Grid refinement tests of a least-squares finite element method for advective transport of reactive species

A time splitting least-squares finite element method (LSFEM) and the 'stiff ODEs' solver LSODE are used to simulate the advective transport of reactive species. Specifically, the rotating cone problem with chemical reactions serves as a model to test the algorithm. A non-linear filter is used to suppress spurious oscillations at each advective time step. All simulations are carried out by using linear and quadratic elements on two mesh systems. Results from the coarse mesh system suggest that the use of robust numerical methods alone will not be able to provide accurate results and point to the need of grid refinement. The grid refinement tests are evaluated by pollutant peak concentrations, pollutant concentration distributions, average relative errors, species mass conservation and distribution ratios and CPU times. Results from the fine mesh system are satisfactory and imply that accurate simulations of the transport of reactive species require adequate grid resolution and robust numerical methods for each individual advective and reactive step.