Numerical solution of a nonconstant coefficient advection diffusion equation in an irregular domain and analyses of numerical dispersion and dissipation

Abstract

This work is a major extension of our previous work in which we have solved a 2D nonconstant coefficient advection diffusion equation with nonconstant advection and constant diffusion terms on a square domain using the coefficient of dissipation D1=D2=0.0004{D}_{1}={D}_{2}=0.0004 using three finite difference methods, namely, Lax–Wendroff, Du Fort–Frankel and nonstandard finite difference methods. In this current work, the first novelty is that we solve a 2D nonconstant advection diffusion equation on an irregular domain with a more complicated initial profile and considered five combinations for values of D1{D}_{1} and D2{D}_{2}. Moreover, the second novelty is the study of numerical dispersion and dissipation of Lax Wendroff scheme for the five combinations of D1{D}_{1} and D2{D}_{2}. Third, we present some numerical profiles from the three methods for the five scenario at two times: T=0.1T=0.1, 1. The fourth novelty is the plot of the modulus of the exact amplification factor, modulus of amplification factor, and relative phase error vs phase angle along xx direction vs phase angle along yy direction for the Lax–Wendroff scheme at x=y=0.5x=y=0.5 for the five scenarios.

Keywords

• advection diffusion
• lax–wendroff
• du fort–frankel
• nonstandard finite difference
• nonconstant coefficient
• stability
• irregular domain