Testing refinement criteria in adaptive discontinuous Galerkin simulations of dry atmospheric convection

Abstract

A method is introduced which allows one to compare the accuracy between different choices of refinement regions even in a case when the exact solution is not known. Essentially this is done by comparing features of the solution that are strongly sensitive to spatial resolution. For a rising warm air bubble the average number of elements required for the adaptive simulation is about a factor three times smaller than the number required for the simulation with the uniform fine-resolution grid. Correspondingly the adaptive simulation is almost three times faster than the uniform simulation, and the advantage of adaptive mesh refinement becomes even more pronounced for larger domains. This result suggests that adaptive mesh refinement should have significant potential for future simulations of atmospheric moist convection when the refinement criterion is chosen carefully.