Publication: Using Exact Jacobians in an Implicit Newton Method for Solving Multiphase Flow in Porous Media
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Using Exact Jacobians in an Implicit Newton Method for Solving Multiphase Flow in Porous Media

- Article in a journal -
 

Area
Geophysics

Author(s)
Henrik Büsing , Johannes Willkomm , Christian H. Bischof , Christoph Clauser

Published in
International Journal of Computational Science and Engineering

Year
2014

Abstract
We present a new numerical approach to solve the fully coupled equations for two-phase flow in porous media with exact Jacobians. The method is based on a space and time discretisation and a linearisation of the arising non-linear algebraic system with Newton's method, where the required Jacobians are obtained with automatic differentiation (ad), providing the exact derivatives. We compare the forward ad differentiation mode to the standard finite difference method and the complex variable method in terms of precision and performance. It turns out that ad performs favourably compared to both methods. We also illustrate the advantages of exact Jacobians in a test example for two-phase flow in porous media investigating the evolution of pressure and saturation in a CO_2 sequestration scenario.

AD Tools
ADiMat

BibTeX
@ARTICLE{
         Busing2014UEJ,
       ad_tools = "ADiMat",
       abstract = "We present a new numerical approach to solve the fully coupled equations for
         two-phase flow in porous media with exact Jacobians. The method is based on a space and time
         discretisation and a linearisation of the arising non-linear algebraic system with Newton's
         method, where the required Jacobians are obtained with automatic differentiation (AD), providing the
         exact derivatives. We compare the forward AD differentiation mode to the standard finite difference
         method and the complex variable method in terms of precision and performance. It turns out that AD
         performs favourably compared to both methods. We also illustrate the advantages of exact Jacobians
         in a test example for two-phase flow in porous media investigating the evolution of pressure and
         saturation in a $CO_2$ sequestration scenario.",
       author = "B{\"u}sing, Henrik and Willkomm, Johannes and Bischof, Christian H. and
         Clauser, Christoph",
       title = "Using Exact {J}acobians in an Implicit {N}ewton Method for Solving Multiphase Flow in
         Porous Media",
       journal = "International Journal of Computational Science and Engineering",
       volume = "9",
       number = "5/6",
       year = "2014",
       pages = "499--508",
       url = "http://dx.doi.org/10.1504/IJCSE.2014.064535",
       doi = "10.1504/IJCSE.2014.064535",
       ad_area = "Geophysics"
}


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