On the integral convergence of numerical schemes calculating gas-dynamic shock waves

A comparative experimental accuracy study of shock-capturing schemes such as RBM(Rusanov–Burstein–Mirin), CWA(Compact high order Weak Approximation) and A-WENO(Alternative Weighted Essentially Non-Oscillatory) schemes is carried out by numerically solving a Cauchy problem with smooth periodic initial data for the Euler equations of gas dynamics. It is shown that in the presence of shock waves, RBM and CWA schemes(in the construction of which nonlinear flux correction is not used) have a higher order of integral convergence, which provides significantly higher accuracy to these schemes (compared to A-WENO scheme) in the areas of shock waves influence, despite noticeable non-physical oscillations at their fronts. This makes it possible to use RBM and CWA schemes as basic ones when constructing combined schemes that monotonically localize shock wave fronts and at the same time maintain higher order accuracy in their influence areas.