Difference between revisions of "Governing equations"

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===Stokes Equations===
In Cartesian coordinates, the Stokes equations are given by,
  & x:\quad \frac{\partial \tau _{xx}}{\partial x}-\frac{\partial P}{\partial x}+\frac{\partial \tau _{xy}}{\partial y}+\frac{\partial \tau _{xz}}{\partial z}=0 \\
& y:\quad \frac{\partial \tau _{yy}}{\partial y}-\frac{\partial P}{\partial y}+\frac{\partial \tau _{xy}}{\partial x}+\frac{\partial \tau _{yz}}{\partial z}=0 \\
& z:\quad \frac{\partial \tau _{zz}}{\partial z}-\frac{\partial P}{\partial z}+\frac{\partial \tau _{zy}}{\partial y}+\frac{\partial \tau _{xz}}{\partial x}=\rho g \\
where ''P'' is the pressure and <big>&tau;</big> is the deviatoric stress tensor. The latter is given by
<big><math>\tau _{ij}=\sigma _{ij}+P\delta _{ij}</math></big>,
where <big>&sigma;</big> is the full stress tensor.
===Constitutive Relation===

Latest revision as of 22:00, 30 July 2009