A modified AUSM⁺-up scheme for simulation of flow around rotary blades

A modified advection upstream splitting method (AUSM⁺-up) scheme is proposed to simulate the quasi-steady flow over rotary blades. Based on the chimera grid methodology, the cell centered finite-volume method (FVM) is used to solve the Reynolds-Averaged Navier-Stokes (RANS) equations described in the blade-attached rotational coordinate system with Spalart-Allmaras (S-A) and k-ω shear-stress-transport (SST) models for turbulence closure. In order to improve the computational efficiency, a full approximation storage (FAS) multi-grid technique combine with a Newton-like implicit lower-upper symmetric-Gauss-Seidel (LU-SGS) scheme with viscous correction is utilized for time stepping. By adding the grid velocity into the cut-off Mach number Mco, a new AUSM⁺-up scheme, named AUSM⁺-up(R) scheme is developed and applied to a variety of different geometries, including helicopter rotors, horizontal axis wind turbine blades and low Reynolds number propellers. It is concluded that the new proposed scheme, AUSM⁺-up(R) scheme, leads to higher resolution and more accurate solution, meanwhile the computational efficiency is almost equivalent to the commonly used Jameson's central scheme.