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Chaos & Complex Systems Seminar
"Shock Waves in Nature and in Numerical Computations"
Date: Tuesday, April 13th
Time: 12:05 pm
Place: 4274 Chamberlin Hall
Speaker: James Rossmanith, UW-Madison, Dept. of Mathematics
Abstract: Shock waves are propagating disturbances that are characterized by an abrupt, nearly discontinuous change in the characteristics of a fluid or plasma. They can occur in a variety of phenomena in both laboratory and natural settings. Mathematically, shock waves are difficult to handle since in general they are not unique solutions of the equations that model them. Computationally, shock waves are difficult to handle for several reasons: (1) most discontinuous cannot be exactly represented on a discrete mesh, (2) standard high-order methods are unstable for shocks, and (3) the numerical schemes must be carefully constructed to yield the physically correct solution.

In this talk I will begin by briefly reviewing the basic theory of shock waves. I will then, mostly through computational examples, describe the various pitfalls in trying to numerically solve equations with shock solutions. Finally, I will describe some strategies based on adaptive mesh refinement to obtain highly accurate numerical solutions.

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