Model finite-volume scheme

The DOM has been extensively and successfully applied to photocatalytic reactors by the Santa Fe (Argentina) group (see Cassano and Alfano 2000, and references therein) and verified against experimental results (Brandi et al., 1999 Romero et al., 2003). Also Trujillo et al. (2007) have recently used a variant of the DOM, called finite volume scheme to model the effect of air bubbles injected in a fixed catalyst reactor. 

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. 

The flow field of the impacting droplet and its surrounding gas is simulated using a finite-volume solution of the governing equations in a 3-D Cartesian coordinate system. The level-set method is employed to simulate the movement and deformation of the free surface of the droplet during impact. The details of the hydrodynamic model and the numerical scheme are described in Sections... 

The finite volume methods have been used to discretised the partial differential equations of the model using the Simple method for pressure-velocity coupling and the second order upwind scheme to interpolate the variables on the surface of the control volume. The segregated solution algorithm was selected. The Reynolds stress turbulence model was used in this model due to the anisotropic nature of the turbulence in cyclones. Standard fluent wall functions were applied and high order discretisation schemes were also used. 

In these equations fi is the coluirm mass of dry air, V is the velocity (u, v, w), and (jf) is a scalar mixing ratio. These equations are discretized in a finite volume formulation, and as a result the model exactly (to machine roundoff) conserves mass and scalar mass. The discrete model transport is also consistent (the discrete scalar conservation equation collapses to the mass conservation equation when = 1) and preserves tracer correlations (c.f. Lin and Rood (1996)). The ARW model uses a spatially 5th order evaluation of the horizontal flux divergence (advection) in the scalar conservation equation and a 3rd order evaluation of the vertical flux divergence coupled with the 3rd order Runge-Kutta time integration scheme. The time integration scheme and the advection scheme is described in Wicker and Skamarock (2002). Skamarock et al. (2005) also modified the advection to allow for positive definite transport. 

The following meso-meteorological and NWP models of FUMAPEX partners were used for urban conditions or for different variants of the urbanisation scheme (user/ developer teams are in brackets) 1. DMI-HIRLAM (DMI) 2. Lokalmodell LM (DWD, MeteoSwiss, EPA Emilia-Romagna) 3. MM5 (CORIA, met.no, UH) 4. RAMS (CEAM, Arianet) 5. Topographic Vorticity-Mode (TVM, Schayes et al., [563]) Me-soscale Model (UCL) 6. Finite Volume Model FVM (EPEE) 7. SUBMESO model (ECN). 

A property of the finite volume method is that numerous schemes and procedures can be designed in order to solve the two-fluid model equations. In addition, the coupling terms can be approximated and manipulated in different ways. Besides, it is very difficult to predict the convergence and stability properties of novel solution methods. These aspects collectively increase the possibility of devising a numerical procedure which, when put to the test, does not converge. 

Computational fluid dynamics (CFD) based on the continuum Navier-Stokes equations Eq. 2 has long been successfully used in fundamental research and engineering design in different fluid related areas. Namrally, it becomes the first choice for the simulation of microfluidic phenomena in Lab-on-a-Chip devices and is still the most popular simulation model to date. Due to the nonlinearity arising from the convention term, Eq. 2 must be solved numerically by different discretization schemes, such as finite element method, finite difference method, finite volume method, or boundary element method. Besides, there are a variety of commercially available CFD packages that can be less or more adapted to model microfluidic processes (e.g., COMSOL (http //www.femlab.com), CFD-ACE+ (http // www.cfdrc.com), Coventor (http //www. coventor.com), Fluent (http //www.fluent.com), and Ansys CFX (http //www.ansys.com). For majority of the microfluidic flows, Re number is... 

An alternative to the above modeling approach is to simulate thermal radiation exchange using a conservative variant of the discrete ordinates (DO) radiation model, called the finite-volume (FV) scheme, implemented in the Fluent software package. 

Finite Volume and Finite Difference Methods for Modeling and Simulation, Table 2 convection-diffusion discretization schemes... 

The model equations were solved numerically by using the commercial software FLUENT 6.2 with finite volume method. The SIMPLEC algorithm was used to solve the pressure-velocity coupling problem in the momentum equations. The second-order upwind spatial discretization scheme was employed for all differential equations. 

Dabdub D, Seinfeld JH (1994) Numerical advective schemes used in air quality models— sequential and paraUeU implementation. Atmos Environ 28(20) 3369-3385 Demirdzic 1, LUekZ, Peric M, (1993) A collocated finite volume method for predicting flows at all speeds. Int J Numer Methods Ruids 16 1029-1050... 

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