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.

中文翻译：

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随机两相 Navier-Stokes 方程的基于核的随机搭配

在这项工作中，我们将随机搭配方法与径向核基函数应用于随机不可压缩两相 Navier-Stokes 方程的不确定性量化。我们的方法是非侵入式的，我们使用现有的流体动力学求解器 NaSt3DGPF 来求解每个给定实现的不可压缩的两相 Navier-Stokes 方程。我们能够凭经验表明，由此产生的基于内核的随机搭配在这种情况下具有很强的竞争力，甚至优于其他一些标准方法。