Kernel-based stochastic collocation for the random two-phase Navier-Stokes equations

Abstract

In this work, we apply stochastic collocation methods with radial kernel basis functions for an uncertainty quantification of the random incompressible two-phase Navier–Stokes equations. Our approach is nonintrusive and we use the existing fluid dynamics solver NaSt3DGPF to solve the incompressible two-phase Navier–Stokes equation for each given realization. We are able to empirically show that the resulting kernel-based stochastic collocation is highly competitive in this setting and even outperforms some other standard methods.