Abstract: By coupling the total energy convective upwind and split pressure (E-CUSP) scheme with the WENO-η scheme, we gave a new scheme (E-CUSP-WENO-η） to solve the one-dimensional shock tube problem. The numerical simulation results show that the new scheme is more accurate in capturing contact discontinuities and shock waves, among which the new scheme (E-CUSP-WENO-η(τ^opt₇)) with higher order optimal global smoothness factor has the least numerical dissipation. The coupled new scheme can capture shock wave more steeply, and the calculation results are accurate and stable.

Key words: Euler equation, computational fluid dynamics, total energy convective upwind and split pressure schemes, weighted essentially non-oscillatory schemes, smoothness factor