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The Performance of a Semi-Lagrangian Transport Scheme for the Advection–Condensation Problem

Pierre PellerinCooperative Centre for Mesoscale Meteorology and Department of Physics, University of Québec at Montréal, Montreal, Quebec, Canada

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René LapriseCooperative Centre for Mesoscale Meteorology and Department of Physics, University of Québec at Montréal, Montreal, Quebec, Canada

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Isztar ZawadzkiCooperative Centre for Mesoscale Meteorology and Department of Physics, University of Québec at Montréal, Montreal, Quebec, Canada

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Abstract

A series of numerical experiments are carried out solving a coupled set 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 transport schemes. Some monotonic transport constraints are experimented with. These tests confirm, for an SL transport, the statement first enunciated by Grabowski and Smoladdewicz within the context of Eulerian transport that monotonic transport constraints are not sufficient to prevent the development of false ripples when integrating coupled field equations. A constraint is developed and successfully applied to the simplified advection–condensation problem. A two dimensional dynamical model based on the fully elastic equations solved with a semi-implicit semi-Lagrangian scheme is used to simulate the classical moist bubble convection problem; these SL solutions are compared to published results obtained with Eulerian models.

These experiments show that 1) the original (unconstrained) SL transport scheme does produce some small ripples, 2) these ripples are smaller than with most Eulerian schemes, but 3) they may be amplified through the interaction with the condensation process when abrupt concentration changes occur; however, 4) in most applications, these ripples do not seem to contaminate unduly the results of SL simulations.

Abstract

A series of numerical experiments are carried out solving a coupled set 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 transport schemes. Some monotonic transport constraints are experimented with. These tests confirm, for an SL transport, the statement first enunciated by Grabowski and Smoladdewicz within the context of Eulerian transport that monotonic transport constraints are not sufficient to prevent the development of false ripples when integrating coupled field equations. A constraint is developed and successfully applied to the simplified advection–condensation problem. A two dimensional dynamical model based on the fully elastic equations solved with a semi-implicit semi-Lagrangian scheme is used to simulate the classical moist bubble convection problem; these SL solutions are compared to published results obtained with Eulerian models.

These experiments show that 1) the original (unconstrained) SL transport scheme does produce some small ripples, 2) these ripples are smaller than with most Eulerian schemes, but 3) they may be amplified through the interaction with the condensation process when abrupt concentration changes occur; however, 4) in most applications, these ripples do not seem to contaminate unduly the results of SL simulations.

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