A method of mesh adaptation is proposed for gradient-based aerodynamic shape optimization. The method consists in coupling an equation for the mesh node coordinates with the discretized Euler equations of gas dynamics in steady state. The variational mesh equation is inspired by Winslow's variable diffusion mapping. The system of mesh and flow equations is solved, instead of the flow equations alone, when performing shape optimization. The solution algorithm of the coupled equations is an approximate Newton method supplemented with an interpolation of the variable diffusivity by radial basis functions.
Tests are carried out for supersonic flow over a wedge, a problem that is used here as a benchmark for the mesh adaptation and for a simple problem of inverse design. At a given design, the method of adaptation improves the accuracy of the calculated drag, a functional that is used in the construction of the inverse problem. The accuracy of the shape, obtained by inverse design, experiences similar improvements due to the mesh adaptation scheme.
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