Analytical and Numerical Approaches to Solving Riemann Problems in Fluid Dynamics

Abstract

The Riemann problem represents an essential problem in fluid dynamics which enables researchers to model shock waves together with both rarefactions and contact discontinuities. The research investigates analytical and numerical methodologies to solve fluid-dynamic Riemann problems and details their functional aspects as well as restrictions. Analytical solutions from the method of characteristics along with exact Riemann solvers form the basis for the research while numerical solutions come from finite volume schemes and Roe's and HLLC Riemann solvers. Numerical methods show both high precision and efficiency in their ability to generate accurate simulations of shock waves and rarefaction structures according to computational results.