Abstract: We study the sonic point glitch of the Burgers' equation, which is formed in a sonic rarefaction fan. The reason of a sonic point glitch and the relation between the sonic point glitch and the entropy condition are discussed. According to these relations, several well-known schemes are classified into two and analyzed. In fact, the sonic point glitch appears only in the case of a transonic rarefaction wave. If the problem to be solved does not include transonic rarefaction waves, the difficulty in computation vanishes. Based on this idea, a new two-step splitting method eliminating the sonic point glitch is proposed. Numerical tests of applying the method to different schemes show that it is good in eliminating the sonic point glitch.

Key words: upwind scheme, Godunov scheme, compressible flow, sonic point glitch, Riemann solver