The effect of numerical methods on the simulation of mid-ocean ridge hydrothermal models.

Carpio, J. and Braack, Malte (2012) The effect of numerical methods on the simulation of mid-ocean ridge hydrothermal models. Theoretical and Computational Fluid Dynamics, 26 (1-4). pp. 225-243.

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Abstract

This work considers the effect of the numerical method on the simulation of a 2D model of hydrothermal systems located in the high-permeability axial plane of mid-ocean ridges. The behavior of hot plumes, formed in a porous medium between volcanic lava and the ocean floor, is very irregular due to convective instabilities. Therefore, we discuss and compare two different numerical methods for solving the mathematical model of this system. In concrete, we consider two ways to treat the temperature equation of the model: a semi-Lagrangian formulation of the advective terms in combination with a Galerkin finite element method for the parabolic part of the equations and a stabilized finite element scheme. Both methods are very robust and accurate. However, due to physical instabilities in the system at high Rayleigh number, the effect of the numerical method is significant with regard to the temperature distribution at a certain time instant. The good news is that relevant statistical quantities remain relatively stable and coincide for the two numerical schemes. The agreement is larger in the case of a mathematical model with constant water properties. In the case of a model with nonlinear dependence of the water properties on the temperature and pressure, the agreement in the statistics is clearly less pronounced. Hence, the presented work accentuates the need for a strengthened validation of the compatibility between numerical scheme (accuracy/resolution) and complex (realistic/nonlinear) models.

Document Type: Article
Research affiliation: OceanRep > The Future Ocean - Cluster of Excellence > FO-R03
Kiel University
OceanRep > The Future Ocean - Cluster of Excellence
Refereed: Yes
ISSN: 0935-4964
Projects: Future Ocean
Date Deposited: 14 May 2014 10:19
Last Modified: 08 Mar 2017 09:31
URI: http://oceanrep.geomar.de/id/eprint/23882

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