Seminars on Numerical Algorithms, Analyses, and Applications: Error estimates of a bi-fidelity method for a multi-phase kinetic-fluid coupled system with random inputs

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:2024-06-21 16:30





Consider kinetic-fluid models for a mixture of flows, where the disperse phase is made of particles with distinct sizes. This leads to a system coupling the incompressible Navier–Stokes equations to the Vlasov–Fokker–Planck equations. Uniform error estimates of a bi-fidelity method for a kinetic-fluid coupled model with random initial inputs in the fine particle regime are proved. The main analytic tool is the hypocoercivity analysis for the multi-phase Navier-Stokes-Vlasov-Fokker-Planck system with uncertainties, considering solutions in a perturbative setting near the global equilibrium. Besides, we have developed an asymptotic-preserving scheme for such multi-phase flow system, efficiently in both kinetic and hydrodynamic regimes. Numerical examples illustrate the accuracy and efficiency of the bi-fidelity method.