Speaker: James Burton, Graduate Student, Department of Mathematical Sciences
Date: Wednesday, October 27, 2021, 3:45 PM – 4:00 PM
Title: A Random Choice Method of the Glimm’s Scheme
Abstract: Numerical methods for the solution of hyperbolic partial differential equations concerns shock formation and propagation. In order to solve the Euler equations of compressible fluid dynamics, one needs to use stable, accurate and robust algorithms for shock computations. In our numerical simulations of compressible multiphase flows in 1D, we use Glimm’s scheme because of its good algorithmic properties. However, this scheme is difficult to extend to multidimensional hyperbolic problems. Glimm’s scheme, designed using the random choice method (RCM), is revisited to investigate convergence properties using low-discrepancy sampling methods. A set of van der Corput sampling sequences and its generalized version Halton sequences are used to determine the sensitivity of the random variables to the approximated solutions. A detailed study is performed to find the optimal choice in sampling sequence. Numerical solutions on the various meshes using different sequences are performed to determine the optimal sampling choice with a good convergence property.
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