February 3, 2020 @ 3:30 pm – 4:30 pm
Speaker: Liu Liu (UT Austin)
Title: A Bi-fidelity method for multiscale kinetic equations with uncertainties
In this talk, we introduce a bi-fidelity numerical method for solving high-dimensional parametric kinetic equations. We first briefly discuss about the Boltzmann equation and its fluid dynamic limit, then introduce a bi-fidelity stochastic collocation method for its uncertainty quantification problem. By combining computational efficiency of the low-fidelity model–chosen as the compressible Euler system–with high accuracy of the high-fidelity (Boltzmann) model, our bi-fidelity approximation can successfully capture well the macroscopic quantities of solution to the Boltzmann equation in the random space. A uniform error estimate of the bi-fidelity method, based on a series of our theoretical work on hypocoercivity for the uncertain kinetic equations, will be shown. Lastly we present numerical results to validate the efficiency and accuracy of our proposed method.