On the practical accuracy of shock-capturing schemes

A method for estimating the accuracy of transmission by the shock-capturing difference scheme of the Rankine-Hugoniot conditions through the shock wave front is proposed. This method includes calculation of the order of integral convergence of the difference solution (instead of using its absolute value as in the L1 norm) on the intervals crossing the shock. In such integration, an error arising before the shock-wave front due to its smearing can be compensated by the similar error of the opposite sign after the wave front. Adduced examples show that this approach allows to obtain the second order of integral convergence on the intervals crossing the shock for some of the classical high-order difference schemes. © 2014, Pleiades Publishing, Ltd.