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High-order gas-kinetic scheme (HGKS) has been well-developed in the pastyears. Abundant numerical tests including hypersonic flow, turbulence, andaeroacoustic problems, have been used to validate its accuracy, efficiency, androbustness. However, there are still rooms for its further improvement.Firstly, the reconstruction in the previous scheme mainly achieves athird-order accuracy for the initial non-equilibrium states. At the same time,the equilibrium state in space and time in HGKS has to be reconstructedseparately. Secondly, it is complicated to get reconstructed data at Gaussianpoints from the WENO-type method in high dimensions. For HGKS, besides thepoint-wise values at the Gaussian points it also requires the slopes in bothnormal and tangential directions of a cell interface. Thirdly, there existsvisible spurious overshoot/undershoot at weak discontinuities from the previousHGKS with the standard WENO reconstruction. In order to overcome thesedifficulties, in this paper we use an improved reconstruction for HGKS. TheWENO with adaptive order (WENO-AO) method is implemented for reconstruction.Awhole polynomial inside each cell is provided in WENO-AO reconstruction. TheHGKS becomes simpler than the previous one with the direct implementation ofcell interface values and their slopes from WENO-AO. The additionalreconstruction of equilibrium state at the beginning of each time step can beavoided as well by dynamically merging the reconstructed non-equilibriumslopes. The new HGKS essentially releases or totally removes the above existingproblems in previous HGKS. The accuracy of the scheme from 1D to 3D from thenew HGKS can recover the theoretical order of accuracy of the WENOreconstruction.In the two- and three-dimensional simulations, the new HGKSshows better robustness and efficiency than the previous scheme in all testcases.

Performance Enhancement for High-order Gas-kinetic Scheme Based on WENO-adaptive-order Reconstruction