[Timm]

Hello everyone!

I'm pretty new to OpenFOAM and finite volume modeling and I'm stuck. What I'm trying to do is to write a solver that, among others, solves the following equation:



where is the velocity, is Lame's first paramenter, the dynamic viscosity and the density. All of which are known at this point but are not constant.

The equation is derived from the momentum balance describing Stokes flow:



where the material in question can be described in the following way:

with

As you can see, the thermodynamic pressure is neglected here! The overall pressure is equal to the viscous pressure. That's because I'm dealing with a very slow flowing material, which is ice.


I think the equation should be solvable. But I just can't figure out how to get the system into OpenFOAM. I tried to rearrange the equation in various ways, to generate Laplacian terms, but when I do so I'm always stuck with some kind of source terms making it all look pretty nasty and leading to no usable results. I also thought of adapting for example simpleFOAM and setting the pressure to zero. But why using pressure prediction and correction, when there's no pressure in the equation? Turbulence is also out of question. Do I miss something, is the problem more difficult than I think, or is it simply not possible? I'd appreciate any comments and hints.


Thanks for reading and your help.


Timm