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The material point method (MPM) is a numerical technique used to simulate the behavior of solids, liquids, gases, and any other continuum material. Especially, it is a robust spatial discretization method for simulating multi-phase (solid-fluid-gas) interactions.
Schematic view of an SPH convolution Flow around cylinder with free surface modelled with SPH. See [1] for similar simulations.. Smoothed-particle hydrodynamics (SPH) is a computational method used for simulating the mechanics of continuum media, such as solid mechanics and fluid flows.
Knowing the terminal velocity, the size and density of the sphere, and the density of the liquid, Stokes' law can be used to calculate the viscosity of the fluid. A series of steel ball bearings of different diameters are normally used in the classic experiment to improve the accuracy of the calculation.
The equation of motion for Stokes flow can be obtained by linearizing the steady state Navier–Stokes equations.The inertial forces are assumed to be negligible in comparison to the viscous forces, and eliminating the inertial terms of the momentum balance in the Navier–Stokes equations reduces it to the momentum balance in the Stokes equations: [1]
For settling particles that are considered individually, i.e. dilute particle solutions, there are two main forces enacting upon any particle. The primary force is an applied force, such as gravity, and a drag force that is due to the motion of the particle through the fluid. The applied force is usually not affected by the particle's velocity ...
For very small particle diameter the latter is locally a constant whose value is given by the undisturbed Eulerian field evaluated at the location of the particle center, () = ((),). The small particle size also implies that the disturbed flow can be found in the limit of very small Reynolds number, leading to a drag force given by Stokes' drag .
Velocity (blue line) and particle excursion (red dots) as a function of the distance to the wall. In fluid dynamics, Stokes problem also known as Stokes second problem or sometimes referred to as Stokes boundary layer or Oscillating boundary layer is a problem of determining the flow created by an oscillating solid surface, named after Sir ...
Basset force for describing the effect of the body's relative motion history on the viscous forces in a Stokes flow; Basset–Boussinesq–Oseen equation for the description of the motion of – and forces on – a particle moving in an unsteady flow at low Reynolds numbers; Darwin drift for the relation between added mass and the Darwin drift ...
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