A 2ND-ORDER UPWIND LEAST-SQUARES SCHEME FOR INCOMPRESSIBLE FLOWS ON UNSTRUCTURED HYBRID GRIDS

A finite-volume method for the solution of a scalar transport equation in a 2D incompressible fluid flow is presented. The 2D transport equa tion is solved in a computational domain divided into polygon triangle s and quadrilaterals allowing the general use of hybrid structured/uns tructured grids, Convection discretization is performed with a new sec ond-order-accurate upwind least-squares scheme (ULSS), and the system of algebraic equations is solved either by the biconjugate gradient st abilized method (BI-CGSTAB) or by the generalized minimal residual met hod (GMRES). The program language C++ was selected in order to manipul ate the mesh data structure easily. Numerical solutions obtained using several different existing convection discretization schemes are comp ared with analytical solutions of several 2D test cases. The evolution of the error norm slope, as a function of the mesh parameters, confir ms that the ULSS scheme is second-order accurate to solve 2D scalar tr ansport equations in hybrid structured/unstructured grids.