Adjoint Based Aerodynamic Shape Optimisation Using Kinetic Meshfree Method

Abstract

The gradient based optimisation algorithms combined with the finite volume or element based adjoint approaches have been very successful in aerodynamic shape optimization (ASO). The meshfree least squares kinetic upwind method (LSKUM), which works on a cloud of points and its connectivity, has the advantage in terms of flexibility of generating a cloud of points and having an arbitrary number of points in the connectivity. The LSKUM based meshfree solvers have been successfully applied to problems involving multi-body configurations and moving boundaries. In the present work, the LSKUM based primal and discrete adjoint meshfree solvers for steady Euler flows have been used to perform aerodynamic shape optimisation. It is well-known that the raw shape sensitivities of a defined objective function are highly oscillatory. In this research, we have used the Sobolev gradient smoothing. An approach is developed to find a suitable choice for the smoothing parameter in the Sobolev gradient algorithm. Numerical results are presented for the shape optimisation of the NACA0012 airfoil at transonic and supersonic flows with aerodynamic and geometric constraints. The performance of the discrete adjoint LSKUM solver in accurate computation of shape sensitivities is demonstrated. The advantages of using LSKUM in aerodynamic shape optimisation have been shown.