Robust explicit formulation of weighted compact nonlinear scheme

This study presents a new weighted compact nonlinear scheme (WCNS). In the WCNS procedure, the linear difference scheme is modified to use the flux on the computational nodes together with that on the midpoints. This modification makes the scheme more robust, but at the same time, more dissipative. We conduct the truncation error analysis and discuss the reasons why this modification makes the scheme robust and dissipative. The standard shock problems are solved with both original and modified WCNS, and the results show that the discontinuity thickness of the modified WCNS increases, and over/undershoots at the discontinuities are suppressed better in WCNS. In addition, the stiff shock tube problems, which cannot be solved by the original WCNS because of negative pressure, can be solved using the modified WCNS without a blow-up of computation. A series of numerical tests show the robustness of the modified WCNS.