Numerical Simulation of Reactive Flow using SHEMAT
SHEMAT handles the following classes of problems: 1. one individual process: groundwater flow; conductive heat transport; diffusive species transport; chemical reactions; 2. two coupled processes: groundwater flow combined with heat transport; groundwate
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2.1 General SHEMAT handles the following classes of problems: 1.
one • • • •
individual process: groundwater flow; conductive heat transport; diffusive species transport; chemical reactions;
2.
two coupled processes: • groundwater flow combined with heat transport; • groundwater flow combined with species transport;
3. three or four coupled processes: • groundwater flow combined with species transport and chemical reactions; • prescribed flow, species and heat transport combined with chemical reactions; • combined groundwater flow, heat and species transport, and chemical reactions. SHEMAT uses a finite difference method to solve the partial differential equation. Three schemes available for the spatial discretization of the advection term in the transport equations: •
a pure upwind scheme;
•
the Il'in flux blending scheme;
•
the Smolarkiewicz diffusion corrected upwind scheme.
The resulting system of equations can be solved explicitly, implicitly or semiimplicitly. For implicit and semi-implicit time-weighting the sets of linear equations are solved iteratively by the strongly implicit procedure (SIP, Weinstein et
al. 1969).
C. Clauser (ed.), Numerical Simulation of Reactive Flow in Hot Aquifers © Springer-Verlag Berlin Heidelberg 2003
6
10m Bartels, Michael Kuhn, and Christoph Clauser
2.2 Governing Equations
2.2.1 General
Variables are identified when they are used the first time. For a quick reference, Table 2.1 lists the quantities and their abbreviations used in this text, and their units used in SHEMAT. Generally, vectors are indicated by bold face, and tensors by underscoring, e.g. v, K for Darcy velocity (specific discharge) and hydraulic conductivity. SHEMAT solves the flow and transport equations on a Cartesian 2-D or 3-D grid with coordinates x, y, z or, alternatively, on a 2-D vertical cylindrically symmetric grid with radius and depth coordinates rand z, respectively. Internally, the x,y,z- and r,z-coordinates are associated with indices I, J, and K and I and K, respectively. SHEMAT uses a block-centered grid, where nodes are located at the center of the grid cells. The origin of the grid is the nodal block in layer k = 1 (at the base of the grid), front left-hand comer. Layer KO is at the top of the grid, i is the column index (x-direction, from left to right), and j the row index (y-direction, from the front to the back) (Fig. 2.1). SHEMAT's graphical user interface, Processing SHEMAT deviates from this convention as it counts K from top to bottom and J from back to front. Users of the package SHEMAT / Processing SHEMAT need not be concerned with these details, however, as both conventions are being made compatible internally. These subtleties need to be kept in mind only, when in this chapter the top layer is associated with the index KO instead of 1, as is the convention used in Processing SHEMAT. The size of the grid may vary from column to column, row to row, and layer to layer. However, the dimension of adjacent nodal blocks should not differ by more than a factor of 1.5.
k
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