Numerical investigation of viscous effects on the nonlinear Burgers equation

Abstract

This research article presents the numerical solution of the viscous Burgers equation. The diagonally implicit fractional step $\theta$ (DIFST) scheme is used for the time discretization and the space derivative is discretized by the conforming finite element method with quadrilateral mesh. The viscosity effect on the shock wave is calculated with an estimation of the $L_2$ error. For comparison of different time discretization schemes, three test problems are computed. The stability and accuracy of the schemes are given by estimating the $L_2$ error norm. Numerical simulation for one- and two-dimensional problems are given and illustrated graphically. The effect of the viscosity parameter on the nonlinearity of the Burger equation is computed. The stability of the schemes for different time steps with CPU time is also given.