An investigation of various Eulerian-Lagrangian localized adjoint methods and Lagrangian-Eulerian finite element methods to solve transport problems

摘要

Highly nonlinear advection-dispersion-reactive equations govern numerous transport phenomena in subsurface media. Accurate, efficient and robust algorithms to solve these equations hold the key to the success of applying numerical models to field problems. The primary purpose of this paper was to inquire about the feasibility of several computational algorithms to approximate the highly nonlinear transport equations of multiphase flow and reactive chemical transport: the Lagrangian-Eulerian decoupling method with an adaptive ZOOMing and Peak/valley Capture (LEZOOMPC) scheme, the Eulerian-Lagrangian Localized Adjoint Method (ELLAM), and the ELLAM-LEZOOMPC algorithm. The intent of the combined algorithm is to optimize the advantages of both LEZOOMPC and ELLAM, having ELLAM inherent property of mass conservation, which is due to the systematic treatment of boundary, and the unique feature of LEZOOMPC, the adaptive mechanism. First, the accuracy and efficiency of the algorithms are compared using two simple one-dimension linear problems. Simulation results indicated that all three methods yield accurate simulations for either initial value or boundary value problem. Except for pure advection cases, ELLAM generated slight peak clipping and numerical spreading. The average CPU time per step illustrated that the efficiency of the three algorithms was LEZOOMPC > ELLAM-LEZOOMPC > ELLAM. So that ELLAM-LEZOOMPC improves ELLAM in both accuracy and efficiency. Second, the robust of the schemes were accessed. Both ELLAM and ELLAM-LEZOOMPC generated small negative concentration. Only LEZOOMPC did not give spurious oscillation. Because of the adaptive mechanism, inherent mass-conservation property and systematic treatment of boundary condition, ELLAM-LEZOOMPC is a feasible method to be used where slight oscillation does not pose numerical difficulties.