UPWIND METHOD FOR SIMULATION OF VISCOUS-FLOW ON ADAPTIVELY REFINED MESHES

A new node-based upwind scheme for the solution of the three-dimensional Navier-Stokes equations on adaptively refined meshes is presented. The method uses a second-order upwind total variation diminishing scheme to integrate the convective terms and discretizes the viscous terms with a new compact central difference technique. Grid adaptation is achieved through directional division of hexahedral cells in response to evolving features as the solution converges. The method is advanced in time with a multistage Runge-Kutta time stepping scheme. Two- and three-dimensional examples establish the accuracy of the inviscid and viscous discretization. These investigations highlight the ability of the method to produce crisp shocks, while accurately and economically resolving viscous layers. The representation of these and other structures is shown to be comparable to that obtained by structured methods. Further three-dimensional examples demonstrate the ability of the adaptive algorithm to effectively locate and resolve multiple scale features in complex three-dimensional flows with many interacting, viscous, and inviscid structures.