Higher-order accurate space-time schemes for computational astrophysics—Part I: finite volume methods

DS Balsara - Living reviews in computational astrophysics, 2017 - Springer
As computational astrophysics comes under pressure to become a precision science, there
is an increasing need to move to high accuracy schemes for computational astrophysics …

High order direct Arbitrary-Lagrangian-Eulerian schemes on moving Voronoi meshes with topology changes

E Gaburro, W Boscheri, S Chiocchetti… - Journal of …, 2020 - Elsevier
We present a new family of very high order accurate direct Arbitrary-Lagrangian-Eulerian
(ALE) Finite Volume (FV) and Discontinuous Galerkin (DG) schemes for the solution of …

High order ADER schemes for continuum mechanics

S Busto, S Chiocchetti, M Dumbser, E Gaburro… - Frontiers in …, 2020 - frontiersin.org
In this paper we first review the development of high order ADER finite volume and ADER
discontinuous Galerkin schemes on fixed and moving meshes, since their introduction in …

High order entropy preserving ADER-DG schemes

E Gaburro, P Öffner, M Ricchiuto, D Torlo - Applied Mathematics and …, 2023 - Elsevier
In this paper, we develop a fully discrete entropy preserving ADER-Discontinuous Galerkin
(ADER-DG) method. To obtain this desired result, we equip the space part of the method …

An efficient class of WENO schemes with adaptive order for unstructured meshes

DS Balsara, S Garain, V Florinski, W Boscheri - Journal of Computational …, 2020 - Elsevier
Recent advances in finite-difference WENO schemes for hyperbolic conservation laws have
resulted in WENO schemes with adaptive order of accuracy. For instance, a WENO-AO (5, 3) …

Central weighted ENO schemes for hyperbolic conservation laws on fixed and moving unstructured meshes

M Dumbser, W Boscheri, M Semplice, G Russo - SIAM Journal on Scientific …, 2017 - SIAM
We present a novel family of arbitrary high order accurate central Weighted ENO (CWENO)
finite volume schemes for the solution of nonlinear systems of hyperbolic conservation laws …

A direct Arbitrary-Lagrangian–Eulerian ADER-WENO finite volume scheme on unstructured tetrahedral meshes for conservative and non-conservative hyperbolic …

W Boscheri, M Dumbser - Journal of Computational Physics, 2014 - Elsevier
In this paper we present a new family of high order accurate Arbitrary-Lagrangian–Eulerian
(ALE) one-step ADER-WENO finite volume schemes for the solution of nonlinear systems of …

[HTML][HTML] Arbitrary-Lagrangian–Eulerian discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshes

W Boscheri, M Dumbser - Journal of Computational Physics, 2017 - Elsevier
We present a new family of high order accurate fully discrete one-step Discontinuous
Galerkin (DG) finite element schemes on moving unstructured meshes for the solution of …

A divergence‐free semi‐implicit finite volume scheme for ideal, viscous, and resistive magnetohydrodynamics

M Dumbser, DS Balsara, M Tavelli… - International Journal for …, 2019 - Wiley Online Library
In this paper, we present a novel pressure‐based semi‐implicit finite volume solver for the
equations of compressible ideal, viscous, and resistive magnetohydrodynamics (MHD). The …

Using the PPML approach for constructing a low-dissipation, operator-splitting scheme for numerical simulations of hydrodynamic flows

I Kulikov, E Vorobyov - Journal of Computational Physics, 2016 - Elsevier
An approach for constructing a low-dissipation numerical method is described. The method
is based on a combination of the operator-splitting method, Godunov method, and piecewise …