Discretized boundary surface reconstruction

TL;DR

This paper introduces a method for reconstructing 2D boundary surfaces from discretization points using cubic splines, aiding meshless numerical simulations of moving boundary problems.

Contribution

It presents a novel cubic spline-based algorithm for boundary surface reconstruction from discretization points, addressing a key challenge in meshless domain discretization.

Findings

Effective boundary reconstruction demonstrated in phase-change simulation

Algorithm provides accurate surface description from scattered points

Facilitates meshless methods for moving boundary problems

Abstract

Domain discretization is an essential part of the solution procedure in numerical simulations. Meshless methods simplify the domain discretization to positioning of nodes in the interior and on the boundary of the domain. However, generally speaking, the shape of the boundary is often undefined and thus needs to be constructed before it can be discretized with a desired internodal spacing. Domain shape construction is far from trivial and is the main challenge of this paper. We tackle the simulation of moving boundary problems where the lack of domain shape information can introduce difficulties. We present a solution for 2D surface reconstruction from discretization points using cubic splines and thus providing a surface description anywhere in the domain. We also demonstrate the presented algorithm in a simulation of phase-change-like problem.