An immersed boundary technique using semi-structured grids for computing compressible viscous flows

Abstract

Summary This paper provides a numerical method based on the immersed boundary ap-proach for computing compressible viscous flows. The efficency of the methodis enhanced by using a flexible local grid refinement technique which is obtainedby coarsening a uniformly fine mesh far from high-gradient flow regions, such asboundarylayers and shocks. Introduction TheImmersedBoundary(IB)methodsimplifiesthegridgenerationprocessforthe simulationof flows with complex and/or moving solid boundaries by avoidingthe need for a body-fitted mesh. The IB technique was originally developed forincompressible flows [1]-[3] using Cartesian grids. Recently, some of the authorshave extended the IB techniquetocompressibleflows [4] usingthepreconditionedNavier–Stokes equations, which allow one to provide accurate and efficient solu-tionsfor a widerangeof theMach number. To date, IB methodsemploystructuredgrids, which allow only limited control on the distributionof the grid pointsin thecomputational domain; in fact, clustering of grid points is needed close to solidboundaries in order to describe its geometry accurately and, since mesh lines runthroughthe entirecomputationaldomain, a highconcentrationofgridpointsisob-tained also in regions away from the solid walls, where flow gradients are usuallysmall. Inordertocopewiththisproblem,aflexiblelocalgridrefinementtechniqueis tobe employed,increasingthe mesh resolutionnear the body.