Error estimates of a bi-fidelity method for a multi-phase Navier-Stokes-Vlasov-Fokker-Planck system with random inputs

2023/08/16 by Shi Jin, Lin, Yiwen, Jin, Shi · 1 citation
Mathematics · Physics and Astronomy · #35Q84 #65M70 #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Markov Chains and Monte Carlo Methods #Numerical Analysis (math.NA) #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.2308.08130

openalex publication_date 2023/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 in this paper. Such a model is a system coupling the incompressible Navier-Stokes equations to the Vlasov-Fokker-Planck equations for a mixture of the flows with distinct particle sizes. 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. This allows us to obtain the error estimates in both kinetic and hydrodynamic regimes.

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