On the dissipation mechanism of Godunov-type schemes

Dissipation mechanisms of Godunov-type schemes are presented in the framework of unified representation. The causes of inaccuracy at the contact discontinuity and the dissipation mechanism in the numerical mass flux of the HLLEM scheme are examined first. A “vacuum preserving property” is defined and the prominent role of the numerical signal speed involved with the rarefaction waves in the expanding region is analyzed. Through a linear perturbation analysis on the odd–even decoupling problem, necessary conditions for designing a shock stable scheme are discussed. As a result, an improved HLLE(HLLE+) scheme is proposed and its dissipation mechanism is analyzed. The diffusivity of the Godunov-type schemes is examined by two-dimensional hypersonic viscous flow.