Wave-appropriate reconstruction of compressible flows: physics-constrained acoustic dissipation and rank-1 entropy wave correction

Abstract

The wave-appropriate reconstruction approach decomposes the reconstruction procedure into characteristic wave families, centralizing non-acoustic waves to minimize dissipation while retaining an upwind bias for acoustic waves. In previous implementations, the acoustic upwind parameter $\eta_a$ was fixed at its maximum value of $1.0$; however, this choice is conservative and motivated a systematic search for the minimum value that is robust across flow regimes. To this end, the CFD solver is treated as a black box within a bounded scalar minimization, which minimizes an accuracy objective for the subsonic inviscid TGV subject to a stability constraint enforced by the supersonic viscous TGV. Because the wave-appropriate framework leaves $\eta_a$ as the sole degree of freedom, the optimization converges in approximately 25 evaluations. The resulting optimal values generalize without retuning across a wide range from subsonic turbulence to hypersonic flows with shocks and contact discontinuities. The second contribution focuses on eliminating the need for an explicit contact-discontinuity detector, which is commonly required in flows involving both shock waves and contact discontinuities. In such cases, the reconstruction deficiency appears solely within the entropy characteristic wave and can be corrected by a rank-1 update along the entropy right eigenvector. The proposed algorithm relies only on the Ducros sensor and is limiter-agnostic, facilitating direct use in other schemes, such as WENO. This approach reduces wall time by $29$--$41\%$ compared to full characteristic decomposition. To further demonstrate the method's generality, introducing a controlled acoustic bias exclusively to the normal momentum in a KEP scheme eliminates spurious vortices in periodic shear layers, confirming that the acoustic stability mechanism operates independently of the discretization framework.