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Solving discontinuous problems with pseudospectral methods

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Pseudospectral schemes are a class of numerical methods successful at solving PDEs (Partial Differential Equations) with high accuracy due to their exponential convergence onto smooth solutions. Unfortunately, when applied to discontinuous problems, such as fluid shocks and material interfaces, pseudospectral solutions lose their superb convergence and suffer from spurious oscillations owing to the Gibbs’ phenomenon. I would like to present one of the proposed remedies for these issues – adaptive smoothing in the reconstruction space, introducing this post-processing technique and briefly discussing our results on its practical application to 1D and 2D problems.

This talk is part of the Cavendish Astrophysics Coffee talks series.

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