SC 740 Presentation Review

 By Deborah Dent

Dr. Kolibal presented a talk on the process of mollification, which can be used to construct approximations of functional derivatives. This process produces approximations that are analytic and suitable for numerically solving partial differential equations (pde). Dr. Kolibal was able to demonstrate the workability of this concept by applying the technique to a hyperbolic PDE, the De Laval nozzle problem in computational fluid dynamics.

He began his presentation by introducing techniques to filter or smooth a noisy function g. Mollifying the function g gives us a function g^ which is smoother than g which allows for the easy numerical computation of g^. He then walked us through the process of constructing g^, constructing the pde to be numerically computable and of obtaining the pde in closed form. He was then able to display graphical output displaying the comparison of approximating g with g^.

Dr. Kolibal followed with applying the technique to the Laval Nozzle Problem, which is a problem of two-dimensional axi-symmetric flow. After presenting details of the process, he was able to display computational results and the convergence of the mollified function.