Adaptive discontinuous Galerkin methods for coupled diffusion- And advection-dominated transport phenomena

Adaptive discontinuous Galerkin methods are formulated to solve reactive transport problems, in particular to simulate the coupled diffusion- and advectiondominated phenomena. Numerical results demonstrate that the flexibility of discontinuous Galerkin methods on treating nonconforming meshes can lead to an efficient and effective implementation of dynamic mesh adaptation. In addition, the dynamic approaches resolve time-dependent transport adequately without slope limiting for both long-term and short-term simulations. Moreover, mass conservation is retained locally during dynamic mesh modification. Comparison studies indicate that the anisotropic mesh adaptation provides more efficient meshes and less numerical diffusion than isotropic approaches for problems involving thin layer phenomena.