粘性の高い非Newton流れのシミュレーション

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In a such simulation of which flow and heat are strongly coupled as non-Newtonian flow with high viscosity, solving a large-scaled nonlinear equation obtained from descretization becomes the main subject. Decoupled method such as SIMPLE was employed as a conventional nonlinear equation. In this method, when the temperature and velocity are strongly coupled, the computation becomes impossible due to a bad convergence. On the other hand, corresponding to the recent progress of computer, coupled method that solves nonlinear equation by means of Newton method became widely noticed. In spite of its required enormous storage, Newton method has also a relatively good convergence ability the case with non-linear. In this paper, mantle convection problem is introduced as an example of numerical simulation for non-Newtonian flow with high viscosity, and coupled method using Newton method is suggested. Modifying the original Newton method, restriction of increment is set for repetition computation. Also a method of fixing the initial value is devised. For solving its linear equation, Bi-CGSTAB, one of the pre-conditioned conjugate gradient method, is employed. Since the coefficient matrix of linear equation has much larger diagonal terms than non-diagonal terms, its convergence is not good with usual Bi-CGSTAB. Therefore, pre-conditioning should be devised. Applying this numerical solution on the simulation of mantle convection, its validity has been found.
日本シミュレーション学会の論文
2000-03-15

粘性の高い非Newton流れのシミュレーション

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