Abstract. A numerical method is presented for the treatment of one-dimensional compressible flames. The method consists of a conservative front tracking algorithm for use near the flame and a high-order finite difference scheme for capturing the hvdrodynamics throughout the rest of the domain. The results presented show that the method effectively models the interaction of gas dynamics with bot...

Models for multiphase-multicomponent flow in porous media are described in systems of PDEs. Solving them using finite difference discretization method can be of three ways; explicit, semi-implicit, and fully implicit. In this study, we present the implementation of an adaptive Newton-Raphson method in the context of IMPECS (Implicit Pressures Explicit Concentrations and Saturations) method of s...

We present a new class of explicit marching schemes for the wave equation in complex geometry. They rely on a simple embedding of the domain in a uniformCartesian grid, which allows for efficient and automatic implementation but creates irregular cells near the boundary. While existing explicit finite difference schemes are generally restricted in the size of the time step that can be taken by ...

A method is described to construct modal fields for an arbitrary oneor two-dimensional refractive index structure. An arbitrary starting field is propagated along a complex axis using the slowly varying envelope approximation (SVEA). By choosing suitable values for the step-size, one mode is maximally increased in amplitude on propagating, until convergence has been obtained. For the calculatio...

In this review paper, the finite difference methods (FDMs) for the fractional differential equations are displayed. The considered equations mainly include the fractional kinetic equations of diffusion or dispersion with time, space and time-space derivatives. In some way, these numerical methods have similar form as the case for classical equations, some of which can be seen as the generalizat...

This paper presents an investigation into the performance evaluation of Finite Difference (FD) method in modeling a rectangular thin plate structure. In case of complex and big construction systems subjected to the arbitrary loads, including a complex boundary conditions, solving of differential equations by analytical methods is almost impossible. Then the solution is application of numerical ...

Discontinuous Galerkin Time Domain Methods for Acoustics and Comparison with Finite Difference Time Domain Methods