Numerical fluid mechanics: Flow effects in space and time

In numerical fluid mechanics, the mechanics of liquids and gases are mathematically modelled and numerically analyzed by using computers.



The mechanics of fluids with the Navier-Stokes equations can be described mathematically. They are used to formulate mass, momentum and energy conservation at the differential element. Approximate solutions can be calculated with the finite element method as well as with the finite volume method. In addition to the Navier-Stokes equations, the mechanics of fluids can also be modelled using the Boltzmann equation. This leads to the Lattice-Bolzmann method, which has gained in importance because of increasing computing power in recent years.



Essentially, a distinction is made between incompressible and compressible fluids, laminar and turbulent flows. If, depending on the application, incompressible behaviour can be assumed in good approximation, the model equations are reduced to the conservation of momentum and the continuity equation, a special form of conservation of mass. Typical application examples are wind generated vibrations of bridges or ocean currents. If, on the other hand, the shape of an aircraft wing is optimized or the mechanics of a shock absorber are analyzed, the flow must be modelled as compressible and the energy conservation must be included in the set of model equations if the influence of temperature is to be investigated. Turbulent flows are characterized by local vortices and strongly fluctuating velocity fields. In contrast to laminar flows, turbulent flows cross the flow lines on which the material particles move.


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