Modal analysis of the flux reconstruction (FR) formulation is performed to obtain the semi-discrete and fully-discrete dispersion relations, using which, the wave properties of physical as well as spurious modes are characterized. The effect of polynomial order, correction function and solution points on the dispersion, dissipation and relative energies of the modes are investigated. Using this...

Vorticity-stream function method and MAC algorithm are adopted to systemically compare the finite volume method (FVM) and finite difference method (FDM) in this paper. Two typical problems—lid-driven flow and natural convection flow in a square cavity—are taken as examples to compare and analyze the calculation performances of FVM and FDMwith variant mesh densities, discrete forms, and treatmen...

We study the asymptotics of two space dimensional reaction-diffusion front speeds through mean zero space-time periodic shears using both analytical and numerical methods. The analysis hinges on traveling fronts and their estimates based on qualitative properties such as monotonicity and a priori integral inequalities. The computation uses an explicit second order upwind finite difference metho...

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...

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...