A High-Order Discontinuous Galerkin Lagrange Projection Scheme for the Barotropic Euler Equations - Archive ouverte HAL Access content directly
Book Sections Year : 2017

A High-Order Discontinuous Galerkin Lagrange Projection Scheme for the Barotropic Euler Equations

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Abstract

This work considers the barotropic Euler equations and proposes a high-order conservative scheme based on a Lagrange-Projection decomposition. The high-order in space and time are achieved using Discontinuous Galerkin (DG) and Runge-Kutta (RK) strategies. The use of a Lagrange-Projection decomposition enables the use of time steps that are not constrained by the sound speed thanks to an implicit treatment of the acoustic waves (Lagrange step), while the transport waves (Projection step) are treated explicitly. We compare our DG discretization with the recent one (Renac in Numer Math 1-27, 2016, [7]) and state that it satisfies important non linear stability properties. The behaviour of our scheme is illustrated by several test cases.
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Dates and versions

hal-02173689 , version 1 (04-07-2019)

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Maxime Stauffert, Christophe Chalons. A High-Order Discontinuous Galerkin Lagrange Projection Scheme for the Barotropic Euler Equations. Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems, pp.63-70, 2017, ⟨10.1007/978-3-319-57394-6_7⟩. ⟨hal-02173689⟩
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