Optimized Schwarz waveform relaxation for Primitive Equations of the ocean

TL;DR

This paper develops an optimized Schwarz waveform relaxation method for the viscous primitive equations of the ocean, using asymptotic analysis and Dirichlet to Neumann operators, with theoretical and numerical validation.

Contribution

It introduces a novel domain decomposition algorithm tailored for ocean primitive equations, incorporating asymptotic analysis for improved efficiency.

Findings

Algorithm is well-posed and convergent.

Numerical results demonstrate efficiency of the method.

Provides a new approach for large-scale ocean modeling.

Abstract

In this article we are interested in the derivation of efficient domain decomposition methods for the viscous primitive equations of the ocean. We consider the rotating 3d incompressible hydrostatic Navier-Stokes equations with free surface. Performing an asymptotic analysis of the system with respect to the Rossby number, we compute an approximated Dirichlet to Neumann operator and build an optimized Schwarz waveform relaxation algorithm. We establish the well-posedness of this algorithm and present some numerical results to illustrate the method.