An Efficient High-Order Gas-Kinetic Scheme with Hybrid WENO-AO Method for the Euler and Navier-Stokes Solutions (Communications in Computational Physics, 2024)
The high-order gas-kinetic scheme (HGKS) features good robustness, highefficiency and satisfactory accuracy,the performance of which can be further improvedcombined with WENO-AO (WENO with adaptive order) scheme for reconstruction.To reduce computational costs in the reconstruction procedure, this paper proposesto combine HGKS with a hybrid WENO-AO scheme. The hybrid WENO-AO schemereconstructs target variables using upwind linear approximation directly if all extremepoints of the reconstruction polynomials for these variables are outside the large stencil. Otherwise, the WENO-AO scheme is used. Unlike combining the hybrid WENOscheme with traditional Riemann solvers, the troubled cell indicator of the hybridWENO-AO method is fully utilized in the spatial reconstruction process of HGKS.During normal and tangential reconstruction, the gas-kinetic scheme flux not onlyneeds to reconstruct the conservative variables on the left and right interfaces but alsoto reconstruct the derivative terms of the conservative variables. By reducing the number of times that the WENO-AO scheme is used, the calculation cost is reduced. Thehigh-order gas-kinetic scheme with the hybrid WENO-AO method retains original robustness and accuracy of the WENO5-AO GKS, while exhibits higher computationalefficiency.
Keywords: Gas-kinetic scheme; hybrid WENO-AO scheme; high-order finite volume scheme; extreme point.