A low diffusion flux splitting method for inviscid compressible flows

• A low diffusion flux splitting method for compressible Euler equations is proposed.
• The new scheme can capture crisp shock profile and exact stationary contact discontinuity.
• Numerical dissipation analysis is carried out.
• Test cases show that the new scheme is free from carbuncle phenomenon.

A low diffusion flux splitting method capable of capturing crisp shock profile and exact contact surface is presented. Here, the flux vector of the Euler equations is split into convective and pressure parts following Toro–Vázquez formulation. The low diffusive property of the present scheme is brought about by adding an anti-diffusion term to the pressure parts. This numerical method can be regarded as an improved version of Toro and Vázquez’s flux splitting schemes (i.e. TV and TV-AWS) which are found to produce shock instabilities and carbuncle phenomena. Numerical results for several carefully chosen one- and two-dimensional test problems are investigated to demonstrate the accuracy and robustness of the proposed scheme.