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Sink flow is the opposite of source flow. The streamlines are radial, directed inwards to the line source. As we get closer to the sink, area of flow decreases. In order to satisfy the continuity equation, the streamlines get bunched closer and the velocity increases as we get closer to the source. As with source flow, the velocity at all ...
The velocity satisfies the continuity equation for incompressible flow: ∇ ⋅ u = 0. {\displaystyle \quad \nabla \cdot \mathbf {u} =0.} Although in principle the stream function doesn't require the use of a particular coordinate system, for convenience the description presented here uses a right-handed Cartesian coordinate system with ...
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.
2D Contour Plot of Taylor Green Vortex. In fluid dynamics, the Taylor–Green vortex is an unsteady flow of a decaying vortex, which has an exact closed form solution of the incompressible Navier–Stokes equations in Cartesian coordinates.
In the analysis of a flow, it is often desirable to reduce the number of equations and/or the number of variables. The incompressible Navier–Stokes equation with mass continuity (four equations in four unknowns) can be reduced to a single equation with a single dependent variable in 2D, or one vector equation in 3D.
Continuity in the Eulerian description is expressed by the spatial and temporal continuity and continuous differentiability of the flow velocity field. All physical quantities are defined this way at each instant of time, in the current configuration, as a function of the vector position x {\displaystyle \mathbf {x} } .
The second equation is the incompressible constraint, stating the flow velocity is a solenoidal field (the order of the equations is not causal, but underlines the fact that the incompressible constraint is not a degenerate form of the continuity equation, but rather of the energy equation, as it will become clear in the following).
() then provides the governing equation for pressure computation. The idea of pressure-correction also exists in the case of variable density and high Mach numbers, although in this case there is a real physical meaning behind the coupling of dynamic pressure and velocity as arising from the continuity equation