Refinement Indicator for Dynamic-Mesh Adaption in Three-Dimensional Shallow-Water Equation Modeling

AbstractOne of the basic articles of discretization-based numerical modeling of three-dimensional shallow water equations is the spatial convergence of the mesh utilized. The process of creating a spatially converged mesh involves refining the mesh until the solution for the quantity of interest does not change within some user-defined tolerance. This process is cumbersome in three-dimensions, and in the absence of a spatially converged mesh, the numerical results may be erroneous. This technical note introduces a norm of the three-dimensional continuity equation residual-based refinement indicator to flag regions of the mesh requiring refinement. The method is implemented through h-adaption in a finite-element method–based code and results of this implementation are presented.