An improved entropy-consistent Euler flux in low Mach number

The paper proposes a low-Mach number extension of entropy-consistent Euler flux, called EC-RoeM. The original EC-Roe flux suffers from accuracy deterioration in low Mach number. To overcome this defect, an enhancement is to rescale the left-moving and right-moving acoustic waves into the scaling of convective velocity through the Mach number function. This scaling function is restrained by a shock indicator and free from the cut-off reference Mach number. The resulting scheme is easily implemented and computational expense is negligible. In addition, it avoids global cut-off problem and preserves time consistency unlike preconditioning techniques. EC-RoeM improves low-speed accuracy and possesses numerical dissipation independent of Mach number. A series of inviscid and viscous flows demonstrate its attraction across wide-ranging applications.