A mass-conservative switching algorithm for modeling fluid flow in variably saturated porous media

作者：Zadeh Kouroush Sadegh^*

来源：Journal of Computational Physics, 2011, 230(3): 664-679.

DOI：10.1016/j.jcp.2010.10.011

• Fluid mechanics
• Richards equation
• Finite element method (FEM)
• Finite difference method (FDM)
• Adaptive time-stepping
• Picard one-point iteration method

Numerical solutions of flow equation in fluid content-based form or in fluid pressure head-based form are often tradeoffs between speed, accuracy, and convenience. The fluid-content based form can be solved quite rapidly with low CPU time and perfect mass balance. However, it cannot be used in saturated regions (as diffusivity function becomes infinite) and strictly becomes invalid in composite, layered, and real heterogeneous porous materials, due to singularity and discontinuity in fluid content profile. This formulation also gives misleading impression that gradient in fluid content causes the flow of fluid in porous materials, where in reality gravity and fluid pressure potential gradient produce the motion. The pressure head-based form, on the other hand, is more flexible but due to its highly nonlinear nature is much more time-consuming and produces poor global mass balance for dry initial conditions. Very fine spatial and temporal discretizations are needed to maintain mass balance property for these scenarios. The mixed form of the flow equation partially solves these issues as it maintains acceptable mass balance and is applicable to layered, heterogeneous, and composite fractured foundations. However, it is only applicable in unsaturated zones. In this study, a switching algorithm was proposed and implemented in which the mass conservative mixed form and the pressure head-based form were, respectively, used in the unsaturated and saturated zones of an initial-boundary value flow problem involving a variably saturated porous medium. The algorithm showed excellent agreement with a reference solution, obtained on a very fine spatiotemporal mesh. The simulator was then calibrated with several real-world large-scale experimental datasets. In all cases, the proposed algorithm exhibited close agreements with the experimental time-space series. The algorithm poses excellent mass balance property and can easily be used in both saturated and unsaturated regions without special treatment of fluid content discontinuities in heterogeneous and layered porous media. The proposed algorithm can also be extended to simulate multiphase and multidimensional flow problems.

• 出版日期2011-2-1