A 2nd order finite-volume unstructured hybrid mesh algorithm for 2D Heat Transfer and incompressible fluid flows

A Finite-Volume method for the numerical integration of the Navier-Stokes equations for 2D incompressible fluid flow is presented in a computational domain divided into polygon triangles and quadrilaterals that can be arbitrary mixed. Convection discretization was performed with a new second order accurate Upwind Least Squares Scheme (ULSS) in the framework of primitive variables where a projection method is used to calculate the pressure field and the system of algebraic equations is solved by the biconjugate gradient stabilized method (BI-CGSTAB) Numerical solutions are compared with analytical solutions of a 2D test case and for the driven cavity flow at Re=100. The evolution of the error norm slope as a function of the mesh parameters, confirm that the ULS Scheme is second order accurate to solve 2D incompressible fluid flow problems.