  An efficient topology optimization method applicable to both continuum and
rarefied gas flows is proposed in the framework of gas-kinetic theory. The
areas of gas and solid are marked by the material density, based on which a
fictitious porosity model is used to reflect the effect of the solid on the gas
and mimic the diffuse boundary condition on the gas-solid interface. The
formula of this fictitious porosity model is modified to make the model work
well in all flow regimes, i.e., from the continuum to free-molecular flow
regimes. To find the optimized material density, a gradient-based optimizer is
adopted and the design sensitivity is obtained by the continuous adjoint
method. To solve the primal kinetic equation and the corresponding adjoint
equation, the numerical schemes efficient and accurate in all flow regimes are
constructed. Several airfoil optimization problems are solved to demonstrate
the good performance and high efficiency of the present topology optimization
method, covering the flow conditions from continuum to rarefied, and from
subsonic to supersonic.
