WITHDRAWN: On the Effect of Implicit Addition Of Flux Hessian On High Speed Flow Simulations

This paper investigates a modified Roe Flux Difference Splitting (FDS) method that implicitly incorporates the flux Hessian into face–flux calculations by blending separate left–right flux states with a single flux constructed from arithmetic-averaged primitive variables, thereby introducing a Hessian-based dissipation term that influences stability and shock resolution. The approach generalizes naturally to other flux types such as Rusanov and HLL. Numerical tests using the supersonic inviscid Woodward–Colella step and an inviscid circular-cylinder configuration demonstrate the advantages of the proposed formulation: standard Roe FDS exhibits large errors at very high Mach numbers, including divergence and carbuncle-type distortions, whereas the modified flux yields improved shock capture and greater robustness. At moderate Mach numbers, both methods produce comparable results. Additional expansion- corner simulations further benchmark the two approaches. The scheme has been implemented experimentally in NASA’s FUN3D solver, although it remains a non-released research feature not yet available to users.