Title

An Adaptive Local Grid Refinement And Peak/Valley Capture Algorithm To Solve Nonlinear Transport Problems With Moving Sharp-Fronts

Keywords

Adaptive local grid refinement; Burger equation; Lagrangian-Eulerian decoupling method with an adaptive ZOOMing and Peak/valley Capture (LEZOOMPC); Multiphase flow; Nonlinear advection-dispersion-reaction equations; Peak/valley capturing

Abstract

Highly nonlinear advection-dispersion-reaction equations govern numerous transport phenomena. Robust, accurate, and efficient algorithms to solve these equations hold the key to the success of applying numerical models to field problems. This paper presents the development and verification of a computational algorithm to approximate the highly nonlinear transport equations of reactive chemical transport and multiphase flow. The algorithm was developed based on the Lagrangian-Eulerian decoupling method with an adaptive ZOOMing and Peak/valley Capture (LEZOOMPC) scheme. It consists of both backward and forward node tracking, rough element determination, peak/valley capturing, and adaptive local grid refinement. A second-order tracking was implemented to accurately and efficiently track all fictitious particles. Shanks' method was introduced to deal with slowly converging case. The accuracy and efficiency of the algorithm were verified with the Burger equation for a variety of cases. The robustness of the algorithm to achieve convergent solutions was demonstrated by highly nonlinear reactive contaminant transport and multiphase flow problems. © Springer Science+Business Media B.V. 2007.

Publication Date

3-1-2008

Publication Title

Transport in Porous Media

Volume

72

Issue

1

Number of Pages

53-69

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s11242-007-9135-2

Socpus ID

39049089483 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/39049089483

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