An accurate LED-BGK solver on unstructured adaptive meshes

Starting from the collisional BGK model of the full Boltzmann equation, we develop an accurate and robust finite volume gas kinetic scheme on unstructured triangular mesh. The numerical approach is composed of two steps-an initial reconstruction step and a gas evolution step. In the initial reconstruction step, the unstructured version of the LED (Local Extremum Diminishing) interpolation is applied to the conservative variables and to compute left nd right states along a node edge. In the gas evolution step, the local integral solution of BGK model is used to compute numerical fluxes at a cell interface. The collisional BGK model provides an alternative to Riemann solvers and possesses many desirable properties that can not be found in Godunov-type schemes. A classic h-refinement adaptive procedure is implemented to increase the spatial resolution of physically important phenomena such as shock waves, contact discontinuities or expansion waves with minimal computational costs and memory overheads. It involves mesh enrichment/coarsening steps to either insert nodes on an edge center in highgradient under-resolved regions or delete nodes in over-resolved regions. Numerical results of several test cases for unsteady compressible inviscid flows are presented. To verify the accuracy and robustness of the current numerical approach, the computed results are compared with the results of structured mesh calculations and other flux splitting methods.