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We design a novel provably stable discontinuous Galerkin spectral element (DGSEM) approximation to solve systems of conservation laws on moving domains. To incorporate the motion of the domain, we use an arbitrary Lagrangian-Eulerian…

Numerical Analysis · Mathematics 2015-11-02 David A. Kopriva , Andrew R. Winters , Marvin Bohm , Gregor J. Gassner

This paper presents high order accurate discontinuous Galerkin (DG) methods for wave problems on moving curved meshes with general choices of basis and quadrature. The proposed method adopts an arbitrary Lagrangian-Eulerian (ALE)…

Numerical Analysis · Mathematics 2020-11-06 Kaihang Guo , Jesse Chan

In this work, we propose an accurate, robust, and stable discretization of the gamma-based compressible multicomponent model by Shyue [J. Comput. Phys., 142 (1998), 208-242] where each component follows a stiffened gas equation of state…

Numerical Analysis · Mathematics 2025-10-10 Rémi Abgrall , Pratik Rai , Florent Renac

We present a robust and accurate discretization approach for incompressible turbulent flows based on high-order discontinuous Galerkin methods. The DG discretization of the incompressible Navier-Stokes equations uses the local…

Fluid Dynamics · Physics 2018-08-01 Niklas Fehn , Wolfgang A Wall , Martin Kronbichler

High-order entropy-stable discontinuous Galerkin methods for the compressible Euler and Navier-Stokes equations require the positivity of thermodynamic quantities in order to guarantee their well-posedness. In this work, we introduce a…

Numerical Analysis · Mathematics 2023-01-04 Yimin Lin , Jesse Chan , Ignacio Tomas

In this work we present a novel second order accurate well balanced Arbitrary-Lagrangian-Eulerian (ALE) finite volume scheme on moving nonconforming meshes for the Euler equations of compressible gasdynamics with gravity in cylindrical…

Numerical Analysis · Mathematics 2018-03-16 Elena Gaburro , Manuel J. Castro , Michael Dumbser

In this paper, we propose two monolithic fully discrete finite element methods for fluid-structure interaction (FSI) based on a novel Piola-type Arbitrary Lagrangian-Eulerian (ALE) mapping. For the temporal discretization, we apply the…

Numerical Analysis · Mathematics 2026-04-09 Shuaijun Liu , Xiaoping Xie

We implement a high-order numerical scheme for the entropy-based moment closure, the so-called M$_N$ model, for linear kinetic equations in slab geometry. A discontinuous Galerkin (DG) scheme in space along with a strong-stability…

Numerical Analysis · Mathematics 2015-06-23 Graham Alldredge , Florian Schneider

A discontinuous Galerkin (DG) method suitable for large-scale astrophysical simulations on Cartesian meshes as well as arbitrary static and moving Voronoi meshes is presented. Most major astrophysical fluid dynamics codes use a finite…

Computational Physics · Physics 2015-06-16 Philip Mocz , Mark Vogelsberger , Debora Sijacki , Ruediger Pakmor , Lars Hernquist

In fluid dynamics, an important problem is linked to the knowledge of the fluid pressure. Recently, another approach to study incompressible fluid flow was suggested. It consists in using a general pressure equation (GPE) derived from…

Fluid Dynamics · Physics 2020-05-14 Adrien Toutant

We present a novel discontinuous Galerkin finite element method for numerical simulations of the rotating thermal shallow water equations in complex geometries using curvilinear meshes, with arbitrary accuracy. We derive an entropy…

Numerical Analysis · Mathematics 2024-01-19 Kieran Ricardo , Kenneth Duru , David Lee

In this paper we propose a new spatially high order accurate semi-implicit discontinuous Galerkin (DG) method for the solution of the two dimensional incompressible Navier-Stokes equations on staggered unstructured curved meshes. While the…

Numerical Analysis · Mathematics 2014-07-07 Maurizio Tavelli , Michael Dumbser

This work presents GALAEXI as a novel, energy-efficient flow solver for the simulation of compressible flows on unstructured meshes leveraging the parallel computing power of modern Graphics Processing Units (GPUs). GALAEXI implements the…

Mathematical Software · Computer Science 2024-10-14 Daniel Kempf , Marius Kurz , Marcel Blind , Patrick Kopper , Philipp Offenhäuser , Anna Schwarz , Spencer Starr , Jens Keim , Andrea Beck

We present a new implicit higher-order finite element (FE) approach to efficiently model compressible multicomponent fluid flow on unstructured grids and in fractured porous subsurface formations. The scheme is sequential implicit:…

Computational Physics · Physics 2016-08-25 Joachim Moortgat , Mohammad Amin Amooie , Mohamad Reza Soltanian

We develop a novel and efficient discontinuous Galerkin spectral element method (DG-SEM) for the spherical rotating shallow water equations in vector invariant form. We prove that the DG-SEM is energy stable, and discretely conserves mass,…

Numerical Analysis · Mathematics 2024-01-19 Kieran Ricardo , David Lee , Kenneth Duru

Grad-div stabilization is a classical remedy in conforming mixed finite element methods for incompressible flow problems, for mitigating velocity errors that are sometimes called poor mass conservation. Such errors arise due to the…

Numerical Analysis · Mathematics 2019-04-12 Mine Akbas , Alexander Linke , Leo G. Rebholz , Philipp W. Schroeder

This work deals with Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES) of turbulent gravity currents, performed by means of a Discontinuous Galerkin (DG) Finite Element method. In particular, a DG-LES approach in which the…

Computational Physics · Physics 2016-12-23 C. Bassi , A. Abbà , L. Bonaventura , L. Valdettaro

We develop a discretely entropy-stable line-based discontinuous Galerkin method for hyperbolic conservation laws based on a flux differencing technique. By using standard entropy-stable and entropy-conservative numerical flux functions,…

Numerical Analysis · Mathematics 2019-05-01 Will Pazner , Per-Olof Persson

An energy stable finite element scheme within arbitrary Lagrangian Eulerian (ALE) framework is derived for simulating the dynamics of millimetric droplets in contact with solid surfaces. Supporting surfaces considered may exhibit…

Numerical Analysis · Mathematics 2022-01-11 Filip Ivančić , Maxim Solovchuk

This paper presents a conservative discontinuous Galerkin method for the simulation of supercritical and transcritical real-fluid flows without phase separation. A well-known issue associated with the use of fully conservative schemes is…

Fluid Dynamics · Physics 2024-10-23 Eric J. Ching , Ryan F. Johnson