Steady viscous flow in a triangular cavity by efficient numerical techniques

Abstract Accurate and efficient calculations of the flow inside a triangular cavity are presented for high Reynolds numbers. The Navier-Stokes equations, expressed in a stream function and vorticity formulation, are solved numerically using finite differences on a transformed geometry. Second-order numerical boundary conditions are derived and Newton's iteration is employed to solve the nonlinear system resulting from the finite difference discretization. Aside from solving the equilateral triangular cavity problem, we have also been able to compute numerical solutions for scalene triangular cavity problems. Our coarse-mesh results for the equilateral triangular cavity problem are compared with finer mesh results in the literature and the agreement is good.