Study on the Flow Fields of Irregular-Shaped Domains by an Algebraic Grid-Generation Technique

Abstract

A finite-difference solution algorithm is developed to solve the Navier-Stokes equations in a nonorthogonal curvilinear coordinate system. The governing equations are written in the strong-conservative-law form. A rectangular computational domain is yielded by Moretti's transformation. The tasks of numerically generating the body-fitted coordinate by partial differential equations are avoided. Hence the matrix of the transformation can be determined by direct analytic differentiation. The discretized conservation equations are derived on a control volume basis and solved by the extended SIMPLE calculation procedure. Numerical results obtained by employing the present methodology will be compared with results from analytical solutions. The relative merits of three numerical representations, i.e., power-law, hybrid, and first-order upwind, for approximating the convection terms in the momentum equations are compared. The results show that the numerical results exhibited excellent agreement with the available analytical solution.