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lines changed Original file line number Diff line number Diff line change @@ -837,6 +837,21 @@ \section{Errors and convergence rate}
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\hydroexdoit {\href {https://github.com/zingale/hydro_examples/blob/master/advection/advection.py}{advection.py}}}
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\end {figure }
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+ \begin {figure }[ht]
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+ \centering
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+ \includegraphics [width=0.8\linewidth ]{fv-gaussian-limiters} \\ [1em]
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+ \includegraphics [width=0.8\linewidth ]{fv-tophat-limiters}
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+ \caption [Effect of different limiters on evolution]
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+ {\label {fig:limiter_panel } The effect of different limiters on the
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+ evolution of a Gaussian initial profile (top) and a tophat initial
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+ profile (bottom), using $ C = 0.8 $ and 5 periods. \\
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+ \hydroexdoit {\href {https://github.com/zingale/hydro_examples/blob/master/advection/advection.py}{advection.py}}}
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+ \end {figure }
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+
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+ As seen in figure~\ref {fig:advnorm }, the choice of limiters can have a great
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+ effect on the accuracy. Figure~\ref {fig:limiter_panel } shows the Gaussian and
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+ tophat profiles with several different limiters.
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+
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\section {Multi-dimensional advection }
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The two-dimensional linear advection equation is:
Original file line number Diff line number Diff line change @@ -202,7 +202,7 @@ \section{Burgers' equation}
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\begin {exercise }[Simple Burgers' solver]
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{Extend your 1-d finite-volume solver for advection (from
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- Exercise~\ref {adv:ex:fv }) to solver Burgers' equation. You will
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+ Exercise~\ref {adv:ex:fv }) to solve Burgers' equation. You will
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need to change the Riemann solver and use the local velocity in the
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construction of the interface states. Run the examples shown in
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Figures~\ref {fig:burgers-rarefaction } and \ref {fig:burgers-shock }}.
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