Computational fluid dynamics calculation domain

Two numerical methods have been used for the solution of the spray equation. In the first method, i.e., the full spray equation method 543 544 the full distribution function / is found approximately by subdividing the domain of coordinates accessible to the droplets, including their physical positions, velocities, sizes, and temperatures, into computational cells and keeping a value of / in each cell. The computational cells are fixed in time as in an Eulerian fluid dynamics calculation, and derivatives off are approximated by taking finite differences of the cell values. This approach suffersfrom two principal drawbacks (a) large numerical diffusion and dispersion... 

Problem understanding In many cases, experiments can provide only reliable integral values. In the case of twin screw extruders, for example, these are the shaft torque and the pressure and the temperature at the extrusion nozzle. Computational fluid dynamics, however, provide local information about pressure, velocity, and temperature within the overall computational domain. The calculation of gradients provides additional information about the shear rate or the heat transfer coefficients. 

Spatial multi-scale methods are based on the paradigm that in many real situations the atomic description is only required within small parts of the simulation domain whereas for the majority the continuum model is still valid. This allows one to apply concurrent continuum and molecular simulations for the respective parts of the simulation domain using a coupling scheme that permits to connect between the two domains. The majority of the spatial domain is calculated by continuum solvers (computational fluid dynamics) which are very fast and only the active part is calculated using molecular simulation methods. In some cases several other coarser-grained (mesoscale) methods than the atomic simulations ones are used as interfaces between the molecular simulation and the continuum domains. Such approaches are called hybrid molecular-continuum methods and allow the simulation of problems that are not accessible either by continuum or by pure molecular simulation methods. 

For non-Newtonian fluids the viscosity p is fitted to flow curves of experimental data. The models for this fit are discussed in the next chapter. The energy equation is also implemented in the code and can be used for temperature-dependent problems, but it is not needed for the simulation of fluid dynamic problems like jet breakup due to the uncoupling of the density in the incompressible formulation. The finite volume scheme uses the Marker and Cell (MAC) method to discretize the computational domain in space. The convective and diffusive terms are discretized with second-order accuracy and the fluxes are calculated with a Godunov-type scheme. 

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