[Physics] How to model water flow with and without friction against other objects

fluid dynamicsfrictionsimulationswater

I am interested in modeling water flow including boundary flow (with friction) against other objects in the path of the water flow.

I'm not a physicist but I am interested to learn the relevant physics (and the corresponding mathematical model) required to begin modeling a generic simulation engine.

I've searched this forum using "model water flow surface friction" search string, and I've read water flow in a sink, and What is the velocity area method for estimating the flow of water?.

Please suggest topics and other search strings, and advise if this is off-topic for this Physics forum. Thanks in advance.

Clarification: I'm looking at

  • no-slip condition (i.e. solid walls)
  • with turbulence

and

  • introduction of another body (with mass) into model for calculating the displaced
    water flow around the body.

Best Answer

Modelling flow of fluids in general is a big research (and industrial) field. This field is called Computational Fluid Dynamics (CFD)

All CFD methods are based on the so-called Navier-Stokes equations and the continuity equation, which is nothing more than conservation of momentum and mass.

There are different flavours in the methods of discretizing these equations:

  • Finite Volume
  • Finite Element
  • Finite Difference

Which all have pro's and cons.

In all these methods, friction is implicitly introduced by the boundary conditions. A common assumption for boundaries, as solid walls, is the so-called no-slip condition. This basically means that the local velocity at the wall is zero. This is basically nothing more than a sink of momentum via the wall shear stress. Making the model neglect friction, you should assume a zero-shear boundary, which means that the wall-normal gradient of the velocity component is zero.

As you're talking about water flows and objects, you know that these flows become turbulent. The non-linear term in the Navier-Stokes equation will be responsible for flow phenomena at lots of scales. Therefor, it is common practice to model this turbulence. Also here, we have different approaches:

  • DNS: Direct Numerical Simulation: No modelling at all, but the smallest grid size is smaller than the smallest turbulent scales
  • LES: Large Eddy Simulation: The Navier-Stokes equation is filtered for different scales. The largest scales are solved for, the smallest sub-filter scales are models
  • RANS: Reynolds Average Navier-Stokes: The Navier-Stokes equations are averaged (over time or realizations), and the non-linear term in the velocity fluctuations (also called Reynolds stress), is modelled, often via some a so-called turbulent viscosity (and by solving additional transport equations for turbulent properties).

Advised reading may be the book by Ferziger and Peric : http://www.amazon.com/Computational-Methods-Fluid-Dynamics-Ferziger/dp/3540420746

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