A High-Order Meshless Bhatnagar-Gross-Krook Scheme Based on Point Collocation

A point collocation method is combined with the Bhatnagar-Gross-Krook (BGK) scheme. The point collocation method is based on reproducing kernel approximations. The BGK scheme developed is evaluated under the finite difference method framework. After the construction of local equilibrium distribution function, the second-order accurate least-square kinetic upwind method is employed to improve the accuracy. Some test cases are explored to validate this meshless method.