Propagation of transient mechanical waves in porous media is numerically investigated in 1D. The framework is the linear Biot’s model with frequency-independant coefficients. The coexistence of a propagating fast wave and a diffusive slow wave makes numerical modeling tricky. A method combining three numerical tools is proposed: a fourth-order ADER scheme with time-splitting to deal with the ti...

Abstract In this paper, we develop high-order asymptotic preserving (AP) schemes for the BGK equation in a hyperbolic scaling, which leads to the macroscopic models such as the Euler and compressible Navier-Stokes equations in the asymptotic limit. Our approaches are based on the so-called micro-macro formulation of the kinetic equation which involves a natural decomposition of the problem to t...

In this paper, we combine a high-order Discontinous Galerkin (DG) method and level set method solving the interface problem in a complex incompressible flow. The scheme is L2 stable and conservative. It improves the mass conservative property of the level set method. Numerical examples demonstrate the high order accuracy of the method and the high resolution especially when the interface underg...

In this paper, a centred universal high-order finite volume method for solving hyperbolic balance laws is presented. The scheme belongs to the family of ADER methods where Generalized Riemann Problems (GRP) building block. solution these problems carried through an implicit Taylor series expansion, which allows works very well stiff source terms. A von Neumann stability analysis out investigate...

In this paper, we consider the issue of convergence toward entropy solutions for high order finite volume weighted essentially non-oscillatory (WENO) scheme and discontinuous Galerkin (DG) finite element method approximating scalar nonconvex conservation laws. Although such high order nonlinearly stable schemes can usually converge to entropy solutions of convex conservation laws, convergence m...

An efficient and scalable global discontinuous Galerkin atmospheric model (DGAM) on the sphere is developed. The continuous flux form of the nonlinear shallow water equations on the cubed-sphere (in curvilinear coordinates) are developed. Spatial discretization is a nodal basis set of Legendre polynomials. Fluxes along internal element interfaces are approximated by a Lax-Friedrichs scheme. A t...

In this paper, we develop discontinuous Galerkin (DG) methods to solve ideal special relativistic hydrodynamics (RHD). In RHD, the density and pressure are positive. Units are normalized so that the speed of light is c = 1. Therefore, the velocity of the fluid has magnitude less than 1. To construct physically relevant numerical approximations, we develop a bound-preserving limiter to the schem...

The coarse grid of numerical weather prediction and climate models requires parametrization models to resolve atmospheric processes that are smaller than the grid size. For parametrization development, these processes are simulated by a high resolution model. At the Royal Netherlands Meteorological Institute, the Dutch Atmospheric Large-Eddy Simulation (DALES) is used [15]. This three-dimension...

To simulate accurately and efficiently aerospace-type flows using solely first-order PDE models, new numerical methods may be required to overcome difficulties introduced by the model. We consider a Discontinuous Galerkin (DG) method that has been shown to possess an asymptotic preservation (AP) property for one-dimensional hyperbolic relaxation systems, in an effort to understand the source of...