In Computational Fluid Dynamics (CFD) it is critical that the numerical solution preserves the total mass of incompressible flows, without introducing spurious sources or sinks. Weak formulations such as the Finite Element Method (FEM) are often preferred, because they implicitly enforce the harmonicity of the approximation. However, these methods typically possess algebraic convergence only and require that a mesh be generated over the computational domain, which may be an expensive task in the event of an expanding fluid.
For that reason, meshless radial basis function (RBF) collocation methods are an appealing alternative to FEM in CFD. We show how to modify the basic setting so that problems involving boundary singularities can also be successfully tackled with RBF collocation. Focussing on an engineering problem (injection molding) we show that RBF collocation can outperform FEM on both simple and non-trivial domains.

CEMAT - Center for Computational and Stochastic Mathematics