By Bengt Andersson; et al
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Extra resources for Computational fluid dynamics for engineers
These faces form a grid pattern throughout the domain. A grid that contains only cells with all internal angles equal to 90◦ is called a structured grid, and this is the type of grid that will be dealt with in this chapter. Since a structured grid requires that the physical geometry itself must be rectangular, this type of grid is not very common in reality. Many industrial cases contain parts of complex geometry that cannot be divided into purely rectangular cells. Grids can be created in 1D, 2D or 3D, depending on the number of computational dimensions.
1), compressibility effects are negligible and the variation of the gas density due to pressure waves can safely be ignored in the flow modelling. The density change due to pressure drops and temperature variations will automatically be compensated for by the state equation that describes how the density is related to pressure and temperature. 3 The equation of motion The momentum balance for the U1 momentum over the volume x1 x2 x3 is given by ⎧ ⎫ ⎧ ⎫ ⎧ ⎫ ⎫ ⎧ ⎬ ⎨ rate of ⎨ rate of ⎬ ⎨ rate of ⎬ ⎨ sum of forces ⎬ = momentum − momentum + acting on .
The equation also appears as the transport equation for various turbulence quantities in Chapter 4. Unfortunately, it is generally not possible to solve equations of this type analytically, since they are nonlinear and often contain both spatial and temporal derivatives. This requires the application of numerical methods. 2 25 Numerical methods for CFD The pioneers of CFD employed finite differences to approximate the governing equations describing fluid mechanics. With finite differences, the partial spatial and temporal derivatives appearing in the equations are approximated through Taylor series.