Case Study: A Visual Tool for Moving Mesh Numerical Methods

Time-dependent partial differential equations are indispensable in scientific and engineering research, where they are used to model physical phenomena such as fluid flow and combustion. Moving mesh numerical solution methods have proven to be particularly well-suited to compute solutions to such problems which change non-uniformly over time. Computer visualization of moving mesh methods is an extension of an approach using computers to study mathematics, first advocated by von Neumann. Uses of this visualization include verifying the correct operation of the numerical algorithm; providing insight into improvements to the numerical algorithm; and interpreting the operation of the numerical algorithm to a larger community of mathematics researchers.