Dear all,

I want to compute three-dimensional,unsteady imcompressible viscous flows with free surface. May I use the fractional step method for continuous equations and momentum equations? Because I am a beginner,I am long for your help and advice.

thanks Annie

Many people use that. What kind of methods will be used for representing the free surface?

dear Junseok Kim I appreciate your help. I plan to use VOF method to deal with the free surface.But I am not sure about the practicality of VOF method.Moreover,I noticed that fractional step method include several methods,that is,iterative method,projection method and pressure correction method.But if I don't want to use iteration which method is better for my situation?

Did you try Zaleski's code?

http://www.lmm.jussieu.fr/~zaleski/drops.html

Dear Junseok Kim Thanks for your help .The code is helpful for me. Would you give me more information about fractional step method,like code and literature.Nobody around can discuss this method with me.I'm anxious to get your help. Thanks again.

Take a look at the paper and references therein.

A. S. Almgren, J. B. Bell, P. Colella, L. H. Howell, and M. L. Welcome, ``A Conservative Adaptive Projection Method for the Variable Density Incompressible Navier-Stokes Equations,''J. Comp. Phys., 142, pp. 1-46, 1998.

For free surface flow, I have an impression (just from the literature) that the evolution is from MAC --> VOF --> Level Set.

So if you are going to write your new code, why not consider Level Set method?

There is a hybrid method which combines good things from VOF and Level Set methods.

I used the multistep methods in solving 3-D parabolic PDES a long time time ago. These books have some information on the fractional step method, sometimes called splitting methods:

William F Ames: Numerical Methods for Partial Differential Equations (second edition)

Yanenko, N. N: The method of fractional steps.

I really appreciate your help. I'll find these references.

Here is a paper using fractional step method cpupled with level set method to solve free surface problems. Pretty accurate results are reported.

Yue, W. et al, 2003, "Numerical simulation of unsteady multidimensional free surface motions by level set method", International Journal for Numerical Methods in Fluids, 42(8), 853-884.

Hope it helps.

Hi there,

Check the following papers regarding the fractional step method and its applications.

[1] Kim, J., and Moin, P., "Application of the fractional-step method to the incompressible Navier-Stokes equations," J. Comput. Phys., Vol. 59, pp. 108, 1985.

[2] Rosenfeld, M., Kwak, D., and Vinokur, M., "A fractional step solution method for unsteady incompressible Navier-Stokes equations in generalized coordinate systems," J. Comput. Phys.94, pp. 102, 1991.

[3] Zang, Y., Street, R. L., and Koseff, J. R., "A Non-staggered grid, fractional step method for time-dependent incompressible Navier-Stokes equations in curvilinear coordinates," J. Comput. Phys.114, pp. 18, 1994.

Hope this helps. Sincerely,

Frederic Felten