Conjugate filter approach for solving Burgers’ equation

We propose a novel scheme for solving Burgers’ equation with all possible values of Reynolds numbers. A low-pass filter is introduced to intelligently eliminate the high frequency errors produced by its conjugate high-pass filters. All conjugate filters are derived from one generating function and have essentially the same degree of regularity, smoothness, time-frequency localization, effective support and bandwidth. Computational accuracy is tested by using both a linear hyperbolic equation and Burgers’ equation at a moderately high Reynolds number for which analytical solution is available. The ability of shock-capturing is validated by using discontinuous initial values. Excellent numerical results indicate that the proposed scheme is efficient, robust and reliable for solving Burgers’ equation and for shock capturing.