On 1D Diffusion Problems with a Gradient-dependent Diffusion Coefficient
Authors: S.C. Jardin, G. Bateman, G.W. Hammett, L.P. Ku
In solving the 1D (flux surface averaged) transport equations for the temperatures and densities in a tokamak, one increasingly encounters highly nonlinear thermal conductivity and diffusivity functions, such as GLF23, that have a strong dependence on the temperature gradients. These arise from a subsidiary microstability based calculation in which the growth rates and hence transport coefficients are sensitive functions of these gradients. When these nonlinear functions are interfaced with a standard transport framework that uses a Crank-Nicholson time advancement, large non-physical oscillations and numerical instabilities can develop. Here we describe a relatively simple modification to the Crank-Nicholson method that cures this difficulty.
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Submitted to Journal of Computational Physics.
Download PPPL-4234 April 2007 (pdf 264 kB).