The paper presents a linear high-order method for advection–diffusion conservation laws on three-dimensional mixed-element unstructured meshes. The key ingredient of the method is a reconstruction procedure in local computational coordinates. Numerical results illustrate the convergence rates for the linear equation and a non-linear hyperbolic system with diffusion terms for various types of meshes.
- very high-order
- Godunov-type methods
Titarev, V. A., & Drikakis, D. (2011). Uniformly high-order schemes on arbitrary unstructured meshes for advection-diffusion equations. Computers and Fluids, 46(1), 467-471. https://doi.org/10.1016/j.compfluid.2010.10.008