Comparison of a modified large-particle method with some high resolution schemes. Two-Dimensional test problems

A number of computational properties of the previously proposed new modification of a large-particle method are studied on the basis of a nonlinear correction of artificial viscosity at the first (Eulerian) stage and a hybridization of fluxes at the second (Lagrangian and final) stage supplemented by a two-step Runge-Kutta algorithm in time. The method has a second order of approximation in space and time on smooth solutions. The computational efficiency of the method is shown compared to several modern high resolution schemes using the forward facing step problem and the double Mach reflection problem.