Quadratic-Reconstruction Finite Volume Scheme for Compressible Flows on Unstructured Adaptive Grids

A second-order ® nite volume cell-centered technique for computing steady-state solutions of the full Euler and Navier± Stokes equations on unstructured meshes is presented. The scheme is designed such that its accuracy is very weakly sensitive to grid distortions. An original quadratic reconstruction with a ® xed stencil and a high- orderux integration by the Gauss quadrature rule is employed to compute the advective term of the equations. Time evolution is presently performed with an explicit multistep Runge± Kutta scheme. A very general adaptation procedure based on h-re® nement and coarsening is developed to improve the resolution of complexow features. The accuracy of the method is demonstrated for a linear equation and for inviscid and viscousow computations withrespecttoconstantandlinearreconstructionschemes.TheinviscidowovertheNACA0012airfoiliscomputed atvariousMachnumbers.Thesecalculationsillustratetheeffectivenessoftheadaptationprocedure.Weinvestigate the supersonicow over a compression ramp to validate the Navier± Stokes solver by using a hybrid grid.

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