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By Reinhard Hinkelmann

Numerical simulation types became crucial in hydro- and environmental sciences and engineering. This monograph provides a basic advent to numerical simulation in setting water in accordance with the answer of the equations for groundwater circulation and shipping tactics, for multiphase and multicomponent circulate and delivery approaches within the subsurface in addition to for circulation and delivery procedures 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 tools and adaptive equipment in addition to quick solvers with specific concentrate on explaining the interactions of the several tools. The publication offers a short evaluation of assorted information-processing options and demonstrates the interactions of the numerical tools with the information-processing concepts so that it will in attaining effective numerical simulations for a variety of functions in setting water.

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Extra resources for Efficient Numerical Methods and Information-Processing Techniques for Modeling Hydro- and Environmental Systems

Example text

Generally, φ denotes the porosity of the porous medium which is the ratio of the void space to the whole volume. Here, φ stands for the effective porosity which only takes mobile water into account. When compared to the porosity, the effective porosity is always smaller, as it does not take water in deadend pores or bounded water at the grain surfaces into account. For smallscale considerations, there are some empirical relationships for the effective porosity; for larger scales, this parameter is unknown a priori and must be estimated (see KINZELBACH (1992 [156])).

Sharp concentration fronts. In such cases, the control volume must be subdivided into subcontrol volumes, where the continuity condition is fulfilled, and certain jump conditions must be taken into account at the discontinuity. For a unique solution of the initial boundary-value problem, initial conditions must be specified in the entire domain Ω as well as boundary conditions along the whole boundary Γ . The initial conditions describe the connection of the solution with the previous time and the initial state of the solution.

As there is often a lack of experimental data, a scaling factor pc / kφ was developed by LEVERETT (1941 [167]) to transfer known parameters, for example, to another medium with a different permeability or porosity or to another two-phase system (from water-gas to water-NAPL) with a different capillary pressure. The assumption is that the scaling factor equals the one in the other porous medium or in another two-phase system. In fractures which are discretely taken into account (see sec. 2), two different possibilities exist for the capillarity.

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