Numerical Simulations of the Inviscid Primitive Equations in a Limited Domain
This work is dedicated to the numerical computations of the primitive equations (PEs) of the ocean without viscosity with the nonlocal (mode by mode) boundary conditions introduced in [RTT05b]. We consider the 2D nonlinear PEs, and firstly compute the solutions in a “large” rectangular domain Ω0 with periodic boundary conditions in the horizontal direction. Then we consider a subdomain Ω1, in which we compute a second numerical solution with transparent boundary conditions. Two objectives are achieved. On the one hand the absence of blow-up in these computations indicates that the PEs without viscosity are well posed when supplemented with the boundary conditions introduced in [RTT05b]. On the other hand they show a very good coincidence on the subdomain Ω1 of the two solutions, thus showing also the computational relevance of these new boundary conditions. We end this study with some numerical simulations of the linearized primitive equations, which correspond to the theoretical results established in [RTT05b], and evidence the transparent properties of the boundary conditions.
Unable to display preview. Download preview PDF.
- [BM97]C. Bernardi and Y. Maday. Spectral methods. In Handbook of numerical analysis, Vol. V, Handb. Numer. Anal., V, pages 209–485. North-Holland, Amsterdam, 1997.Google Scholar
- [PR05]M. Petcu and A. Rousseau. On the Δ-primitive and Boussinesq type equations. Advances in Differential Equations, to appear, 2005.Google Scholar
- [RTT05a]A. Rousseau, R. Temam, and J. Tribbia. Boundary conditions for an ocean related system with a small parameter. In Nonlinear PDEs and Related Analysis, volume 371, pages 231–263. Gui-Qiang Chen, George Gasper and Joseph J. Jerome Eds., Contemporary Mathematics, AMS, Providence, 2005.Google Scholar
- [RTT05b]A. Rousseau, R. Temam, and J. Tribbia. Boundary conditions for the 2D linearized PEs of the ocean in the absence of viscosity. Discrete and Continuous Dynamical Systems, to appear, 2005.Google Scholar