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tum-pbs / PhiFlow

A differentiable PDE solving framework for machine learning
MIT License
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what differential equation does the velocity satisfy #144

Closed whw-alex closed 9 months ago

whw-alex commented 9 months ago

Hi! I have trouble understanding what differential equation the velocity in https://tum-pbs.github.io/PhiFlow/Fluid_Simulation.html satisfies. And why is that?

holl- commented 9 months ago

Hey, the velocity evolves according to the Navier-Stokes equations consisting of the advection and diffusion terms (u⋅∇)u−ν∇²u (equation under "Operator Splitting"). The incompressibility constraint ∇ · u = 0 is implemented via the pressure-term ∇p. The gravity term g is not simulated here.

If you have further questions, let me know!

whw-alex commented 9 months ago

Thanks for your answer! I wonder if you can tell me the relationship between 0.1 in v = diffuse.explicit(v, 0.1, dt) and the variable ν. Highly appreciate your work!

holl- commented 9 months ago

The 0.1 is the diffusivity / viscosity. It is exactly ν in the equation. It's inversely proportional to the Reynolds number.

whw-alex commented 9 months ago

Thank you so much!