Mapped Fourier Methods for stiff problems in toroidal geometry

Herve Guillard 1
1 CASTOR - Control, Analysis and Simulations for TOkamak Research
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : Fourier spectral or pseudo-spectral methods are usually extremely efficient for periodic problems. However this efficiency is lost if the solutions have zones of rapid variations or internal layers. For these cases, a large number of Fourier modes are required and this makes the Fourier method unpractical in many cases. This work investigates the use of mapped Fourier method as a way to circumvent this problem. Mapped Fourier method uses instead of the usual Fourier interpolant the composition of the Fourier interpolant with a mapping in such a way that in the computational space, the functions to represent are not stiff. This work gives some examples of the usefulness of this method and apply it to a simple model of pellet injection in tokamaks as an example of its potential interest for complex multi dimensional problem.
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Herve Guillard. Mapped Fourier Methods for stiff problems in toroidal geometry. [Research Report] RR-8566, INRIA. 2014, pp.17. ⟨hal-01023050⟩

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