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2.16.4 First order upwind advection

Although the upwind scheme is the underlying scheme for the robust or non-linear methods given later, we haven't actually supplied this method for general use. It would be very diffusive and it is unlikely that it could ever produce more useful results than the positive higher order schemes.

Upwind bias is introduced into many schemes using the abs function and is allows the first order upwind flux to be written:

$\displaystyle F_x$ $\displaystyle =$ $\displaystyle U \overline{ \tau }^i - \frac{1}{2} \vert U\vert \delta_i \tau$ (2.184)
$\displaystyle F_y$ $\displaystyle =$ $\displaystyle V \overline{ \tau }^j - \frac{1}{2} \vert V\vert \delta_j \tau$ (2.185)
$\displaystyle F_r$ $\displaystyle =$ $\displaystyle W \overline{ \tau }^k - \frac{1}{2} \vert W\vert \delta_k \tau$ (2.186)

If for some reason, the above method is required, then the second order flux limiter scheme described later reduces to the above scheme if the limiter is set to zero.

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Next: 2.17 Non-linear advection schemes Up: 2.16 Linear advection schemes Previous: 2.16.3 Centered fourth order   Contents
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