Stable numeric scheme for diffusion equation with a stiff transport

Abstract

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.