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Copy file name to clipboardExpand all lines: doc/.src/chapters/advec/advec.do.txt
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FIGURE: [fig-advec/gaussian_LF_C08, width=800 frac=1] Advection of a Gaussian function with a leapfrog scheme and $C=0.8$, $\Delta t = 0.001$ (left) and $\Delta t=0.01$ (right). label{advec:1D:LF:fig1:C08}
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MOVIE: [https://raw.githubusercontent.com/hplgit/fdm-book/master/doc/pub/book/html/mov-advec/gaussian/LF/C08_dt01.ogg] Advection of a Gaussian function with a leapfrog scheme and $C=0.8$, $\Delta t = 0.01$. label{advec:1D:LF:mov1:C08:dt1}
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MOVIE: [https://raw.githubusercontent.com/hplgit/fdm-book/master/doc/pub/book/html/mov-advec/gaussian/LF/C08_dt001.ogg] Advection of a Gaussian function with a leapfrog scheme and $C=0.8$, $\Delta t = 0.001$. label{advec:1D:LF:mov1:C08:dt2}
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Advection of the Gaussian function with a leapfrog scheme, using $C=0.8$ and $\Delta t = 0.01$ can be seen in a "movie file":
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"${docraw}/mov-advec/gaussian/LF/C08_dt01.ogg". Alternatively, with $\Delta t = 0.001$, we get this "movie file":
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"${docraw}/mov-advec/gaussian/LF/C08_dt001.ogg".
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FIGURE: [fig-advec/cosinehat_LF_C08, width=800 frac=1] Advection of half a cosine function with a leapfrog scheme and $C=0.8$, $\Delta t = 0.001$ (left) and $\Delta t=0.01$ (right). label{advec:1D:LF:fig2:C08}
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MOVIE: [https://raw.githubusercontent.com/hplgit/fdm-book/master/doc/pub/book/html/mov-advec/cosinehat/UP/C08_dt01.ogg] Advection of half a cosine function with a leapfrog scheme and $C=0.8$, $\Delta t = 0.01$. label{advec:1D:LF:mov2:C08:dt1}
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MOVIE: [https://raw.githubusercontent.com/hplgit/fdm-book/master/doc/pub/book/html/mov-advec/cosinehat/UP/C08_dt001.ogg] Advection of half a cosine function with a leapfrog scheme and $C=0.8$, $\Delta t = 0.001$. label{advec:1D:LF:mov2:C08:dt2}
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Advection of the cosine hat function with a leapfrog scheme, using $C=0.8$ and $\Delta t = 0.01$ can be seen in a "movie file":
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"${docraw}/mov-advec/cosinehat/LF/C08_dt01.ogg". Alternatively, with $\Delta t = 0.001$, we get this "movie file":
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"${docraw}/mov-advec/cosinehat/LF/C08_dt001.ogg".
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=== Analysis ===
@@ -424,15 +424,13 @@ error.
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FIGURE: [fig-advec/gaussian_UP_C08, width=800 frac=1] Advection of a Gaussian function with a forward in time, upwind in space scheme and $C=0.8$, $\Delta t = 0.01$ (left) and $\Delta t=0.001$ (right). label{advec:1D:UP:fig1:C08}
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MOVIE: [mov-advec/gaussian/UP/C08_dt001/movie.ogg] Forward in time, upwind in space, $C=0.8$, $\Delta t = 0.01$. label{advec:1D:UP:mov1:C08:dt1}
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MOVIE: [mov-advec/gaussian/UP/C08_dt001/movie.ogg] Forward in time, upwind in space, $C=0.8$, $\Delta t = 0.005$. label{advec:1D:UP:mov1:C08:dt2}
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Advection of the Gaussian function with a with a forward in time, upwind in space scheme, using $C=0.8$ and $\Delta t = 0.01$ can be seen in a "movie file":"${docraw}/mov-advec/gaussian/UP/C08_dt001/movie.ogg". Alternatively, with $\Delta t = 0.005$, we get this "movie file":
FIGURE: [fig-advec/cosinehat_UP_08, width=800 frac=1] Advection of half a cosine function with a forward in time, upwind in space scheme and $C=0.8$, $\Delta t = 0.001$ (left) and $\Delta t=0.01$ (right). label{advec:1D:UP:fig2:C08}
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MOVIE: [mov-advec/cosinehat/UP/C08_dt01.ogg] Advection of half a cosine function with a forward in time, upwind in space scheme and $C=0.8$, $\Delta t = 0.01$. label{advec:1D:UP:mov2:C08:dt1}
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MOVIE: [mov-advec/cosinehat/UP/C08_dt001.ogg] Advection of half a cosine function with a forward in time, upwind in space scheme and $C=0.8$, $\Delta t = 0.001$. label{advec:1D:UP:mov2:C08:dt2}
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Advection of the cosine hat function with a with a forward in time, upwind in space scheme, using $C=0.8$ and $\Delta t = 0.01$ can be seen in a "movie file":"${docraw}/mov-advec/cosinehat/UP/C08_dt01.ogg". Alternatively, with $\Delta t = 0.001$, we get this "movie file":
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"${docraw}/mov-advec/cosinehat/UP/C08_dt001.ogg".
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The amplification factor can be computed using the
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