2 - Computing advection
Advecting generic value \(f\) along \(u\)
- Idea Compute value of \(f\) at time \(t\) at fixed position grid \(p\) in moving back at \(t-\Delta t\).
- Value of \(f\) advected at point \(p\) at time \(t\) was at position \(p_{prev}=p-\Delta t\;v(p,t)\) at time \(t-\Delta t\).
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- \(\Rightarrow f(p,t)=f(p_{prev},t-\Delta t)\)
- \(p_{prev}\) is not a grid point coordinates: Use interpolation
- Can use Bilinear interpolation
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- \(f(p_{prev})= (1-\alpha)\,(1-\beta)\;p_{00}+(1-\alpha)\,\beta\, p_{01}+\alpha\,(1-\beta)\;p_{10}+\alpha\,\beta\; p_{11} \)
