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In fluid mechanics, displacement occurs when an object is largely immersed in a fluid, pushing it out of the way and taking its place. The volume of the fluid displaced can then be measured, and from this, the volume of the immersed object can be deduced: the volume of the immersed object will be exactly equal to the volume of the displaced fluid.
1. Divide the domain into discrete control volume. 2. Place the nodal point between end points defining the physical boundaries. Boundaries/ faces of the control volume are created midway between adjacent nodes. 3. Set up the control volume near the edge of domain such that physical as well as control volume boundaries will coincide with each ...
The ratio of the volume of a sphere to the volume of its circumscribed cylinder is 2:3, as was determined by Archimedes. The principal formulae derived in On the Sphere and Cylinder are those mentioned above: the surface area of the sphere, the volume of the contained ball, and surface area and volume of the cylinder.
The term “Volume of Fluid method” and it acronym “VOF” method were coined in the 1980 Los Alamos Scientific Laboratory report, “SOLA-VOF: A Solution Algorithm for Transient Fluid Flow with Multiple Free Boundaries,” by Nichols, Hirt and Hotchkiss [6] and in the journal publication “Volume of Fluid (VOF) Method for the Dynamics of ...
Hirsch, C. (1990), Numerical Computation of Internal and External Flows, Volume 2: Computational Methods for Inviscid and Viscous Flows, Wiley. Laney, Culbert B.(1998), Computational Gas Dynamics, Cambridge University Press. LeVeque, Randall(1990), Numerical Methods for Conservation Laws, ETH Lectures in Mathematics Series, Birkhauser-Verlag.
Immersed Boundary Method for Uniform Meshes in 2D, A. Fogelson, Utah; IBAMR : Immersed Boundary Method for Adaptive Meshes in 3D, B. Griffith, NYU. IB2d: Immersed Boundary Method for MATLAB and Python in 2D with 60+ examples, N.A. Battista, TCNJ; ESPResSo: Immersed Boundary Method for soft elastic objects; CFD IBM code based on OpenFoam
A smooth embedding is an injective immersion f : M → N that is also a topological embedding, so that M is diffeomorphic to its image in N. An immersion is precisely a local embedding – that is, for any point x ∈ M there is a neighbourhood, U ⊆ M, of x such that f : U → N is an embedding, and conversely a local embedding is an ...
Once it fully sinks to the floor of the fluid or rises to the surface and settles, Archimedes principle can be applied alone. For a floating object, only the submerged volume displaces water. For a sunken object, the entire volume displaces water, and there will be an additional force of reaction from the solid floor.