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An efficient topology optimization method applicable to both continuum andrarefied gas flows is proposed in the framework of gas-kinetic theory. Theareas of gas and solid are marked by the material density, based on which afictitious porosity model is used to reflect the effect of the solid on the gasand mimic the diffuse boundary condition on the gas-solid interface. Theformula of this fictitious porosity model is modified to make the model workwell in all flow regimes, i.e., from the continuum to free-molecular flowregimes. To find the optimized material density, a gradient-based optimizer isadopted and the design sensitivity is obtained by the continuous adjointmethod. To solve the primal kinetic equation and the corresponding adjointequation, the numerical schemes efficient and accurate in all flow regimes areconstructed. Several airfoil optimization problems are solved to demonstratethe good performance and high efficiency of the present topology optimizationmethod, covering the flow conditions from continuum to rarefied, and fromsubsonic to supersonic.

An efficient topology optimization method for steady gas flows in all flow regimes