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lines changed Original file line number Diff line number Diff line change @@ -55,7 +55,7 @@ $k+1$ appears as:
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\begin {align*}
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\Uc ^{m+1 ,(k+1 )} = \Uc ^{m,(k+1 )}
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- &+ \delta t_m\left [\Advs {\Uc ^{m,(k+1 )}} - \Advs {\Uc ^{m,(k)}}\right ] + \\
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+ &+ \delta t_m\left [\Advs {\Uc ^{m,(k+1 )}} - \Advs {\Uc ^{m,(k)}}\right ] \\
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&+ \delta t_m\left [\Rbs {\Uc ^{m+1 ,(k+1 )}} - \Rbs {\Uc ^{m+1 ,(k)}}\right ]\\
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&+ \int _{t^m}^{t^{m+1 }}\Advs {\Uc ^{(k)}} + \Rbs {\Uc ^{(k)}}d\tau .
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\end {align*}
@@ -105,13 +105,13 @@ Both SDC formulations result in an ODE system of the form:
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.. math ::
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- \frac {d\Uc }{dt} = \Rb (\Uc ) + \mbox {advective terms}
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+ \frac {d\Uc ^ \prime }{dt} = \Rb (\Uc ^ \prime ) + \mbox {advective terms}
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- where $\U c$ is only
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+ where $\U c^ \p rime $ is only
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.. math ::
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- \Uc = \left ( \begin {array}{c} \rho X_k \\ \rho e \end {array} \right )
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+ \Uc ^ \prime = \left ( \begin {array}{c} \rho X_k \\ \rho e \end {array} \right )
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since those are the only components with reactive sources.
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The ``SDC `` burner includes storage for the advective terms.
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