Büsing, H. and Willkomm, J. and Bischof, Christian and Clauser, C. (2011):
Using exact Jacobians in an implicit Newton method for solving multiphase flow in porous media.
In: Int. J. Computational Science and Engineering, Inderscience, ISSN 1742-7185,
[Article]
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 favourable 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 CO2 sequestration scenario.
| Item Type: | Article |
|---|---|
| Erschienen: | 2011 |
| Creators: | Büsing, H. and Willkomm, J. and Bischof, Christian and Clauser, C. |
| Title: | Using exact Jacobians in an implicit Newton method for solving multiphase flow in porous media |
| Language: | English |
| 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 favourable 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 CO2 sequestration scenario. |
| Journal or Publication Title: | Int. J. Computational Science and Engineering |
| Publisher: | Inderscience |
| Uncontrolled Keywords: | multiphase flow; porous media; implicit Newton method; exact Jacobians; automatic differentiation; CO2 sequestration; ADiMat; Matlab |
| Divisions: | 20 Department of Computer Science 20 Department of Computer Science > Scientific Computing |
| Date Deposited: | 16 May 2013 11:28 |
| Additional Information: | to appear |
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