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Stable numeric scheme for diffusion equation with a stiff transport

机译：具有刚性传输的扩散方程的稳定数值格式

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摘要

It is known that the anomalous transport in fusion devices is governed by gradient-driven instabilities and is characterised by an offset linear dependence of the heat and particle fluxes on the corresponding gradients. The dependence is very strong so that a small change in gradients causes a huge variation of fluxes thus giving rise to the so-called stiff transport. This feature makes the standard numeric schemes for a parabolic equation strongly unstable so that plasma simulations with transport codes require very small time steps. In this paper, a modification of the standard finite difference scheme is suggested that eliminates this kind of numerical instability. It is shown that the implementation of the technique allows the time step for stiff transport models to be increased by several orders of magnitude. Generalisation to more advanced numeric schemes and to a system of parabolic equations is straightforward. Crown Copyright (C) 2008 Published by Elsevier B.V. All rights reserved.
机译：众所周知，聚变装置中的异常传输受梯度驱动的不稳定性支配，其特征在于热量和颗粒通量对相应梯度的线性偏移依赖性。这种依赖性非常强，以至于梯度的微小变化会引起通量的巨大变化，从而引起所谓的刚性传输。此功能使抛物线方程的标准数值方案非常不稳定，因此带有传输代码的等离子体模拟需要非常小的时间步长。在本文中，建议对标准有限差分方案进行修改，以消除这种数值不稳定性。结果表明，该技术的实现使刚性运输模型的时间步长增加了几个数量级。推广到更高级的数值方案和抛物线方程组很简单。 Crown版权所有（C）2008，Elsevier B.V.保留所有权利。

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