A skeletal high-order structure preserving scheme for advection-diffusion equations

Julien Moatti

doi:10.1007/978-3-031-40864-9_29

A skeletal high-order structure preserving scheme for advection-diffusion equations

Numerical Analysis 2023-10-20 v2 Numerical Analysis

Authors: Julien Moatti

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Abstract

We introduce a nonlinear structure preserving high-order scheme for anisotropic advection-diffusion equations. This scheme, based on Hybrid High-Order methods, can handle general meshes. It also has an entropy structure, and preserves the positivity of the solution. We present some numerical simulations showing that the scheme converges at the expected order, while preserving positivity and long-time behaviour.

Keywords

numerical schemes for partial differential equations finite difference schemes advection-diffusion equations

Cite

@article{arxiv.2303.12062,
  title  = {A skeletal high-order structure preserving scheme for advection-diffusion equations},
  author = {Julien Moatti},
  journal= {arXiv preprint arXiv:2303.12062},
  year   = {2023}
}

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