By Ekkehard Holzbecher
The publication has goals: to introduce simple innovations of environmental modeling and to facilitate the appliance of the thoughts utilizing glossy numerical instruments similar to MATLAB and FEMLAB. it's detailed in any respect typical scientists facing the surroundings: technique and chemical engineers, physicists, chemists, biologists, biochemists, hydrogeologists, geochemists and ecologists. FEMLAB is a common supplement to MATLAB, because it is a distinct instrument for these projects which can't be played with the elemental MATLAB software.
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Example text
C = -1 Inf 3 2 Obviously, in three entries the element-wise division is performed. In the second entry of the first row Inf stands for infinity, which is the result of a division by zero8 . /A C = 1 1 1 1 The matrix with entries 1 everywhere is the unit matrix of pointwise matrix multiplication. 8) ⎝· · · ··· ··· ···⎠ 0 0 ··· 1 This matrix is a diagonal matrix, as there are non-zero elements only in the main diagonal from the top left to the bottom right. The unit matrix within the matrix algebra corresponds to the 1 in usual multiplications using 8 In contrast to school knowledge, division by zero is allowed in MATLAB R .
2 Modeling Steps 31 differential equations by computational methods and finally to perform postprocessing tasks. A schematic overview of the procedure is given in Fig. 1 (see also: Holzbecher 1998). At first a conceptual model has to be formulated. From the available scientific and technical expertise and knowledge, as well as the experience with observations of the system in question, a concept has to be set up. The concept involves all processes, which could be relevant for the studied system. e.
The concentration also has the unit [M/L ] and measures the mass within a volume of fluid. The content of chloride Cl− in seawater amounts to 19 g/l. One has to extend the mass definition in situations, where the fluid does not fill the entire volume. Then the total mass per space volume is expressed by θc with porosity θ as additional factor. Porosity is dimensionless and measures the volumetric share of the fluid phase on the total volume. The physical 3 dimension of the product is thus further [M/L ].