Averaging principle for the stochastic convective Brinkman-Forchheimer equations

TL;DR

This paper proves a strong averaging principle for the stochastic 2D convective Brinkman-Forchheimer equations with multiplicative Gaussian noise, revealing how multiscale stochastic effects can be effectively averaged in fluid flow models within porous media.

Contribution

It introduces a novel averaging principle for the stochastic 2D SCBF equations with multiplicative noise, utilizing Khasminskii's time discretization method.

Findings

Established a strong averaging principle for stochastic 2D SCBF equations.

Demonstrated the effectiveness of Khasminskii's method in this context.

Analyzed the impact of multiplicative Gaussian noise on fluid flow models.

Abstract

The convective Brinkman-Forchheimer equations describe the motion of incompressible fluid flows in a saturated porous medium. This work examines the multiscale stochastic convective Brinkman-Forchheimer (SCBF) equations perturbed by multiplicative Gaussian noise in two and three dimensional bounded domains. We establish a strong averaging principle for the stochastic 2D SCBF equations, which contains a fast time scale component governed by a stochastic reaction-diffusion equation with damping driven by multiplicative Gaussian noise. We exploit the Khasminkii's time discretization approach in the proofs.