How Numerical Diffusion Impacts the Level Set Method in 1D and 2D

David Starinshak
Department of Mathematics
University of Michigan
Ann Arbor, Michigan, USA


This talk involves common issues associated with applying the level set method to multimaterial compressible flow calculations. Issues are organized into 1D and 2D effects and interpreted in terms of numerical diffusion inherent to most compressible flow solvers. In the first part of the talk, I will examine losses in species mass conservation resulting from numerical diffusion in 1D. I will offer a straightforward modification of the level set method which demonstrates significant reduction in mass errors for a variety of flows. Results are presented for linearly-advected contact waves and shock-interface interactions. In the second part of the talk, I will discuss the issue of representing three or more materials using multiple level set functions in 2D. I will show that conventional level set methods can generate ambiguous representations due to numerical diffusion. I will introduce a new representation model that is robust to numerical diffusion effects, generalizes to an arbitrary numbers of materials, and offers improved tracking of sub-grid interface geometry. Results are presented for three-material and five-material shock tube problems. >