Identification of diffusion parameters in a nonlinear convection–diffusion equation using the augmented Lagrangian method |
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| Authors: | T K Nilssen K H Karlsen T Mannseth X-C Tai |
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| Institution: | (1) Department of Economics and Business Administration, University of Agder, Servicebox 422, 4604 Kristiansand, Norway;(2) Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053, Blindern, 0316 Oslo, Norway;(3) Centre for Integrated Petroleum Research, P. O. Box 7800, 5020 Bergen, Norway;(4) Department of Mathematics, University of Bergen, Johannes Brunsgt. 12, 5008 Bergen, Norway |
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| Abstract: | Numerical identification of diffusion parameters in a nonlinear convection–diffusion equation is studied. This partial differential
equation arises as the saturation equation in the fractional flow formulation of the two-phase porous media flow equations.
The forward problem is discretized with the finite difference method, and the identification problem is formulated as a constrained
minimization problem. We utilize the augmented Lagrangian method and transform the minimization problem into a coupled system
of nonlinear algebraic equations, which is solved efficiently with the nonlinear conjugate gradient method. Numerical experiments
are presented and discussed.
This work was partially supported by the Research Council of Norway (NFR), under grant 128224/431. |
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| Keywords: | Parameter estimationa Inverse problems Nonlinear convection– diffusion equation Augmented Lagrangian methods Porous media flow Permeability |
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