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

TL;DR

This paper introduces a non-intrusive kernel-based stochastic collocation method for quantifying uncertainty in the random two-phase Navier-Stokes equations, demonstrating competitive performance with existing techniques.

Contribution

The work applies radial kernel basis functions to stochastic collocation in two-phase Navier-Stokes equations, showing improved efficiency and accuracy over standard methods.

Findings

Kernel-based stochastic collocation outperforms some standard methods.

The approach is non-intrusive and compatible with existing fluid dynamics solvers.

Empirical results demonstrate high competitiveness of the method.

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 non-intrusive 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.