An accurate fourth order discrete unified gas-kinetic scheme (DUGKS) on two dimensional unstructured mesh is presented for all flow regimes. The DUGKS provides a finite volume method for multiscale flow computations w...
An accurate fourth order discrete unified gas-kinetic scheme (DUGKS) on two dimensional unstructured mesh is presented for all flow regimes. The DUGKS provides a finite volume method for multiscale flow computations with asymptotic preserving property. With the discretization of particle velocity space, two auxiliary distribution functions with the inclusion of collision effect are introduced to keep conservation property. By expanding the Maxwellian distribution into a series of velocity polynomials,non-equilibrium effect can be easily presented. For better temporal and spatial accuracy, the Lax-Wendroff type time stepping method and cubic spline reconstruction are adopted to construct a fourth-order DUGKS. On both structured grid and unstructured hybrid mesh, this method has flexible mesh adaptation. Some numerical test cases, including benchmark cavity flows under different mesh resolutions and flow around circular cylinder, are conducted to validate this method. Comparison results with original DUGKS also show the better accuracy. This fourth-order DUGKS gives as satisfy results as two-order schemes with much coarser mesh and lower computational cost.
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