Publication Details

Category Text Publication
Reference Category Book chapters
DOI 10.1063/1.4825924
Title (Primary) Automatic time stepping with Newton-Raphson method for two-phase fluid flow in porous media
Title (Secondary) Proceedings of the 11th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM-2013), Rhodes, GR
Author Wang, W. ORCID logo ; Taron, J; Görke, U.-J.; Kolditz, O. ORCID logo
Publisher Simos, T.; Psihoyios, G.; Tsitouras, C.
Source Titel AIP Conference Proceedings
Year 2013
Department ENVINF
Volume 1558
Page From 1986
Page To 1988
Language englisch
Keywords Automatic time stepping; Newton-Raphson method; two-phase flow; porous media
UFZ wide themes RU5;
Abstract In the numerical simulations of flow in partially saturated porous media, high computational efficiency is an essential requirement when large scale applications such as the fluid flow field in a CO2 storage repository, are under consideration. In the present work, our aim is to enhance the computational efficiency by improving numerical algorithms. To this purpose, we apply a theoretically based time stepping method for the partial differential equations of fluid flow in partially saturated porous media. The time stepping method is embedded with automatic control and integrated into the Newton-Raphson linearization.With the time stepping method, the prediction of time step size depends upon the errors of the solutions between two successive nonlinear iterations and the solutions between two successive time steps. A good nonlinear convergence means small error in nonlinear iteration and therefore leads to an adequate time step size prediction. In the present study we linearize the two-phase flow equations with analytical Jacobians for the finite element discretization of their weak forms. The analytical Jacobian is suited for any material model and produces quadratic nonlinear convergence for commonly used models such as van Genuchten and Brooks-Corey. An example of modeling a 3D CO2 storage model is presented to demonstrate the computational behavior and the efficiency of the time stepping method.
Persistent UFZ Identifier https://www.ufz.de/index.php?en=20939&ufzPublicationIdentifier=14231
Wang, W., Taron, J, Görke, U.-J., Kolditz, O. (2013):
Automatic time stepping with Newton-Raphson method for two-phase fluid flow in porous media
In: Simos, T., Psihoyios, G., Tsitouras, C. (eds.)
Proceedings of the 11th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM-2013), Rhodes, GR
AIP Conference Proceedings 1558
AIP Press, Woodbury, NY, p. 1986 - 1988 10.1063/1.4825924