New Finite Volume Method for rotating channel flows involving boundary layers

TL;DR

This paper introduces a new finite volume method to numerically solve rotating Stokes equations with boundary layers, providing accurate solutions at small viscosities relevant for fluid flows under rotation.

Contribution

The paper develops a novel finite volume method tailored for rotating boundary layer problems, enabling precise numerical solutions for singular perturbation equations.

Findings

Derivation of correctors for boundary layer variations.

Implementation of the new finite volume method (NFVM).

Numerical results demonstrating NFVM's effectiveness.

Abstract

We investigate in this article the boundary layers appearing for a fluid under moderate rotation when the viscosity is small. The fluid is modeled by rotating type Stokes equations known also as the Barotropric mode equations in the primitive equations theory. First we derive the correctors that describe the sharp variations at large Reynolds number (i.e., small viscosity). Second, thanks to a new finite volume method (NFVM) we give numerical solutions of the rotating Stokes system at small viscosity. The NFVM can be applied to a large class of singular perturbation problems.