Adjoint based optimal control of dissipation in kinetic schemes

To resolve many flow features accurately, like accurate capture of suction peak in case of subsonic flows or crisp shocks in flows with discontinuities or to minimise the loss in stagnation pressure or even flow separation in viscous flows requires an accurate and low dissipative numerical scheme. It has been found that the first order Kinetic Flux Vector Split (KFVS) scheme is more dissipative. However, numerical dissipation can be reduced either by $h$-refinement or $p$-refinement or a combination of both, which requires more computational time and memory. In this paper we present a low dissipative modified KFVS (m-KFVS) method with molecular velocity dependent dissipation control function by still using the first order stencil. However, the dissipation generated by m-KFVS may not be minimal and hence the dissipation control vector is in general not optimal. The m-KFVS solver is then combined with discrete adjoint solver to find the optimal dissipation control vector, which results in minimal numerical dissipation. Numerical results are presented for standard inviscid test cases based on m-KFVS and m-KFVS-adjoint methods