A new stabilised curvature computation method using the level set function

Abstract

Computation of the curvature is an essential task during the simulation of processes such as bio-film growth and two-phase fluid flow wherein the interfacial forces play a crucial role in the determination of the state of stress. Existing methods for computing the curvature at the interface are not very accurate and exhibit unwanted numerical oscillations. In this work, a novel method is proposed to compute the mean curvature of the interface accurately. As opposed to Bruchon method which has only one stabilising term that can bias the results, the proposed method includes a pair of counteracting stabilising terms that remove any such bias. A comparative investigation of the proposed method with other existing techniques is also presented to demonstrate the superior performance. The paper also illustrates the application of the proposed curvature computation method for the flow through pipe problem in the last section.