THE PERFORMANCE OF A SEMI-LAGRANGIAN TRANSPORT SCHEME FOR THE ADVECTION-CONDENSATION PROBLEM

A series of numerical experiments are carried out solving a coupled se t of equations for advection and condensation with a semi-Lagrangian ( SL) transport scheme. Canonical validation tests in one dimension show that SL suffers less numerical aberrations than many Eulerian transpo rt schemes. Some monotonic transport constraints are experimented with . These tests confirm, for an SL transport, the statement first enunci ated by Grabowski and Smolarkiewicz within the context of Eulerian tra nsport that monotonic transport constraints are not sufficient to prev ent the development of false ripples when integrating coupled field eq uations. A constraint is developed and successfully applied to the sim plified advection-condensation problem. A two-dimensional dynamical mo del based on the fully elastic equations solved with a semi-implicit s emi-Lagrangian scheme is used to simulate the classical moist bubble c onvection problem; these SL solutions are compared to published result s obtained with Eulerian models. These experiments show that 1) the or iginal (unconstrained) SL transport scheme does produce some small rip ples, 2) these ripples are smaller than with most Eulerian schemes, bu t 3) they may be amplified through the interaction with the condensati on process when abrupt concentration changes occur; however, 4) in mos t applications, these ripples do not seem to contaminate unduly the re sults of SL simulations.