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：我们提出了一种用于各向异性对流扩散方程的非线性保结构高阶格式。该格式基于混合高阶方法，可处理一般网格。它同时具有熵结构，并保持解的正性。我们给出了一些数值模拟结果，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。