Anisotropic and dynamic mesh adaptation for discontinuous Galerkin methods applied to reactive transport

Mesh adaptation strategies are proposed for discontinuous Galerkin methods applied to reactive transport problems, with emphasis on dynamic and anisotropic adaptation. They include an anisotropic mesh adaptation scheme and two isotropic methods using an L²(L²) norm error estimator and a hierarchic error indicator. These dynamic mesh adaptation approaches are investigated using benchmark cases. Numerical results demonstrate that the three approaches resolve time-dependent transport adequately without slope limiting for both long-term and short-term simulations. It is shown that these results apply to problems where either diffusion or advection dominates in different subdomains. Moreover, for these schemes, mass conservation is retained locally during dynamic mesh modification. Comparison studies indicate that the anisotropic mesh adaptation provides the most efficient meshes and has the least numerical diffusion among the three adaptation approaches.