We develop a numerical solver for three-dimensional poroelastic wave propagation, based on high-order discontinuous Galerkin (DG) method, with the Biot equation formulated as first order conservative velocity/strain hyperbolic system. To derive an upwind flux, we find exact solution to Riemann problem; also consider attenuation mechanisms both in Biot’s low- and high-frequency regimes. Using ei...

It is well known that semi-discrete high order discontinuous Galerkin (DG) methods satisfy cell entropy inequalities for the square entropy for both scalar conservation laws and symmetric hyperbolic systems, in any space dimension and for any triangulations [39, 36]. However, this property holds only for the square entropy and the integrations in the DG methods must be exact. It is significantl...

In this paper, we develop a family of high order cut discontinuous Galerkin (DG) methods for hyperbolic conservation laws in one space dimension. Ghost penalty stabilization is used to stabilize the scheme small elements. Analysis shows that our proposed have similar stability and accuracy properties as standard DG on regular mesh. We also prove method with piecewise constants total variation d...

We analyze a general concept of limiters for a high order DG scheme written for a 1-D problem. The limiters, which are local and do not require extended stencils, are incorporated into the solution reconstruction in order to meet the requirement of monotonicity and avoid spurious solution overshoots. A limiter β will be defined based on the solution jumps at grid interfaces. It will be shown th...

We show that recently studied discontinuous Galerkin discretizations in their lowest order version are very similar to the MAC finite difference scheme. Indeed, applying a slight modification, the exact MAC scheme can be recovered. Therefore, the analysis applied to the DG methods applies to the MAC scheme as well and the DGmethods provide a natural generalization of the MAC scheme to higher or...

Abstract High order schemes have been investigated for quite a long time, and the flux reconstruction (FR) scheme proposed by Huynh recently attracts attention of researchers due to its simplicity efficiency. Building framework that bridges discontinuous Galerkin (DG) spectral difference (SD) schemes, FR recovers DG SD conveniently with careful selection parameters. In this article, is realized...

Abstract In this paper, we present a novel spatial reconstruction scheme, called AENO , that results from special averaging of the ENO polynomial and its closest neighbour, while retaining stencil direction decided by choice. A variant m-AENO, modified (m-ENO) neighbour. The concept is thoroughly assessed for one-dimensional linear advection equation non-linear hyperbolic system, in conjunction...