A novel meshless method for incompressible flow calculations

This paper presents a novel explicit meshless solver for incompressible flows using the multidimensional characteristic relations of artificial compressibility equations. The main objective of this research is using the recently introduced multi-dimensional characteristic based (MCB) scheme in order to prevent the instabilities and comparing it with the results obtained by the one dimensional characteristic based (CB) method. An explicit four-stage Runge–Kutta scheme was used for meshless calculations and local time stepping and residual smoothing are used to accelerate convergence. The MCB and CB meshless methods are used for solving two incompressible flows including flow in a lid-driven cavity and the steady and unsteady flows past a circular cylinder. The results obtained using new proposed MCB meshless method show high accuracy and better convergence rate respect to CB scheme and the results are in good agreement with standard benchmark solutions in the literature.