Computing high-Reynolds number vortical flows: A highly accurate method with a fully meshless formulation

Publisher Summary This chapter discusses advancements in vortex methods that provide for a fully meshless formulation. The vortex method (VM) is a meshless approach to solving the Navier–Stokes equations, which concentrates computational elements in the physical domain of interest and exactly satisfies the free-space boundary conditions of external flows. Although the vortex method is in essence grid-free, commonly a mesh is used for interpolation of quantities such as velocity (vortex-in-cell method), or for the remeshing of the vortex particles in a spatial adaptation algorithm for fully Lagrangian formulations. This chapter discusses implementation of a parallel, meshless vortex method using the PETSc library. Spatial adaptation is provided grid-free by applying radial basis function interpolation. Parallel computations of the interaction of two co-rotating vortices produce results that compare very well with previous results using spectral methods, but with much reduced problem size. This demonstrates a high-accuracy meshless method for high-Reynolds number flows. Grid-convergence studies result in an observed second order of convergence, ascribed to convection error.