Article: Owkes M, Desjardins O; (2015) “A Mesh-decoupled Height Function Method for Computing Interface Curvature”, Journal of Computational Physics, 281: 285-300
Abstract: In this paper, a mesh-decoupled height function method is proposed and tested. The method is based on computing height functions within columns that are not aligned with the underlying mesh and have variable dimensions. Because they are decoupled from the computational mesh, the columns can be aligned with the interface normal vector, which is found to improve the curvature calculation for under-resolved interfaces where the standard height function method often fails. A computational geometry toolbox is used to compute the heights in the complex geometry that is formed at the intersection of the computational mesh and the columns. The toolbox reduces the complexity of the problem to a series of straightforward geometric operations using simplices. The proposed scheme is shown to compute more accurate curvatures than the standard height function method on coarse meshes. A combined method that uses the standard height function where it is well defined and the proposed scheme in under-resolved regions is tested. This approach achieves accurate and robust curvatures for under-resolved interface features and second-order converging curvatures for well-resolved interfaces. (C) 2014 Elsevier Inc. All rights reserved.