A positivity-preserving ALE finite element scheme for convection-diffusion equations in moving domains
A new high-resolution scheme is developed for convection-diffusion problems in domains with moving boundaries. A finite element approximation of the governing equation is designed within the framework of a conservative Arbitrary Lagrangian Eulerian (ALE) formulation. An implicit flux-corrected transport (FCT) algorithm is implemented to suppress spurious undershoots and overshoots appearing in convection-dominated problems. A detailed numerical study is performed for P(1) finite element discretizations on fixed and moving meshes. Simulation results for a Taylor dispersion problem (moderate Peclet numbers) and for a convection-dominated problem (large Peclet numbers) are presented to give a flavor of practical applications. (C) 2011 Elsevier Inc. All rights reserved.
finite elements convection-diffusion equation moving boundaries flux-corrected transport conservative ale formulation