Advection-Dispersion with Adaptive Eulerian-Lagrangian Finite Elements

Abstract

Advection-dispersion is generally solved numerically with methods that treat the problem from one of three perspectives. These are described as the Eulerian reference, the Lagrangian reference or a combination of the two that will be referred to as Eulerian-Lagrangian. Methods that use the Eulerian-Lagrangian approach incorporate the computational power of the Lagrangian treatment of advection with the simplicity of the fixed Eulerian grid. A modified version of a relatively new adaptive Eulerian-Lagrangian finite element method is presented for the simulation of advection-dispersion. In the vicinity of steep concentration fronts, moving particles are used to define the concentration field. A modified method of characteristics called single-step reverse particle tracking is used away from steep concentration fronts. An adaptive technique is used to insert and delete moving particles as needed during the simulation. Dispersion is simulated by a finite element formulation that involves only symmetric and diagonal matrices. Based on preliminary tests on problems with analytical solutions, the method seems capable of simulating the entire range of Peclet numbers with Courant numbers well in excess of 1.