Roles of Multi-Dimensional Velocity Components in All-Speed Numerical Flux SLAU

View Video Presentation: https://doi.org/10.2514/6.2022-4033.vid

In the computational fluid dynamics of compressible fluid flow, all-speed numerical flux functions have been employed to treat from low-speed flow (M ~ 0.01) to hypersonic flow (M > 3) stably. As one of the all-speed schemes, the SLAU scheme, which is formulated with multi-dimensional velocity components (normal and parallel to a cell interface), is widely employed. On the other hand, as a variant of SLAU, the mSLAU scheme, which adopts only a velocity component normal to a cell interface instead of multi-dimensional velocity components, is used for rotorcraft calculations. However, employing only a cell interface normal velocity component is controversial. Although it is considered that multi-dimensional velocity components make SLAU robust, the stability effects of the components have not been investigated in detail. Therefore, we delved into the stability effects by solving some benchmark problems employing SLAU or mSLAU. Consequently, we revealed that in certain cases, mSLAU caused slow convergence and numerical instability depending on the grid quality.