Numerical Study of an Indicator Function for Front-Tracking Methods

Abstract

In this paper, we present a detailed derivation and numerical investigation of an indicator function for front-tracking methods. We use the discrete Dirac delta function to construct an indicator function from a set of Lagrangian points and solve the resulting discrete Poisson equation with the zero Dirichlet boundary condition using an iterative method. We present several computational tests to investigate the effect of parameters such as distance between points, uniformity of the distance, and types of the Dirac delta functions on the indicator function.