Compact High-Order Gas-Kinetic Scheme for Three-Dimensional Flow Simulations

Abstract

A third-order compact gas-kinetic scheme is proposed for three-dimensional compressible flow computations. The new scheme is based on three key ingredients: the time-accurate gas evolution model for interface flux, the Hermite weighted essentially nonoscillatory reconstruction, and the two-stage temporal discretization. In contrast to the Riemann-solver-based methods, due to the use of time-accurate flux function the proposed scheme can achieve a third-order temporal accuracy with two stages instead of three stages in the standard Runge–Kutta method. As an extension of the existing high-order reconstructions, a Hermite weighted essentially nonoscillatory reconstruction is specifically designed for the current scheme with the implementation of the constrained least-square technique, which subsequently improves the accuracy and robustness of the compact scheme. There is no trouble cell identification in the current scheme. A third-order accuracy can be achieved even with curved boundary. Numerical examples for both smooth and discontinuous flows show the robustness and high accuracy of the compact third-order scheme, which has a comparable performance as the fifth-order noncompact gas-kinetic scheme. A large Courant–Friedrichs–Lewy number around 0.5 can be used in the computations.