Third-order modified coefficient scheme based on essentially non-oscillatory scheme

A third-order numerical scheme is presented to give approximate solutions to multi-dimensional hyperbolic conservation laws only using modified coefficients of an essentially non-oscillatory (MCENO) scheme without increasing the base points during construction of the scheme. The construction process shows that the modified coefficient approach preserves favourable properties inherent in the original essentially non-oscillatory (ENO) scheme for its essential non-oscillation, total variation bounded (TVB), etc. The new scheme improves accuracy by one order compared to the original one. The proposed MCENO scheme is applied to simulate two-dimensional Rayleigh-Taylor (RT) instability with densities 1:3 and 1:100, and solve the Lax shock-wave tube numerically. The ratio of CPU time used to implement MCENO, the third-order ENO and fifth-order weighed ENO (WENO) schemes is 0.62:1:2.19. This indicates that MCENO improves accuracy in smooth regions and has higher accuracy and better efficiency compared to the original ENO scheme.