Difference between revisions of "Template:Equations of motion time domain without body condition"
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Laplace's equation through out the fluid | Laplace's equation through out the fluid | ||
<center><math> | <center><math> | ||
− | \Delta\Phi\left( \mathbf{x,}t\right) =0,\ \ \mathbf{x}\in\Omega | + | \Delta\Phi\left( \mathbf{x,}t\right) =0,\ \ \mathbf{x}\in\Omega. |
</math></center> | </math></center> | ||
At the bottom surface we have no flow | At the bottom surface we have no flow | ||
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and the dynamic condition (the linearized Bernoulli equation) | and the dynamic condition (the linearized Bernoulli equation) | ||
<center><math> | <center><math> | ||
− | \zeta = -\partial_{t}\Phi,\ \ z=0,\ x\in F | + | \zeta = -\partial_{t}\Phi,\ \ z=0,\ x\in F. |
</math></center> | </math></center> |
Revision as of 11:31, 21 August 2009
The equations of motion in the time domain, in non-dimensional form, so that gravity is unity, are Laplace's equation through out the fluid
At the bottom surface we have no flow
At the free surface we have the kinematic condition
and the dynamic condition (the linearized Bernoulli equation)