Numerical Approximation of the Inviscid 3D Primitive Equations in a Limited Domain

TL;DR

This paper introduces nonlocal boundary conditions and numerical schemes for the inviscid 3D primitive equations, demonstrating their effectiveness through simulations on nested domains.

Contribution

It proposes novel nonlocal boundary conditions and splitting-up numerical schemes for the inviscid 3D primitive equations, enabling improved simulations.

Findings

Successful implementation of boundary conditions for higher modes

Effective numerical schemes for nonlinear primitive equations

Simulation results on nested domains show promising accuracy

Abstract

A new set of nonlocal boundary conditions are proposed for the higher modes of the 3D inviscid primitive equations. Numerical schemes using the splitting-up method are proposed for these modes. Numerical simulations of the full nonlinear primitive equations are performed on a nested set of domains, and the results are discussed.