A viscous all-speed solver development based on Roe upwind scheme in unstructured database

In this paper, a viscous all-speed flow solver has been developed based on Roe upwind scheme in unstructured database. In the presented method, stiffness of the compressible governing equations in low-speed region reduces using the preconditioning form. In calculating the artificial viscosity of a Roe upwind scheme, multiple matrices multiplication are needed. Frink reduced these costly operations by simplification of the matrices multiplication to some flux components which are related to distinct eigenvalues. In this research similar to Frink work, the equations of artificial viscosity in preconditioning Roe upwind scheme obtained and presented in the flux components form. This is a generalized form that can be easily switched to the preconditioned or non-preconditioned form. This is useful in converting any original Roe upwind scheme to the preconditioning form and also has application in adjoint optimization method. Results of the computer code were compared with experimental data of single and two-element airfoils in both preconditioning and non-preconditioning form. The results show that the non-preconditioning compressible solver hardly converged in low-speed regions while the preconditioned form converged more rapidly.