Hi,

I am very much new to these things so please excuse my ignorance.

Background: I need to solve the unsteady Stokes equations in a liquid bridge between two spheres. Assuming axisymmetry and fore-aft symmetry this leaves a domain with two flat sides (the centrelines), one side that is the arc of a circle, and one side that is a curved free surface, intersecting the circular arc with a contact angle that can be small (almost 0). Note that all boundaries are stationary.

The basic question: is it possible to obtain a grid that will allow me to solve the equations using the F.D. method despite the fairly acute corner of the domain?

Sorry to waffle, thanks.

Rob

As Finite Difference requires structured grid, the Transfinite Interpolation (TFI) Method of Grid generation may be employed for this problem. For important corner points, clustering around that corner would be suitable.

(1). Why not take a look at Joe Thompson's book "Numerical Grid Generation", available free on Internet, with Fortran codes attached including various schemes.

Thanks to everyone for their replies. Does anyone out their know of any textbooks that address the problem of sharp corners in domains, and/or anything good on finite volume methods?

Hi Robin:

The FV method can accomodate any kinds of grid. Therefore, it's suitable for complex geometries. The grid defines only the Control Volume(CV) boundaries, and need not be related to a coordinate systems. If CVs boundary is the same as the surface integrals which represent convective n' diffusive fluxes, the F.V. method is conservative.

Disadvantages of F.V. method:

FV requires two levels of approximation: interpolation n' integration, difficult to develop in 3D (Ref: Book " Computational Methods for Fluid Dynamics", J.H.Ferziger).

Hope this helps.

Peter

what's the hyperlink for this book, John?

Many thanx.

peter

Numerical Grid Generation by Thompson, Warsi and Mastin is available at

http://www.erc.msstate.edu/education/gridbook/