Multi-scale numerical simulation of a tsunami using mesh adaptive methods

Mesh adaptive methods are typically categorised as either h-adaptive or r-adaptive. In two dimensions, the former involve operations altering the number of mesh degrees of freedom by the insertion or deletion of element edges, while the latter hold both the number of degrees of freedom and the mesh topology fixed and redistribute mesh
entities (vertices, edges and elements) geometrically. Anisotropic mesh adaptivity seeks to incorporate aspects of both h- and r-adaptivity, providing a hybrid (hr) approach. As such, anisotropic mesh adaptivity benefits from the h-adaptive ability to completely regenerate a mesh before it gains tangled nodes, as well as the r-adaptive ability to allow degrees of freedom to follow features of fluid flow, such as a tsunami wave. A hybrid mesh adaptive approach is ideal for tsunami problems, since the important features we would like to accurately resolve are clustered in a relatively small region of ocean, which itself moves as time progresses. A standalone finite element shallow water solver is constructed for solving tsunami modelling problems, along with an anisotropic mesh adaptivity library capable of adaption both to fields related to the flow (such as fluid speed) and as guided by adjoint solution data.