SIMULATING A SOLID
I was experimenting with simulating a solid by creating a liquid with the correct specific heat, density, and conductivity but gave it a giant viscosity. It seemed to work. Does that seem reasonable?
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Invalid approach for solid
Without substance movement (flow) and pressure differences the solves will not work (converge), so your approach is invalid. At best you might be able to simulate creeping flow but even then the convergence rate will be extremely slow.