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An adaptive higher-order unstructured finite volume solver for turbulent compressible flows Jalali, Alireza


The design of aircraft depends increasingly on the use of Computational Fluid Dynamics (CFD) in which numerical methods are employed to obtain approximate solutions for fluid flows. One route to improve the numerical accuracy of CFD simulations is higher-order discretization methods. Moreover, finite volume discretizations are the method of choice in commercial CFD solvers and also in computational aerodynamics because of intrinsic conservative and shock-capturing properties. Considering that nearly all practical flows with aerodynamic applications are classified as turbulent, we develop a higher-order finite volume solver for the Reynolds Averaged Navier-Stokes (RANS) solution of turbulent compressible flows on unstructured meshes. Higher-order flow solvers must account for boundary curvature. Since turbulent flow simulations require anisotropic cells in shear layers, we use an elasticity analogy to project the boundary curvature into the interior faces and prevent faces from intersecting near curved boundaries. Furthermore, we improve the accuracy of solution reconstruction and output quantities on highly anisotropic cells with curvature using a local curvilinear coordinate system. A robust turbulence model for higher-order discretizations is fully coupled to the system of RANS equations and an efficient solution strategy is adopted for the convergence to the steady-state solution. We present our higher-order results for simple and complicated configurations in two dimensions. These results are verified by comparison against well-established numerical and experimental values in the literature. Our results show the advantages of higher-order methods in obtaining a more accurate solution with fewer degrees of freedom and also fast and efficient convergence to the steady-state solutions. Moreover, we propose an hp-adaptation algorithm for the unstructured finite volume solver based on residual-based and adjoint-based error indicators. In this approach, we enhance the local accuracy of the discretization via h-refinement or p-enrichment based on the smoothness of the solution. Mesh refinement is carried out by local cell division and introducing non-conforming interfaces in the mesh while order enrichment is obtained by local increase of the polynomial order in the reconstruction process. Our results show that this strategy leads to accuracy and efficiency improvements for several types of compressible flow problems.

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