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In continuum mechanics and thermodynamics, a control volume (CV) is a mathematical abstraction employed in the process of creating mathematical models of physical processes. In an inertial frame of reference , it is a fictitious region of a given volume fixed in space or moving with constant flow velocity through which the continuuum (a ...
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 ...
When the above equation is formally integrated over the Control volume, ... John C., et al., (1997), Computational Fluid mechanics and Heat Transfer, 2nd Ed., Taylor ...
The conservation laws may be applied to a region of the flow called a control volume. A control volume is a discrete volume in space through which fluid is assumed to flow. The integral formulations of the conservation laws are used to describe the change of mass, momentum, or energy within the control volume.
Fluid mechanics is the branch of physics concerned with the mechanics of fluids ... This can be expressed as an equation in integral form over the control volume.
The convective form emphasizes changes to the state in a frame of reference moving with the fluid. The conservation form emphasizes the mathematical interpretation of the equations as conservation equations for a control volume fixed in space (which is useful from a numerical point of view).
where Ω represents the control volume. Since this equation must hold for any control volume, it must be true that the integrand is zero, from this the Cauchy momentum equation follows. The main step (not done above) in deriving this equation is establishing that the derivative of the stress tensor is one of the forces that constitutes F i. [1]
Sometimes it is necessary to consider a finite arbitrary volume, called a control volume, over which these principles can be applied. This finite volume is denoted by Ω and its bounding surface ∂Ω. The control volume can remain fixed in space or can move with the fluid.