Development and analysis of an adaptive transport scheme

An approach to solving the advection dominated atmospheric mass transport problem which adaptively constructs and updates the computational mesh is implemented and analyzed. The formulation of the mesh adaptation algorithm allows for information from other model processes as well as transport to influence mesh refinement. Comparisons to other methods are limited to a pure advection test problem. The scheme is based on a Petrov–Galerkin finite element method using quadratic interpolating polynomials over triangular elements. The temporal component of the transport equation is discretized using the Crank–Nicolson method. A single time step is applied to the entire domain regardless of mesh refinement levels. Two means of upwind biasing the solution via modification of the finite element weighting functions are investigated. Criteria for refining and unrefining the mesh based on advective flux and an estimate of the error are proposed and compared. The effects of varying the number of time steps taken between mesh refinements are analyzed. Results for adapted mesh solutions of a test problem are shown to be superior to corresponding uniform mesh finite element solutions. Comparisons to several other popular uniform mesh advection schemes indicate either equal or improved accuracy for the adapted mesh solutions.