Abstract
In this work, we propose an improved discrete gas-kinetic scheme (DGKS) for viscous incompressible and compressible flows based on the modified circular function. The improved scheme restores the flaw of the previous DGKS and recovers the correct macroscopic energy equation. Modifications are first made on the previous circular function by relocating some portion of the particles in the phase velocity space from the circle to the circular center. By adjusting the portion of particles at the circular center, the true diffusive flux for the energy equation can be recovered, and thus, the correct macroscopic energy equation is obtained. Based on the modified circular function, a D2Q5 discrete velocity model is developed, which enhances the computational efficiency. This discrete velocity model is then incorporated into the finite volume framework for the reconstruction of numerical fluxes on the cell interface. Numerical tests on incompressible and compressible flows are performed for comprehensive validation of the proposed solver. Improved accuracy is observed in the test examples, and the computational results show good agreement with the reference data.
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