Fast dynamic grid deformation based on Delaunay graph mapping

A simple and efficient dynamic grid deformation technique is proposed for computing unsteady flow problems with geometrical deformation, relative body movement or shape changes due to aerodynamic optimisation and fluid–structure interaction. A Delaunay graph of the solution domain is first generated, which can be moved easily during the geometric dynamic deformation, even for very large distortion. A one to one mapping between the Delaunay graph and the computational grid is maintained during the movement. Therefore the new computational grid after the dynamic movement can be generated efficiently through the mapping while maintaining the primary qualities of the grid. While most dynamic grid deformation techniques are iterative based on the spring analogy, the present method is non-iterative and much more efficient. On the other hand, in comparison with dynamic grid techniques based on transfinite interpolation for structured grids, it offers both geometric and cell topology flexibility, which is crucial for many unsteady flow problems involving geometric deformation and relative motions. The method is demonstrated through some typical unsteady flow test cases, including a pitching aerofoil in a fixed domain boundary, relative movement between multi-element aerofoils due to flap deployment for high lift, a deformable sphere in a fixed cube, and a three-dimensional flexible wing with large deformation.