Analysis of 2D Burger's equation using numerical and semi-analytic techniques

Abstract

The effect of advective and diffusive components are studied using the 2D Burgers’ equation. The diffusive term is influenced by the Reynolds number. Spatial discretization is performed using radial basis collocation, while the temporal direction is discretized using $4^{th}$ Runge-Kutta method. To analyze the error behavior, the closed-form solution of 2D Burgers’ equation is derived analytically using a generalized bivariate homotopy perturbation approach. A comprehensive discussion and comparison of both numerical and semi-analytical solutions are presented in terms of absolute error, as well as $\Vert e \Vert_{\infty}$ and $\Vert e \Vert_{2}$ error norms. The effect of Reynolds number on the diffusion component is illustrated graphically. Algorithm for both numerical and analytical techniques have been implemented in MATLAB R2023.