Coupling mesh and flow in viscous fluid calculations on unstructured triangular finite elements

Several ingredients for mesh adaption by deformation are discussed in the case of a laminar Navier-Stokes flow and applied to the capture of boundary layers and shocks, The mesh system involves an attraction-repulsion model introduced in(13), in which attraction is devoted to adaption and repulsion to mesh quality (avoiding overlapping). The mesh adaption is first considered in a static mode: a given mesh and the corresponding flow are taken into account as a background in which flow values used for adaption are interpolated; this provides a new adapted mesh. Then global iteration of several static adaptions can be performed by recomputing the flow, The efficiency is first discussed with a 1-D example, Then a parametrical study of the adaption strategy is performed for 2-D examples, such as the calculation of the supersonic flow past a ramp and the flow around a NACA airfoil.