| 12 – Transformations metrics | ||
The main metrics evaluated in the CFD Sinflow Library 1.0 are that which allow us obtaining the area of the elemental volume, and it is given by the Jacobian in the center of this volume. The lengths of East-West faces are  . The lengths of North-South faces are  . |
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Therefore, to evaluate a and g at the interfaces of the elemental volumes, Eq. (3.4) and (3.5), we use the following metrics: East face of the elemental volume: |
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(12.1) |
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(12.2) |
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(12.3) |
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(12.4) |
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Points A, B, C and are the vertices of the elemental volume P of figure (12.1). |
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 Figure 12.1 – Numerical evaluation of metrics. |
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One remark should be done concerning to fictitious volumes: the metrics values at these volumes are equal to the metrics of the adjacent volumes, which belongs to the physical domain. NOTICE: - We always make an interpolation in x and y when it is necessary to evaluate data in points where these informations are not known, and never is calculated an average of the metrics (errors regarding to metric averages – [1]). The metrics in the center of the volume are also used in chapter 6 in order to calculate aP e gPand also in (14.7) and (14.8), in the evaluation of the Cartesian components of energy flux vector. |
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