Elastic Mesh Deformation for Internal Flows with Moving Boundaries - Mohammed, Ali Alaa Abdelkareem Awad (Department of Mechanical Engineering, 2024)
This project aims to study elastic-based mesh deformation for internal flow problems with obstructions. As such a tank with a flexible internal beam serves as the tested case employed in this work. As such a computer code was developed and the elastic deformation was implemented via the Finite Element Galerkin method with two methods to control the element's distortion near the moving boundaries, Jacobian-based stiffening modification and the distance criterion method. Verification of the scheme was performed by conducting the same test as described in a journal and comparing the obtained results. The project focused on mesh deformation resulting from prescribing the displacements to the inner boundaries of the beam. The results were validated by assessing mesh quality using aspect ratio as a metric, for the 2D unstructured triangular mesh, the element mesh quality showed improvement when the Jacobian-based stiffening method was applied, which involved excluding the determinant of the Jacobian from the stiffness matrix formulation. Similarly, for the 3D unstructured mesh, the aspect ratio improved from elements collapsing to a value close to 1. In both cases, optimal mesh quality was achieved using the distance criterion method for 2D and 3D structured meshes. Specifically, for the 2D structured mesh, the aspect ratio demonstrated improvement, while for the 3D structured mesh, a further enhancement was also observed.