... suggest that this can be traced back to inadequate numerical treatment of the inviscid fluxes. The purpose of this study is an extension to the well-known Harten, Lax, van Leer, Einfeldt (HLLE) Riemann solver to overcome this issue. Design/methodology/approach It explicitly takes into account...

... variables across the interface between cells is required, and this average is chosen to be the arithmetic mean for computational efficiency, leading to arithmetic averaging. This is in contrast to usual ‘square root’averages found in this type of Riemann solver where the computational expense can...