A fast meshless method coupled with artificial dissipation for solving 2D Euler equations

A meshless method using a cloud of points has become an important research topic in computational fluid dynamics due to its benefits, flexibility, and accuracy of results. In this paper, a fast meshless method has been developed for the solution of two dimensional Euler equations, with artificial dissipation used in the discretization second and fourth order derivatives based on a new clouds of points strategy. Additionally, an explicit five-stage Runge–Kutta scheme is utilized to reach the steady state solution. A local time-stepping method and a residual averaging are implemented to accelerate the density residual convergence. This paper compares the computational efficiency of the proposed meshless approach, one finite volume method, and one meshless method in the literatures by solving two aeronautical applications. Numerical results show that the proposed meshless approach has same accuracy and much lower computational cost when compared to the other two methods. Numerical study demonstrates that the proposed approach is promising for aerodynamics design problems.

► A fast meshless method has been developed for two dimensional Euler equations.
► The proposed approach is validated by one example.
► Two aeronautical applications are calculated.
► Numerical results show the efficiency and accuracy of the proposed approach.