method for weakly compressible two‐phase flows under a Baer–Nunziato type model with generic equations of state and pressure and velocity …

B Re, R Abgrall - … Journal for Numerical Methods in Fluids, 2022 - Wiley Online Library
Within the framework of diffuse interface methods, we derive a pressure‐based Baer–
Nunziato type model well‐suited to weakly compressible multiphase flows. The model can …