Finite volume evolution Galerkin methods — A survey

Abstract

FVEG methods have been developed over the last dozen years to approximate unsteady hyperbolic equations in several space dimensions. In this survey the algorithmic origins of the methods are described. Then a detailed derivation of the methods is given, followed by evidence of their stability and accuracy.Finally several examples of their application are given.

Adaptive discontinuous evolution Galerkin method for dry atmospheric flow

“…In [32] we derived exact integral representation and approximate evolution operators for three-dimensional hyperbolic conservation laws and presented the results of the FVEG method for the acoustic equation. The FVEG method has been shown to be more accurate than standard FV methods based on the one-dimensional Riemann solver, see also, [28] for further references. In order to illustrate high accuracy, stability and robustness also for the new DEG method we will concentrate on two-dimensional dry atmospheric flows and standard meteorological test cases.…”

Runge-Kutta Discontinuous Local Evolution Galerkin Methods for the Shallow Water Equations on the Cubed-Sphere Grid

“…the wave propagation in heterogeneous media [1], the Euler equations of gas dynamics [28], and the SWEs [4,9,15,29] with well-balanced property with or without dry beds. A survey of finite volume EG method was presented in [25]. The LEG method was proposed in [42] to simplify the evaluation of the EG numerical fluxes by taking the limit of the approximate evolution operator at time level t n as the time t n + τ approaches t n .…”