By Reinhard Hinkelmann
Numerical simulation types became quintessential in hydro- and environmental sciences and engineering. This monograph provides a common advent to numerical simulation in setting water in line with the answer of the equations for groundwater move and delivery procedures, for multiphase and multicomponent movement and delivery strategies within the subsurface in addition to for stream and delivery strategies in floor waters. It screens intimately the state-of-the-art of discretization and stabilization tools (e.g. Finite-Difference, Finite-Element and Finite-Volume Methods), parallel equipment and adaptive equipment in addition to quick solvers with specific specialize in explaining the interactions of the various equipment. The e-book provides a short evaluate of assorted information-processing ideas and demonstrates the interactions of the numerical tools with the information-processing recommendations with a view to in achieving effective numerical simulations for a variety of functions in surroundings water.
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Extra info for Efficient Numerical Methods and Information-Processing Techniques for Modeling Hydro- and Environmental Systems
41) In the BC model, pd stands for the entry pressure, which is the capillary pressure required to displace the wetting phase from the largest pores. The BC parameter λ characterizes the grain-size distribution. A small value describes a single grain-size material, while a large value indicates highly non-uniform material. Se denotes the eﬀective (water) saturation and Swr the residual water saturation. In the VG model, n, m = 1 − 1/n, α are form parameters characterizing the pore-space geometry.
The ﬂow and transport equation are both linear, the ﬂow equation is of elliptic or parabolic type and the transport equation is of mixed parabolic / hyper¨ bolic type. For further reading, see BEAR (1972 ), HAFNER (1992 ), LEGE et al. (1996 ), KOLDITZ (1997 ), or SCHOTTING (1998 ). 4 Mathematical model concept for two-phase ﬂow processes in the subsurface If two ﬂuid phases are not or only slightly miscible into each other, a twophase ﬂow model concept for a porous medium must be applied (see ﬁgs.
If a pressure formulation is used, the pressures of the wetting and the nonwetting phases pw and pn are the primary variables and the resulting system is of mixed parabolic / hyperbolic type. This formulation is based on an inverse function which describes the saturation depending on the capillary pressure. The inverse function only exists if the capillary-pressure gradient is greater ∂pc > 0). With such a function, the saturations can be eliminated. than zero ( ∂S w Two-phase ﬂow processes in the subsurface 43 However, in many practical examples, for example, in the case of discrete fractures or transitions between heterogeneities, the capillary pressure gradient is very small or even zero, so that the pressure formulation cannot be chosen.