Interface Reconstruction Using Gaussian Processes for Volume of Fluid Methods

We present a novel framework for reconstructing material interfaces on a local stencil

using Gaussian process (GP) modeling. Interface-capturing methods, like the volume-of-

fluid method, track interfaces between fluid components by evolving the volume fraction

of components and advecting component volumes between computational cells, making

accurate reconstruction of the material interfaces on each cell crucial to the success of the

method. The nonparametric nature of GP regression naturally allows for efficient

reconstruction of interfaces on arbitrary stencils in any geometry using precomputed

weights. We demonstrate that GP-based reconstructions significantly outperform finite-

difference least-squares approaches, such as the Youngs method¹, without the need for

costly iterations.