Inquiry on Characteristic Methods Support

[HC Zhang]

Dear all，

I want to implement a Semi-Lagrangian DG method (a type of characteristic method) for solving advection-dominated problems. The method is primarily based on tracing characteristics, as the upstream cells used in the computation are obtained by solving along the characteristic curves, while the current computational grid remains fixed. Besides, the upstream cell will be divided into a few subdomains by the background grid (the same as the current grid). Each subdomain has its basic functions.

Given that this method requires a robust characteristic tracing capability, I would like to ask whether the deal.II supports any built-in tools or frameworks for characteristic-based methods, or if there are recommended approaches or existing examples in deal.II that could facilitate this.

Thank you for your time and assistance.

Best regards,

Haicheng

[Wolfgang Bangerth]

Haicheng:

I don't think that deal.II has any algorithms specifically for characteristic
tracing already built in. The closest I can think is Rene Gassmoeller's
methods for particle tracing, which you can find here:
https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2018GC007508
https://arxiv.org/pdf/1612.03369
I imagine that algorithms for determining characteristics will use many
similar tools.

In general, if you want to know what people have been doing with deal.II, this
is always a good resource:
https://dealii.org/community/publications/
There is a search box (well hidden to the left of the "clear" button) where
you can filter for publications that have specific keywords in their title.

Best
W.

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Wolfgang Bangerth email: bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/