# Diff of /trunk/doc/user/levelset.tex

revision 3378 by caltinay, Fri Nov 12 05:55:50 2010 UTC revision 3379 by gross, Wed Nov 24 04:48:49 2010 UTC
# Line 133  into Equation (\ref{TAYLOR EXPANSION}) Line 133  into Equation (\ref{TAYLOR EXPANSION})
133  %  %
134  %where $\delta_{ij}$ is the Kronecker $\delta$-symbol, which is a matrix with ones for its diagonal entries ($i = j$) and zeros for the remaining entries ($i \neq j$). The body force $f$ in Equation (\ref{GENERAL NAVIER STOKES COM}) is the gravity acting in the $x_{3}$ direction and is given as $f = -g \rho \delta_{i3}$.  %where $\delta_{ij}$ is the Kronecker $\delta$-symbol, which is a matrix with ones for its diagonal entries ($i = j$) and zeros for the remaining entries ($i \neq j$). The body force $f$ in Equation (\ref{GENERAL NAVIER STOKES COM}) is the gravity acting in the $x_{3}$ direction and is given as $f = -g \rho \delta_{i3}$.
135  %The Stokes equations is a saddle point problem, and can be solved using a Uzawa scheme. A class called StokesProblemCartesian in Escript can be used to solve for velocity and pressure.  %The Stokes equations is a saddle point problem, and can be solved using a Uzawa scheme. A class called StokesProblemCartesian in Escript can be used to solve for velocity and pressure.
136  %In order to keep numerical stability, the time-step size needs to be below a certain value, known as the Courant number. The Courant number is defined as:  %In order to keep numerical stability, the time-step size needs to be below a certain value, known as the Courant number \index{Courant number}\index{CFL condition}. The Courant number is defined as:
137  %  %
138  %  %
139  %C = \frac{v \delta t}{h}.  %C = \frac{v \delta t}{h}.
# Line 269  The iteration throughout the time-steps Line 269  The iteration throughout the time-steps
269  the boundary conditions, viscosity, and body forces; the solving of the Stokes problem for velocity and pressure; then the  the boundary conditions, viscosity, and body forces; the solving of the Stokes problem for velocity and pressure; then the
270  level set procedure.  level set procedure.
271  The output of the level set function, velocity and pressure is saved to file.  The output of the level set function, velocity and pressure is saved to file.
272  The time-step size is selected based on the Courant condition.  The time-step size is selected based on the Courant–Friedrichs–Lewy condition (CFL condition)\index{Courant number}\index{CFL condition}.
273  Due to the number of elements in the computational mesh, the simulation may take a long time to complete on a desktop computer,  Due to the number of elements in the computational mesh, the simulation may take a long time to complete on a desktop computer,
274  so it is preferable to run it on the super computer.  so it is preferable to run it on the super computer.
275  At present, the fine mesh is required to capture the details of the fluid motion and for numerical stability.    At present, the fine mesh is required to capture the details of the fluid motion and for numerical stability.
# Line 367  while t_step <= t_step_end: Line 367  while t_step <= t_step_end:
367
368    #save interface, velocity and pressure    #save interface, velocity and pressure
369    saveVTK("phi2D.%2.4i.vtu"%t_step,interface=func,velocity=velocity,pressure=pressure)    saveVTK("phi2D.%2.4i.vtu"%t_step,interface=func,velocity=velocity,pressure=pressure)
370    #Courant condition    #CFL condition
371    dt = 0.4*Lsup(mesh.getSize())/Lsup(velocity)    dt = 0.4*Lsup(mesh.getSize())/Lsup(velocity)
372    t_step += 1    t_step += 1
373

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