By Bengt Andersson; et al
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The inner volume is stepped in time and the flow is distributed to the connecting cells in the outer volume. In some CFD programs it is also possible to use the average flow to obtain a steady-state solution. By proper choice of a rotating or sliding mesh it is even possible to obtain good average properties of a stirred-tank reactor. g. viscosity, density, diffusion, heat conductivity and surface tension, will vary locally due to variations in temperature, pressure and composition of the fluid.
3 Symmetry and axis boundary conditions The time taken for simulations can be reduced significantly by using the geometrical symmetry of the problem. Mirror symmetry can halve or even further reduce the calculation region, and rotational symmetry, by defining a rotation axis, reduces a problem from 3D to 2D, which can decrease the time taken for simulation by several orders of magnitude. g. buoyancy-driven flows have a tendency to have several possible solutions depending on the initial conditions, and enforced symmetry conditions can produce erroneous results.
30) A major drawback with the second-order upwind scheme is that it is unbounded. g. the van Leer scheme. The definitions will be stated here. The van Leer scheme If |φ E − 2φ P + φ W | ≤ |φ E − φ W |, the value of φ at the eastern face is (cf. Eq. 29)) φe = φP + (φE − φP ) (φP − φW ) . 31) φe = φP . 32) Otherwise (cf. Eq. 25)), The velocity is assumed to be positive. The van Leer scheme implements the unbounded second-order upwind scheme, Eq. e. the second derivative of φ is ‘small’. Otherwise, the first-order upwind scheme, Eq.
Computational fluid dynamics for engineers by Bengt Andersson; et al