TESTING OF THE HYBRID LARGE-PARTICLE METHOD USING TWO-DIMENSIONAL RIEMANN PROBLEMS

Abstract

The possibilities of the hybrid large-particle method using known and new Riemann problems in two-dimensional domains studied. The method includes a predictor step and a corrector step. Monotonicity is provided in two ways. Nonlinear scalar artificial viscosity with a limiter, as well as nonlinear hybrid correction of convective fluxes, is used. The numerical algorithm has a second-order approximation in space and time on smooth solutions. The method was tested using two-dimensional Riemann problems and compared with modern high-resolution schemes, such as WENO5 (Weighted Essentially Non-Oscillatory Scheme), Conservative limiting method for high-order compact schemes, and others. Centrally symmetric problems with a complex shock-wave structure and the development of instability at the contact boundary are studied in detail. Test calculations demonstrated high resolution, low dissipation, and stability of the method.

Keywords

• hybrid large-particle method
• two-dimensional riemann problems
• high resolution