The Meshless Method for CFD

For decades, the finite element method (FEM) and the finite difference/finite volume methods (FDM/FVM) have been the dominant numerical schemes employed in most scientific computation. A common difficulty in the FEM and the FDM/FVM is the considerable amount of time and effort required to discretize and index the domain elements. In addition, all these traditional methods are often slowly convergent. A novel numerical technique called “meshless methods” (or “mesh-free methods”) has been strong development and has attracted attention. A common feature of meshless methods is that neither domain nor surface meshing is required during the solution process. Advances in the development and application of meshless techniques show they can be strong competitors to the more classical mesh-based numerical approaches. Research in meshless methods has continued to grow, and is now being considered by some researchers as the numerical method of the next generation.