# Eulerian approach

The geometrical flexibility of the VOF scheme can be significantly improved if in its formulation, instead of using a fixed framework, a combination of a Lagrangian-Eulerian approach is adopted. The most common approach to develop such a combined framework is the application of the Arbitrary [c.102]

Equation (12.43) is called an Eulerian approach because the behavior of the species is described relative to a fixed coordinate system. The equation can also be considered to be a transport equation for particles when they are [c.1177]

The plane of the rotor blade cross-section representing the flow field configuration at the start of mixing in a partially filled single-blade mixer is shown in Figure 5.1. Initial distribution of the compound inside the mixer chamber corresponds to a fill factor of 71 per cent and is chosen arbitrarily. It is evident that the flow field within this domain should be modelled as a free surface regime with random moving boundaries. Available options for the modelling of such a flow regime are explained in Chapter 3, Section 5. In this example, utilization of the volume of fluid (VOF) approach based on an Eulerian framework is described. To maintain simplicity we neglect elastic effects and the variations of compound viscosity with mixing, and focus on the simulation of the flow corresponding to a generalized Newtonian fluid. In the VOF approach [c.142]

Simplification achieved by using a constant mesh in the modelling of the flow field in a single-blade mixer is not applicable to twin-blade mixers. Although the model equations in both simulations are identical the solution algorithm for twin-blade mixers cannot be based on the VOF method on a fixed domain and instead the Arbitrary Lagrangian-Eulerian (ALE) approach, described in Chapter 3, Section 5.2, should be used. However, the overall geometry of the plane of the rotors blades cross-section is known and all of the required mesh configurations can be generated in advance and stored in a file to speed up the calculations. Figure 5.4 shows the finite element mesh corresponding to 19 successive time steps from the start of the simulation in a typical twin-blade tangential rotor mixer. The finite element mesh configurations correspond to counter-rotating blades with unequal rotational velocities set to generate an mieven stress field for enhancing dispersive mixing efficiency. Calculation of mesh velocity, required for modification of the free surface equation (see Equation (3.73)) at each time step, is based on the following equations (Ghoreishy, 1997) [c.146]

A similar computational exercise was performed by Guirao et al. (1979). They used a code based on the Eulerean FCT approach. Blasts produced by four different, but energetically equivalent, sources [c.106]

See pages that mention the term

**Eulerian approach**:

**[c.87] [c.206] [c.105]**

Practical aspects of finite element modelling of polymer processing (2002) -- [ c.87 ]