Governing equations on integral form: Difference between revisions

@@ Line 217: / Line 217: @@
 ==== Summary ====
-\noindent The integral form of the governing equations for inviscid compressible flow has been derived\\
+The integral form of the governing equations for inviscid compressible flow has been derived
-\noindent Continuity:\\
+Continuity:
-\[\frac{d}{dt}\iiint_{\Omega} \rho d\mathscr{V}+\oiint_{\partial \Omega}\rho \mathbf{v}\cdot \mathbf{n} dS=0\]\\
+<math display="block">
+\frac{d}{dt}\iiint_{\Omega} \rho dV+\iint_{\partial \Omega}\rho \mathbf{v}\cdot \mathbf{n} dS=0
+</math>
-\noindent Momentum:\\
+Momentum:
-\[\frac{d}{dt}\iiint_{\Omega} \rho \mathbf{v} d\mathscr{V}+\oiint_{\partial \Omega} \left[(\rho\mathbf{v}\cdot\mathbf{n})\mathbf{v}+p\mathbf{n}\right]dS=\iiint_{\Omega}\rho \mathbf{f}d\mathscr{V}\]\\
+<math display="block">
+\frac{d}{dt}\iiint_{\Omega} \rho \mathbf{v} dV+\iint_{\partial \Omega} \left[(\rho\mathbf{v}\cdot\mathbf{n})\mathbf{v}+p\mathbf{n}\right]dS=\iiint_{\Omega}\rho \mathbf{f}dV
+</math>
-\noindent Energy:\\
+Energy:
-\[\frac{d}{dt}\iiint_{\Omega}\rho e_o d\mathscr{V}+\oiint_{\partial \Omega}\rho h_o(\mathbf{v}\cdot\mathbf{n})dS=\iiint_{\Omega}\rho\mathbf{f}\cdot\mathbf{v}d\mathscr{V}+\iiint_{\Omega} \dot{q}\rho d\mathscr{V}\]
+<math display="block">
+\frac{d}{dt}\iiint_{\Omega}\rho e_o dV+\iint_{\partial \Omega}\rho h_o(\mathbf{v}\cdot\mathbf{n})dS=\iiint_{\Omega}\rho\mathbf{f}\cdot\mathbf{v}dV+\iiint_{\Omega} \dot{q}\rho dV
+</math>

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