Modified SLAU2 scheme with enhanced shock stability

• Modifications are proposed to SLAU2 scheme to remove post shock oscillations.
• Canonical test cases are used to demonstrate the efficacy of this modification.
• These modifications have no detrimental effect on convergence.

Two alternate modifications are proposed to the dissipation term in the mass flux computation of the low dissipation AUSM scheme (SLAU2) developed recently by Kitamura and Shima [1,2]. These modifications are required to remove the odd–even type instability that results in lateral oscillations behind oblique shocks predicted by MUSCL based higher order versions of SLAU2. The first modification involves switching between the original term in SLAU2 and one similar to corresponding term in AUSM+-up. The second modification involves use of density gradient aligned velocity instead of total velocity in SLAU2 (or face normal velocity as in AUSM+-up) in calculation of Mach number that is required for computing this term. It is observed that the second alternative not only delivers better results but also has a more easily differentiable numerical flux that enables easier implicit computations while not altering the simplicity of original SLAU2. The method also renders SLAU2 with a good balance between shock stability and contact capturing ability.