An efficient and reliable numerical study for the 2D nonlinear coupled Burgers equation simulating many physical phenomena.

In this paper, an accurate and reliable fully discretized linear numerical scheme has been developed for solving two-dimensional nonlinear coupled Burgers equation given by pre-defined initial and boundary values. The scheme is constructed based on the weighted finite differences utilizing a Richtmyer-type linearization in place of nonlinear terms appearing in the two-dimensional nonlinear coupled Burgers equation. It should be known that this linearization is used for the first time in this study for a two-dimensional nonlinear coupled partial differential equation. The performance and reliability of the present method are verified using four different widely-used examples, three of which have exact solutions and one has no an exact solution. To make sure that the current scheme exhibits good results, some error norms and convergence rate of the obtained approximate numerical solutions for each example are calculated and a comparison is made with other ones existing in the literature for the same parameter values. It has also been shown that the scheme is unconditionally stable for 0. 5 ≤ θ ≤ 1. [ABSTRACT FROM AUTHOR]