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

TL;DR

This paper establishes uniform error estimates for a bi-fidelity method applied to a coupled kinetic-fluid model with random initial data, covering both kinetic and hydrodynamic regimes.

Contribution

It provides the first rigorous error analysis for a bi-fidelity approach to a multi-phase Navier-Stokes-Vlasov-Fokker-Planck system with uncertainties.

Findings

Error estimates are uniform across regimes.

The method effectively handles random initial conditions.

Analysis is based on hypocoercivity techniques.

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.