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arXiv · 2308.08130

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

Yiwen Lin·Shi Jin
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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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Yiwen Lin, Shi Jin. 2023-08-16. Error estimates of a bi-fidelity method for a multi-phase Navier-Stokes-Vlasov-Fokker-Planck system with random inputs. https://arxiv.org/abs/2308.08130

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