scholarly journals High–order Discontinuous Galerkin Methods on Polyhedral Grids for Geophysical Applications: Seismic Wave Propagation and Fractured Reservoir Simulations

2021 ◽  
pp. 159-225
Author(s):  
Paola F. Antonietti ◽  
Chiara Facciolà ◽  
Paul Houston ◽  
Ilario Mazzieri ◽  
Giorgio Pennesi ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Discontinuous Galerkin ◽  
Seismic Wave ◽  
Discontinuous Galerkin Methods ◽  
Seismic Wave Propagation ◽  
High Order ◽  
Galerkin Methods ◽  
Fractured Reservoir ◽  
Reservoir Simulations

scholarly journals A high-order Discontinuous Galerkin method for the seismic wave propagation

2009 ◽  
Vol 27 ◽  
pp. 70-89 ◽  
Author(s):  
Sarah Delcourte ◽  
Loula Fezoui ◽  
Nathalie Glinsky-Olivier
Keyword(s):  
Wave Propagation ◽  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Seismic Wave ◽  
Seismic Wave Propagation ◽  
High Order

scholarly journals A Novel Robust Strategy for Discontinuous Galerkin Methods in Computational Fluid Mechanics: Why? When? What? Where?

2021 ◽  
Vol 8 ◽  
Author(s):  
Gregor J. Gassner ◽  
Andrew R. Winters
Keyword(s):  
Wave Propagation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
Computational Physics ◽  
High Order ◽  
Galerkin Methods ◽  
Partial Differential ◽  
Dg Methods

In this paper we will review a recent emerging paradigm shift in the construction and analysis of high order Discontinuous Galerkin methods applied to approximate solutions of hyperbolic or mixed hyperbolic-parabolic partial differential equations (PDEs) in computational physics. There is a long history using DG methods to approximate the solution of partial differential equations in computational physics with successful applications in linear wave propagation, like those governed by Maxwell’s equations, incompressible and compressible fluid and plasma dynamics governed by the Navier-Stokes and the Magnetohydrodynamics equations, or as a solver for ordinary differential equations (ODEs), e.g., in structural mechanics. The DG method amalgamates ideas from several existing methods such as the Finite Element Galerkin method (FEM) and the Finite Volume method (FVM) and is specifically applied to problems with advection dominated properties, such as fast moving fluids or wave propagation. In the numerics community, DG methods are infamous for being computationally complex and, due to their high order nature, as having issues with robustness, i.e., these methods are sometimes prone to crashing easily. In this article we will focus on efficient nodal versions of the DG scheme and present recent ideas to restore its robustness, its connections to and influence by other sectors of the numerical community, such as the finite difference community, and further discuss this young, but rapidly developing research topic by highlighting the main contributions and a closing discussion about possible next lines of research.

High-Order Mesh Generation for Discontinuous Galerkin Methods Based on Elastic Deformation

2016 ◽  
Vol 8 (4) ◽  
pp. 693-702
Author(s):  
Hongqiang Lu ◽  
Kai Cao ◽  
Lechao Bian ◽  
Yizhao Wu
Keyword(s):  
Finite Element Method ◽  
Discontinuous Galerkin ◽  
Mesh Generation ◽  
Discontinuous Galerkin Methods ◽  
Elasticity Modulus ◽  
High Order ◽  
Galerkin Methods ◽  
Governing Equations ◽  
Numerical Tests ◽  
Cubic Polynomial

AbstractIn this paper, a high-order curved mesh generation method for Discontinuous Galerkin methods is introduced. First, a regular mesh is generated. Second, the solid surface is re-constructed using cubic polynomial. Third, the elastic governing equations are solved using high-order finite element method to provide a fully or partly curved grid. Numerical tests indicate that the intersection between element boundaries can be avoided by carefully defining the elasticity modulus.

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