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.

翻译：针对各向异性平流-扩散方程，我们提出一种非线性结构保持高阶格式。该格式基于混合高阶方法，可适用于一般网格，并具有熵结构且保持解的正性。数值模拟表明，该格式在保持正性和长时间行为的同时，以预期阶数收敛。