Numerical simulations are performed to study the propagation of elastic waves in a 2-D random heterogeneous medium such as concrete. To reduce spurious numerical artefacts to a negligible level, a fourth-order time-domain numerical scheme and an immersed interface method are used together. Effective properties of the equivalent homogeneous medium are extracted and compared to the predictions of...

We extend the Explicit Jump Immersed Interface Method (EJIIM) to stationary two phase Stokes equations with discontinuous viscosity. As the underlying finite difference method the discretization in velocity and pressure variables is used on a staggered grid. The resulting algorithm converges with second order in velocity and first in pressure. The iteration count for solving the resulting linea...

Keywords: Traditional finite element method Elliptic equation with matrix-valued coefficients Body-fitting grids Sharp-edged interface Symmetric positive definite a b s t r a c t The traditional finite element method has a number of nice properties, and thus it is highly desired for matrix-valued coefficient elliptic equations with sharp-edged interfaces. However , its efficient implementation ...

We study the L1-error estimates for the upwind scheme to the linear advection equations with a piecewise constant coefficients modeling linear waves crossing interfaces. Here the interface condition is immersed into the upwind scheme. We prove that, for initial data with a bounded variation, the numerical solution of the immersed interface upwind scheme converges in L1-norm to the differential ...

We present a meshless particle method for Poisson and diffusion problems on domains with discontinuous coefficients and possibly inhomogeneous boundary conditions. The method is based on a domain-decomposition approach with suitable interface and boundary conditions between regions of different diffusivities, and on using discretization-corrected particle strength exchange operators [B. Schrade...

In this chapter we present a new method for simulating the motion of a disperse particle phase in a carrier gas through porous media. We assume a sufficiently dilute particle-laden flow and compute, independently of the disperse phase, the steady laminar fluid velocity using the Immersed Boundary (IB) method. Given the velocity of the carrier gas, the equations of motion for the particles exper...