Numerical methods are developed to simulate the wave propagation in heterogeneous 2D fluid / poroelastic media. Wave propagation is described by the usual acoustics equations (in the fluid medium) and by the low-frequency Biot’s equations (in the porous medium). Interface conditions are introduced to model various hydraulic contacts between the two media: open pores, sealed pores, and imperfect...

We consider the second-order in time Strang-splitting approximation for tensorial (e.g. vector-valued and matrix-valued) Allen-Cahn equations. Both linear propagator nonlinear are computed explicitly. For case, we prove maximum principle unconditional energy dissipation a judiciously modified functional. The functional is close to classical up O(τ) where τ splitting step. matrix-valued sharp ma...

The numerical solution of large and sparse nonsymmetric linear systems of algebraic equations is usually the most time consuming part of time-step integrators for differential equations based on implicit formulas. Preconditioned Krylov subspace methods using Strang block circulant preconditioners have been employed to solve such linear systems. However, it has been observed that these block cir...

In this paper, we consider the solution of ordinary diierential equations using boundary value methods. These methods require the solutions of one or more unsymmetric, large and sparse linear systems. Krylov subspace methods with the Strang block-circulant preconditioners are proposed for solving these linear systems. We prove that our preconditioners are invertible and all the eigenvalues of t...

In this paper, we propose a new very simple numerical method for solving liquidgas compressible flows. Such flows are difficult to simulate because classical conservative finite volume schemes generate pressure oscillations at the liquid-gas interface. We extend to several dimensions the random choice scheme that we have constructed in [13]. The extension is performed through Strang dimensional...

A space-time adaptive method is presented for the reactive Euler equations describing chemically reacting gas flow where a two species model is used for the chemistry. The governing equations are discretized with a finite volume method and dynamic space adaptivity is introduced using multiresolution analysis. A time splitting method of Strang is applied to be able to consider stiff problems whi...

For the time integration of stii transport-chemistry problems from air pollution modelling, standard ODE solvers are not feasible due to the large number of species and the 3D nature. The popular alternative, standard operator splitting, introduces artiicial transients for short-lived species. This complicates the chemistry solution, easily causing large errors for such species. In the framewor...

Abstract In this paper, we propose a new conservative semi-Lagrangian (SL) finite difference (FD) WENO scheme for linear advection equations, which can serve as a base scheme for the Vlasov equation by Strang splitting [4]. The reconstruction procedure in the proposed SL FD scheme is the same as the one used in the SL finite volume (FV) WENO scheme [3]. However, instead of inputting cell averag...

In the present study, a discontinuous Galerkin (DG) framework is developed to simulate chemically reacting flows. The algorithm combines a double-flux method to account for variable thermodynamic properties, a Strang-splitting scheme for the stiff reaction chemistry, a robust WENO-based shock limiter, and the non-linear viscous-diffusive transport is discretized using the BR2 method. The algori...