A Third-Order Meshless Method for Simulation of Two-Dimensional Inviscid Compressible Flows

In this study, a third-order meshless method is presented through adopting WENO-Z reconstruction as a substitute for traditional linear reconstruction. In order to achieve a third-order reconstruction of WENO-Z, the required three-point stencils are created by introducing ghost points on the lines through each pair of the central and satellite points of the meshless cloud. The flow variables of the ghost point are evaluated by a proposed interpolation technique, in which only available information associated with the cloud is utilized. Based on each resultant stencil of the ghost-central-satellite points, the WENO-Z is then implemented for computing the variables at the midpoints between the central and satellite points of the cloud. In this way, the resulting meshless method could be expected to be of third-order accuracy while obtaining an oscillation-free property. A series of typical model cases, including linear advection of sinusoid wave, convection of an isentropic vortex, and two well-known shock-tube problems, are selected to be simulated for validation. The expected third-order of accuracy and inherit ability of shock capturing are achieved regardless of whether the meshless points distributed are regular or irregular. In addition, a set of subsonic, transonic, and supersonic flows over aerodynamic bodies like single-and multi-element airfoils are also demonstrated for the compressible Euler equations, and obtained numerical results compare well with the reference data in the literature.