Governing equations on differential form: Difference between revisions

From Flowpedia
Line 96: Line 96:
==== Summary ====
==== Summary ====


\noindent The governing equations for compressible inviscid flow on partial differential form:\\
The governing equations for compressible inviscid flow on partial differential form:


\[\frac{\partial \rho}{\partial t} + \nabla\cdot(\rho\mathbf{v})=0\]
<math display="block">
\frac{\partial \rho}{\partial t} + \nabla\cdot(\rho\mathbf{v})=0
</math>


\[\frac{\partial}{\partial t}(\rho \mathbf{v}) + \nabla\cdot(\rho \mathbf{v}\mathbf{v}) + \nabla p = \rho \mathbf{f}\]
<math display="block">
\frac{\partial}{\partial t}(\rho \mathbf{v}) + \nabla\cdot(\rho \mathbf{v}\mathbf{v}) + \nabla p = \rho \mathbf{f}
</math>


\[\frac{\partial}{\partial t}(\rho e_o) + \nabla\cdot(\rho h_o\mathbf{v}) = \rho\mathbf{f}\cdot\mathbf{v} + \dot{q}\rho\]
<math display="block">
\frac{\partial}{\partial t}(\rho e_o) + \nabla\cdot(\rho h_o\mathbf{v}) = \rho\mathbf{f}\cdot\mathbf{v} + \dot{q}\rho
</math>


=== The Differential Equations on Non-Conservation Form ===
=== The Differential Equations on Non-Conservation Form ===