Estimation of curvature from volume fractions using parabolic reconstruction on two-dimensional unstructured meshes

JOURNAL OF COMPUTATIONAL PHYSICS

卷:351

Article

Evrard, Fabien¹  Denner, Fabian¹  van Wachem, Berend¹ 

[1] Imperial Coll London, Dept Mech Engn, Exhibit Rd, London SW7 2AZ, England

关键词: Curvature;    Volume fraction;    Unstructured mesh;    Volume-of-fluid;    Height-function;   

DOI  :  10.1016/j.jcp.2017.09.034

来源: Elsevier

【 摘 要 】

This paper proposes a method to estimate the curvature of an interface represented implicitly by discrete volume fractions on an unstructured two-dimensional mesh. The method relies on the computation of local parabolic reconstructions of the interface. The parabolic reconstruction of the interface in a given computational cell is obtained by solving a local non-linear minimisation problem, and only requires additional information from two neighbouring cells. This compactness ensures a robust behaviour on poorly-resolved interfaces. The proposed method is proven to be analogous to the height-function method for Cartesian configurations with consistent heights, and can be interpreted as a generalisation of the height-function method to meshes of any type. Tests are conducted on a range of interfaces with known curvature. The method is shown to converge with mesh refinement with the same order of accuracy as the height-function method for all three types of meshes tested, i.e. Cartesian, triangular, and polygonal. (C) 2017 The Authors. Published by Elsevier Inc.

【 授权许可】

Free