The effect of numerical methods on the simulation

Authors: J Carpio M Braack

Publish Date: 2011/05/21

Volume: 26, Issue: 1-4, Pages: 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 highpermeability axial plane of midocean 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 semiLagrangian 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

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