UBC Theses and Dissertations
Mesh adaptation for wakes via surface insertion Malik, Shahzaib
In this thesis, we present a new procedure for mesh adaptation for wakes. The approach starts by tracking the wake centerline with an initial isotropic unstructured mesh. A vertex-centered finite volume method is used, and the velocity field is obtained from solution reconstruction. The velocity data is integrated numerically using an adaptive fourth-order Runge-Kutta method. We insert the wake centerline into the existing unstructured mesh as an internal boundary and use a metric-based anisotropic mesh adaptation to generate anisotropic cells in regions with large second derivatives of flow variables. In the second step, the problem is solved on adapted mesh and a new wake centerline is tracked. We then move the previous wake centerline (which is now a part of adapted mesh) to match the centerline obtained from the adapted mesh. To move the wake centerline, a solid mechanics analogy is used and the linear elasticity equation is solved on the adapted mesh. As a result, the displacement is propagated throughout the mesh and the already adapted regions along the wake centerline are preserved. The process is then followed for subsequent cycles of anisotropic mesh adaptation to obtain a more accurate approximation of the wake centerline. As an alternate strategy for obtaining an anisotropic mesh in the wake, we take the first geometry, together with the captured wake centerline from an unstructured triangular mesh, as an initial geometry to produce a quad dominant mesh, using an advancing layer method. The correctness of the streamline tracking algorithm is verified using an analytical velocity field. The mesh morphing approach is tested using the method of manufactured solutions, demonstrating that the linear finite element solution is second-order accurate. The results of laminar flow test cases for the attached and separated flow are presented and compared with some well-established numerical results in the literature. Our results show that the advancing layer mesh is more efficient in resolving the wake. In the end, one case for turbulent subsonic flow is considered. For turbulent flow, a cell-centered finite volume method is used and we only track the wake centerline at different angles of attack.
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