In this paper, two different finite differences schemes are presented for numerical solution of two-dimensional moving boundary problem. The methods are illustrated by solving sample problem in two-dimensional solidification of the square prism. The finite difference schemes developed for this purpose are based on the method of lines using interpolation polynomials. The fully explicit method de...

Many geophysical phenomena are characterized by properties that evolve over a wide range of scales which introduce difficulties when attempting to model these features in one computational method. We have developed a high-order finite difference method for the elastic wave equation that is able to efficiently handle varying temporal and spatial scales in a single, stand-alone framework. We appl...

Here we review a hybrid lattice Boltzmann algorithm to solve the equations of motion of cholesteric liquid crystals. The method consists in coupling a lattice Boltzmann solver for the Navier-Stokes equation to a finite difference method to solve the dynamical equations governing the evolution of the liquid crystalline order parameter. We apply this method to study the growth of cholesteric blue...

Mixed convection heat transfer in two-dimensional liddriven rectangular cavity filled with air (Pr =0.71) is studied numerically. A hybrid scheme with multiple relaxation time Lattice Boltzmann Method (MRT-LBM) is used to obtain the velocity field while the temperature field is deduced from energy balance equation by using the Finite Difference Method (FDM). The main objective of this work is t...

This article is devoted to the numerical analysis of two classes of iterative methods that combine integral formulas with finite-difference Poisson solvers for the solution of elliptic problems. The first method is in the spirit of the Schwarz domain decomposition method for exterior domains. The second one is motivated by potential calculations in free boundary problems and can be viewed as a ...

In a companion presentation, we have discussed the theory of a mesoscopic/macroscopic model, which can be viewed as an augmented drift-diffusion model. Here, we describe how that model is used. The device we consider for this presentation is the one dimensional GaAs n+-n-n+ structure of length 0.8μm. First, a full hydrodynamic (HD) model, proven reliable when compared with Monte Carlo simulatio...

This study proposes one-dimensional advection–diffusion equation (ADE) with finite differences method (FDM) using implicit spreadsheet simulation (ADEISS). By changing only the values of temporal and spatial weighted parameters with ADEISS implementation, solutions are implicitly obtained for the BTCS, Upwind and Crank–Nicolson schemes. The ADEISS uses iterative spreadsheet solution technique. ...