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 mesh-dependent 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.
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