Three-dimensional third-order gas-kinetic scheme on hybrid unstructured meshes for Euler and Navier–Stokes equations

In this paper, a third-order gas-kinetic scheme is developed on the three-dimensional hybrid unstructured meshes for compressible inviscid and viscous flows. classical weighted essentially non-oscillatory (WENO) scheme, high-order spatial accuracy achieved by non-linear combination of lower order polynomials. However, meshes, procedures, including selection candidate stencils calculation linear weights, become extremely complicated, especially problems. To overcome drawbacks, WENO reconstruction tetrahedron, pyramid, prism hexahedron. A general strategy given big stencil sub-stencils topologically independent weights are used in reconstruction. unified interpolation also volume integral different types control volumes, as well flux integration over cell interfaces. Incorporate with two-stage fourth-order temporal discretization, explicit schemes unsteady With lower–upper symmetric Gauss–Seidel (LU-SGS) methods Jacobi iteration, implicit steady accelerate computation, both implemented graphics processing unit (GPU) using compute device architecture (CUDA). Especially, parallel iteration used. The speedup GPU code suggests potential large scale computation. variety numerical examples, from subsonic to supersonic flows, presented validate robustness