# For the latest version, is there a case for turbulence of pipe flow?

A quick question, does Gualsphysics can simulate pipe flow which Reynolds number up to 8000.

A quick question, does Gualsphysics can simulate pipe flow which Reynolds number up to 8000.

## Comments

The question regards SPH in general and not DualSPHysics in particular, in my view. It depends on how you model viscosity, then on the true size of the domain, and your compute devices.

If you use an artificial viscosity alpha, in a 3D problem the effective viscosity you are simulating is (10 * alpha * sound speed * smoothing length) which are all user-defined parameters in SPH. If you put this value at the denominator of the Reynold number you get

Reynolds number = Mach number * 0.1/artificial viscosity * (domain length scale /smoothing length)or in symbols

Re = Ma * 0.1 / alpha * D/hThe Mach number has to be max 0.1 for weak compressibility to apply. Here, once you know the velocity scale (a sort of max expected value), you choose the artificial sound of speed accordingly.

The artificial viscosity is a free parameter: I have seen values of 0.01-0.1 used. Have a look at what other researchers did with problems like yours.

Therefore, the Reynolds number you can match is left to depend on the ratio (D/h), which you can compute.

Since with the Wendland kernel, normally recommended, the smoothing length h is twice the interparticle distance dp, D/dp determines the number of particles N that you end up having in your domain. This number of particles determines the memory requested from the GPU. If your GPU can give you that memory, you know that DualSPHysics can simulate the pipe flow at Reynolds number you have in mind.

(How long it takes is another story. The time step picked up by the solver will depend on the speed of sound, the artificial viscosity, and the smoothing length again. The compute time depends on your problem's specifics.)

Say: Re=8000, Ma=0.1, alpha=0.01 leads to D/dp=8000 (sounding a rather high demand, if you ask me). You can use the same maths to estimate the maximum Reynolds number that you can afford to simulate in your situation.

Please double check; happy to be corrected. For other options to model viscosity I leave it to other forum fellows.