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anchor | ProxyBLSolution |
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alignment | left |
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x_D(s) = \begin{cases}\dot f(s) \cdot t_D, & \mbox{if } s < s^*\\1- \dot f(s) \cdot t_D, & \mbox{if } s \geq s^*\end{cases}
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where
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body | --uriencoded--\displaystyle \dot f(s) = \frac%7Bd f%7D%7Bds%7D |
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| first derivative of the fractional flow function |
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body | --uriencoded--\displaystyle \ddot f(s) = \frac%7Bd%5e2 f%7D%7Bds%5e2%7D |
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| second derivative of the fractional flow function |
Algebraic equation
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can be used to find a solution of
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in terms of saturation over time and distance:
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