Deformation of CFD Meshes with Anisotropic Cells in a Viscous Boundary Layer Using Line-Implicit Methods

Various numerical applications in the context of multidisciplinary high-fidelity aircraft design, e.g. fluid-structure interaction or shape optimization, require the consideration of changes in the geometry of the aircraft shape. Such geometry changes can be realized using mesh deformations, and we demonstrate such a volume mesh deformation method based on elasticity analogy in conjunction with line-implicit solvers. Line-implicit solvers have already been successfully used in CFD simulations with strongly anisotropic cells in a viscous boundary layer, and are now applied to mesh deformation problems of such meshes. In this approach, the solution of a block-tridiagonal subsystem of the Jacobian matrix is computed exactly using the Thomas algorithm. Here, the selection of the tridiagonal part – representing the lines – is of crucial importance for the speed of convergence. A new algorithm for line identification is presented and compared with existing ones. Also, a comparison and combination of these methods with multigrid methods is performed and the implications for industrially relevant test cases are demonstrated.