Development of a discontinuous approach for modeling fluid flow in heterogeneous media using the numerical manifold method

Hu, Mengsu; Wang, Yuan; Rutqvist, Jonny

doi:10.1002/nag.2390

Development of a discontinuous approach for modeling fluid flow in heterogeneous media using the numerical manifold method

Journal Article · Thu Jun 04 04:00:00 EDT 2015 · International Journal for Numerical and Analytical Methods in Geomechanics

DOI:https://doi.org/10.1002/nag.2390· OSTI ID:1400925

Hu, Mengsu ^[1]; Wang, Yuan ^[1]; Rutqvist, Jonny ^[2]

College of Civil and Transportation Engineering Hohai University Nanjing 210098 China, Earth Sciences Division Lawrence Berkeley National Laboratory Berkeley CA 94720 U.S.A.
Earth Sciences Division Lawrence Berkeley National Laboratory Berkeley CA 94720 U.S.A.

Summary

In the numerical modeling of fluid flow in heterogeneous geological media, large material contrasts associated with complexly intersected material interfaces are challenging, not only related to mesh discretization but also for the accurate realization of the corresponding boundary constraints. To address these challenges, we developed a discontinuous approach for modeling fluid flow in heterogeneous media using the numerical manifold method (NMM) and the Lagrange multiplier method (LMM) for modeling boundary constraints. The advantages of NMM include meshing efficiency with fixed mathematical grids (covers), the convenience of increasing the approximation precision, and the high integration precision provided by simplex integration. In this discontinuous approach, the elements intersected by material interfaces are divided into different elements and linked together using the LMM. We derive and compare different forms of LMMs and arrive at a new LMM that is efficient in terms of not requiring additional Lagrange multiplier topology, yet stringently derived by physical principles, and accurate in numerical performance. To demonstrate the accuracy and efficiency of the NMM with the developed LMM for boundary constraints, we simulate a number of verification and demonstration examples, involving a Dirichlet boundary condition and dense and intersected material interfaces. Last, we applied the developed model for modeling fluid flow in heterogeneous media with several material zones containing a fault and an opening. We show that the developed discontinuous approach is very suitable for modeling fluid flow in strongly heterogeneous media with good accuracy for large material contrasts, complex Dirichlet boundary conditions, or complexly intersected material interfaces. Copyright © 2015 John Wiley & Sons, Ltd.

View Accepted Manuscript (Publisher)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 1400925

Journal Information:: International Journal for Numerical and Analytical Methods in Geomechanics, Journal Name: International Journal for Numerical and Analytical Methods in Geomechanics Journal Issue: 17 Vol. 39; ISSN 0363-9061

Publisher:: Wiley Blackwell (John Wiley & Sons)Copyright Statement

Country of Publication:: United Kingdom

Language:: English

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