A Very Efficient Class of HOC Schemes for the One-Dimensional Euler Equations of Gas Dynamics

Abstract

This manuscript introduces a class of higher order compact schemes for the solution of one dimensional (1-D) Euler equations of gas dynamics. These schemes are fourth order accurate in space and second or lower order accurate in time, depending on a weighted average parameter μ. The robustness and efficiency of our proposed schemes have been validated by applying them to three different shock-tube problems of gas dynamics, including the famous SOD shock-tube problem. Later on, the 1-D convergent-divergent nozzle problem (De laval nozzle problem) is also considered and numerical simulations are performed. In all the cases, our computed numerical solutions are found to be in excellent match with the exact solutions or available results in the existing literature. Overall the schemes are found to be efficient and accurate.