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：---- 我们介绍了一种基于混合高阶方法的非线性结构保持高阶方案，用于处理各向异性平流扩散方程。该方案可以处理一般网格，具有熵结构，在保持解的正性的同时，我们展示了一些数值模拟结果，表明方案以预期的收敛阶收敛，并保持正性和长时间行为。