Application of a solution to the Riemann problem in the SPH method

In the proposed version of the SPH (Smoothed Particle Hydrodynamics) method, it is assumed that solution of the Riemann problem can be used to calculate the interaction between particles in an SPH medium. This approach can be used to develop a code without introducing an artificial viscosity and ensure that the resulting solution is highly accurate and monotone in the neighborhood of a contact boundary between different media.