Recent Progresses on a Meshless Euler Solver for Compressible Flows

Abstract

The conventional CFD solvers depend on a mesh to discretize the domain. Due to the flexible nature of meshless methods, which do not require a mesh, we re-examine several meshless solvers for possible applications to moving boundary problems. Like many meshdependent solvers, second order meshless solvers suffer from convergence problems for transonic and supersonic flows with shock waves. In this work we develop a convergent limiter following ideas for finite volume solvers. The meshless solver is tested with a supersonic flow in a channel and subsonic flow over an airfoil and rigid body, and machine zero convergence is achieved for both the testing cases. We plan to run more benchmark problems, and further extend the present meshless solver to handle moving boundary problems. Nomenclaturec = shape parameter Cp = pressure coefficient dt = time step f, g = generic functions F1 = Flux vector in x-direction F2 = Flux vector in y-direction G = Flux vector along a given direction i = index of reference node j = index of supporting node k = index of neighboring nodes NI = number of supporting nodes n = time index during navigation Q = Vector of conservative variables r = distance between two nodes T = temperature x = position vector = limiter = radial basis function M  = Mach number of the free stream

Algebraic-volume meshfree method for application in finite volume solver

“…The spatial derivatives of Euler equation were discretised by the moving-least square scheme on each cloud of points. The progress of meshfree method for inviscid flow simulation was reviewed in [33].…”