Development of an implicit high order gridless method for inviscid compressible flows

In this paper, an implicit high order discretization has been developed for gridless method. In recent decade, gridless method using a distribution of points has become an important research topic in computational fluid dynamics. Gridless method usually uses the first order Taylor series for discretization of the space derivatives at any points. This paper presents an extension of high order for a central difference gridless method and investigates the results accuracy and performance of this method for solving inviscid compressible flows. Euler equations have been solved in two dimensional using second and fourth order artificial dissipation terms. These terms make a fast gridless method. The method of discretization in time, Explicit and dual-time implicit time discretization are used. In order to reduce the computational cost, local time stepping and residual smoothing techniques are utilized to speed up convergence. The capabilities and accuracy of the method are compared with finite volume method and experimental data for airfoils in transonic and supersonic flows. Results show that the second order accuracy solutions with fewer point distributions indicate higher accuracy when compared to the first order accuracy solutions in transonic and supersonic flows.