Extending the AUSM⁺-up scheme into the gridless method

In this paper, the AUSM⁺-up scheme is extended into the gridless method. A quadrantal point infilling strategy is developed to generate point and combine clouds of points automatically. On the base of the distributed clouds of points, local least-squares curve fits and the AUSM⁺-up scheme are used to obtain the numerical flux. An explicit multistage Runge-Kutta algorithm is used to advance the flow equations in time, at the same time local time stepping technique and residual averaging are employed to accelerate the convergence of solution. In order to demonstrate the accuracy and applicability of the method, the NACA0012 airfoil in transonic flow, multi-element airfoil complex flow and a pair of NACA0012 airfoils in supersonic and in hypersonic flow are computed.