An efficient numerical scheme for Burgers' equation

摘要

This paper applies the multiquadric (MQ) as a spatial approximation scheme for solving the nonlinear Burgers' equation. For comparison purposes, a low order explicit finite difference approximation of the time derivative is employed. By decreasing the time step of the computation, it is shown that the major numerical error is from the time integration instead of the MQ spatial approximation. The numerical results indicate that this MQ offers an excellent approximation for all possible values of Reynolds number. An adaptive algorithm is also developed to adjust the MQ interpolation points to the peak of the shock wave which is shown to provide an improved numerical result. Numerical comparisons are made with most of the existing numerical schemes for solving the Burgers' equation.