Abstract: Compact scheme with spectral-like resolution has higher accuracy than other schemes on the same grid template, as well as the structure of compact scheme is very simple, so that it has attracted more and more attention. The key problem in the usage of compact scheme is how to smoothly capture discontinuities (such as shocks and contact faces). In order to solve the problems, a third-order Limited Flux Compact (LFC) scheme is constructed. This scheme is similar to non-oscillatory, no free parameter, and dissipative scheme. This scheme is successfully used to simulate shock waves, contact discontinuities in non-viscous flows. This scheme is also used to simulate a two-dimensional viscous flow. Calculation results confirm its high accuracy and high resolutions, good ability in capture shock and no oscillation.

Key words: CFD, numerical method, compact scheme, limited flux, shock capture, high-order computational scheme