Development of Roe-type scheme for all-speed flows based on preconditioning method

The problems of mixed low-speed/high-speed flows are not solved properly with existing compressible method. Based on preconditioning technology, a new scheme, All-Speed-Roe scheme, is proposed. Compared with Roe scheme, it decreases the effect of acoustic speed in its numerical dissipation when Mach numbers decrease. Compared with traditional preconditioned Roe scheme, it overcomes the limit of being cut-off by the global Mach number through modifying the eigenvalues only and has the good convergence acceleration rate for low-Mach-number flows through multiplying the spatial residual by the preconditioner. From another perspective, All-Speed-Roe scheme suggests that there is no necessity to replace the physical acoustic speed in denominator with pseudo-acoustic speed. In theory, All-Speed-Roe scheme is suitable for all speed flow calculations with capturing shock and simulating low-Mach-number flows. The numerical results of Euler nozzle flow, RANS of NASA rotor 37 flow, Euler simulation, Large Eddy Simulation (LES) and Detached Eddy Simulation (DES) of high-loaded blade T106 flow show that All-Speed-Roe scheme can replace traditional preconditioned Roe scheme because it is easier for programming, more robust in computations, more accurate in spatial, and has good convergence rate.