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solution methds-applied computational fluid dynamicssolution methods-applied computational fluid dynamicssolution methods-applied computational fluid dynamicssolution methods-applied computational fluid dynamics.ppt

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solution methds-applied computational fluid dynamicssolution methods-applied computational fluid dynamicssolution methods-applied computational fluid dynamicssolution methods-applied computational fluid dynamics

* Properties of numerical schemes All numerical schemes must have the following properties: Conservativeness: global conservation of the fluid property ? must be ensured. Boundedness: values predicted by the scheme should be within realistic bounds. For linear problems without sources, those would be the maximum and minimum boundary values. Fluid flow is non-linear and values in the domain may be outside the range of boundary values. Transportiveness: diffusion works in all directions but convection only in the flow direction. The numerical scheme should recognize the direction of the flow as it affects the strength of convection versus diffusion. The central differencing scheme does not have the transportiveness property. The other schemes that were discussed have all three of these properties. * Solution accuracy Higher order schemes will be more accurate. They will also be less stable and will increase computational time. It is recommended to always start calculations with first order upwind and after 100 iterations or so to switch over to second order upwind. This provides a good combination of stability and accuracy. The central differencing scheme should only be used for transient calculations involving the large eddy simulation (LES) turbulence models in combination with grids that are fine enough that the Peclet number is always less than one. It is recommended to only use the power law or QUICK schemes if it is known that those are somehow especially suitable for the particular problem being studied. * Pressure We saw how convection-diffusion equations can be solved. Such equations are available for all variables, except for the pressure. Gradients in the pressure appear in the momentum equations, thus the pressure field needs to be calculated in order to be able to solve these equations. If the flow is compressible: The continuity equation can be used to compute density. Temperature follows from the enthalpy equation. Pressure can then be calculated from