Numerical Methods for Propagating Fronts

In many physical problems, a key aspect is the motion of a propagating front separating two components. As fundamental as this may be, the development of a numerical algorithm to track the moving front accurately is difficult. In this report, we describe some previous theoretical and numerical work. We begin with two examples to motivate the problem, followed by some analytical results. These theoretical results are then used as a foundation for two different types of numerical schemes. Finally, we describe the application of one of these schemes to our work in combustion.

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