in this paper we investigate a nonlinear evolution model described by the rosenau-kdv equation. we propose a three-level average implicit finite difference scheme for its numerical solutions and prove that this scheme is stable and convergent in the order of o(τ2 + h2). furthermore we show the existence and uniqueness of numerical solutions. comparing the numerical results with other methods in...

A numerical method is proposed to simulate the propagation of transient poroelastic waves across 2D heterogeneous media, in the low frequency range. A velocity-stress formulation of Biot’s equations is followed, leading to a first-order system of partial differential equations. This system is splitted in two parts: a propagative one discretized by a fourth-order ADER scheme, and a diffusive one...

In this paper we demonstrate the performance of a slope limiting procedure combined with a discontinuous Galerkin (DG) finite element solver for 2D compressible Euler equations. The slope limiter can be categorized into van Albada type and is differentiable. This slope limiter is modified from a similar limiter used in finite volume solvers to suit the needs of the DG solver. The gradient in an...

We present a holistic optimization of the ADER-DG finite element software SeisSol targeting the Intel © Xeon Phi TM x200 processor, codenamed Knights Landing (KNL). SeisSol is a multi-physics software package performing earthquake simulations by coupling seismic wave propagation and the rupture process. The code was shown to scale beyond 1.5 million cores and achieved petascale performance when...

This work concerns the solution of generalized Riemann problems. To this end, we consider the ADER scheme of Titarev & Toro (2002), which relies on a generalization of the classical Godunov scheme. Another solution method is the power series expansion of LeFloch & Raviart (1988). We analyze the two resulting approximation schemes, where we show that for scalar 1d problems the Toro-Titarev solve...

Theflux reconstruction (FR)methodology provides a unifying description ofmany high-order schemes, including a particular discontinuous Galerkin (DG) scheme and several spectral difference (SD) schemes. In addition, the FR methodology has been used to generate new classes of high-order schemes, including the recently discovered ‘energy stable’ FR schemes. These schemes, which are often referred ...

In this work we present a framework for enforcing discrete maximum principles in discontinuous Galerkin (DG) discretizations. The developed schemes are applicable to scalar conservation laws as well hyperbolic systems. Our methodology limiting volume terms is similar recently proposed methods continuous approximations, while DG flux require novel stabilization techniques. Piecewise Bernstein po...

The accurate conservative level set (ACLS) method of Desjardins et al. [O. Desjardins, V. Moureau, H. Pitsch, An accurate conservative level set/ghost fluid method for simulating turbulent atomization, J. Comput. Phys. 227 (18) (2008) 8395–8416] is extended by using a discontinuous Galerkin (DG) discretization. DG allows for the scheme to have an arbitrarily high order of accuracy with the smal...