This paper deals with the numerical modeling of wave propagation in porous media described by Biot’s theory. The viscous efforts between the fluid and the elastic skeleton are assumed to be a linear function of the relative velocity, which is valid in the low-frequency range. The coexistence of propagating fast compressional wave and shear wave, and of a diffusive slow compressional wave, makes...

We describe a high-order accurate space-time discontinuous Galerkin (DG) method for solving compressible flow problems on two-dimensional moving domains with large deformations. The DG discretization and space-time numerical fluxes are formulated on a three-dimensional space-time domain. The scheme is implicit, and we solve the resulting non-linear systems using a parallel Newton-Krylov solver....

Abstract A fully coupled high order discontinuous Galerkin (DG) solver for viscoelastic Oldroyd B fluid flow problems is presented. Contrary to known methods combining DG the discretization of convective terms material model with standard finite element (FEM) and using elastic viscous stress splitting (EVSS) its derivatives, a local (LDG) formulation first described hyperbolic convection‐diffus...

Abstract This paper is concerned with the rigorous error analysis of a fully discrete scheme obtained by using central fluxes discontinuous Galerkin (dG) method in space and Peaceman–Rachford splitting time. We apply to general class wave-type problems show that resulting approximations as well derivatives thereof satisfy bounds order polynomial degree used dG discretization two In particular, ...

ADER schemes are numerical methods, which can reach an arbitrary order of accuracy in both space and time. They are based on a reconstruction procedure and the solution of generalized Riemann problems. However, for general boundary conditions, in particular of Dirichlet type, a lack of accuracy might occur if a suitable treatment of boundaries conditions is not properly carried out. In this wor...

We present a new perspective on the use of weighted essentially nonoscillatory (WENO) reconstructions in high-order methods for scalar hyperbolic conservation laws. The main focus this work is nonlinear stabilization continuous Galerkin (CG) approximations. proposed methodology also provides an interesting alternative to WENO-based limiters discontinuous (DG) methods. Unlike Runge–Kutta DG sche...

In this paper we develop non-linear ADER schemes for time-dependent scalar linear and non-linear conservation laws in one, two and three space dimensions. Numerical results of schemes of up to fifth order of accuracy in both time and space illustrate that the designed order of accuracy is achieved in all space dimensions for a fixed Courant number and essentially non-oscillatory results are obt...

In this paper, we propose an optimally convergent discontinuous Galerkin (DG) method for nonlinear third-order ordinary differential equations. Convergence properties the solution and two auxiliary variables that approximate first second derivatives of are established. More specifically, prove is L2-stable provides optimal (p+1)-th order accuracy smooth solutions when using piecewise p-th degre...

This is an extension of our earlier work [9] in which a high order stable method was constructed for solving hyperbolic conservation laws on arbitrarily distributed point clouds. An algorithm of building a suitable polygonal mesh based on the random points was given and the traditional discontinuous Galerkin (DG) method was adopted on the constructed polygonal mesh. Numerical results in [9] sho...