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In fluid dynamics, the Buckley–Leverett equation is a conservation equation used to model two-phase flow in porous media. [1] The Buckley–Leverett equation or the Buckley–Leverett displacement describes an immiscible displacement process, such as the displacement of oil by water, in a one-dimensional or quasi-one-dimensional reservoir.
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.
Any existing fluid solver can be coupled to a solver for the fiber equations to solve the Immersed Boundary equations. Variants of this basic approach have been applied to simulate a wide variety of mechanical systems involving elastic structures which interact with fluid flows.
Flux F through a surface, dS is the differential vector area element, n is the unit normal to the surface. Left: No flux passes in the surface, the maximum amount flows normal to the surface.
Finite volume method (FVM) is a numerical method. FVM in computational fluid dynamics is used to solve the partial differential equation which arises from the physical conservation law by using discretisation. Convection is always followed by diffusion and hence where convection is considered we have to consider combine effect of convection and ...
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 ...
Example 1: If a block of solid stone weighs 3 kilograms on dry land and 2 kilogram when immersed in a tub of water, then it has displaced 1 kilogram of water. Since 1 liter of water weighs 1 kilogram (at 4 °C), it follows that the volume of the block is 1 liter and the density (mass/volume) of the stone is 3 kilograms/liter.
The control volume integration of the steady part of the equation is similar to the steady state governing equation's integration. We need to focus on the integration of the unsteady component of the equation. To get a feel of the integration technique, we refer to the one-dimensional unsteady heat conduction equation. [3]