Computational fluid dynamics algorithm

Scheuerer G. Solution algorithms and implementations strategies for Eulerian-Eulerian multiphase-flow models. Proceedings of ACFD 2000 International Conference on Applied Computational Fluid Dynamics, Beijing, 2000. 

The computational fluid dynamics investigations listed here are all based on the so-called volume-of-fluid method (VOF) used to follow the dynamics of the disperse/ continuous phase interface. The VOF method is a technique that represents the interface between two fluids defining an F function. This function is chosen with a value of unity at any cell occupied by disperse phase and zero elsewhere. A unit value of F corresponds to a cell full of disperse phase, whereas a zero value indicates that the cell contains only continuous phase. Cells with F values between zero and one contain the liquid/liquid interface. In addition to the above continuity and Navier-Stokes equation solved by the finite-volume method, an equation governing the time dependence of the F function therefore has to be solved. A constant value of the interfacial tension is implemented in the summarized algorithm, however, the diffusion of emulsifier from continuous phase toward the droplet interface and its adsorption remains still an important issue and challenge in the computational fluid-dynamic framework. 

Computational fluid dynamics involves the analysis of fluid flow and related phenomena such as heat and/or mass transfer, mixing, and chemical reaction using numerical solution methods. Usually the domain of interest is divided into a large number of control volumes (or computational cells or elements) which have a relatively small size in comparison with the macroscopic volume of the domain of interest. For each control volume a discrete representation of the relevant conservation equations is made after which an iterative solution procedure is invoked to obtain the solution of the nonlinear equations. Due to the advent of high-speed digital computers and the availability of powerful numerical algorithms the CFD approach has become feasible. CFD can be seen as a hybrid branch of mechanics and mathematics. CFD is based on the conservation laws for mass, momentum, and (thermal) energy, which can be expressed as follows ... 

In real production situations where geometric complexity and flow configurations warrant three-dimensional numerical simulations, computational fluid dynamic codes may be required to capture the complicated physicochemical hydrodynamics. This approach may begin to become feasible with the availability of powerful computers and efficient numerical algorithms. 

All computations are performed using the code OpenFOAM [17], an open source computational fluid dynamics (CFD) toolbox, utilizing a cell-center-based finite volume method on a fixed unstructured numerical grid and employing the solution procedure based on the pressure implicit with splitting of operators (PISO) algorithm for coupling between pressure and velocity in transient flows [18]. 

Basic Finite Volume Algorithms Used in Computational Fluid Dynamics... 

ViSTA-FlowLib is a software framework developed at the Institute for Scientific Computing of RWTH Aachen University [386]. It comprises algorithms for the interactive visualization of data sets produced by Computational Fluid Dynamics (CFD). Special attention is paid to unsteady and large-scale data sets. 

Slurry bubble column reactor for methanol and other hydrocarbons productions from synthesis gas is an issue of interest to the energy industries throughout the world. Computational fluid dynamics (CFD) is a recently developed tool which can help in the scale up. We have developed an algorithm for computing the optimum process of fluidized bed reactors. The mathematical technique can be applied to gas solid, liquid-solid, and gas-liquid-solid fluidized bed reactors, as well as the LaPorte slurry bubble column reactor. Our computations for the optimum particle size show that there is a factor of about two differences between 20 and 60 pm size with maximum granular-like temperature (turbulent kinetic energy) near the 60 pm size particles. 

Accurate CFD (computational fluid dynamic) simulation of the flow in stirred tanks requires correct specification of both the geometry and the physical conditions of the flow. While specification of the geometry, the gridding, and the solution algorithm is relatively straightforward, some other issues remain difficult. The most challenging problem is definition of a physically accurate, computationally tractable impeller or impeller model which incorporates the effect of the tank geometry. This... 

Kloss, C. Goniva, C. Hager, A. Amberger, S. Pirker, S. (2012) Models, algorithms and validation for opensource DEM and CFD-DEM. Progress in Computational Fluid Dynamics 12, 140-152. 

Nowadays, the use of numerical methods associated with different algorithms of Computational Fluid Dynamics (CFD) to determine the concentration of the vapor cloud of hazardous substances released into the atmosphere, in space and time, has grown considerably (Cornier 2008, Middha 2009, Dharmavaram, 2005). CFD is found in some commercial software tools such as CFX, FLACS and FLUENT. The CFD tools transform... 

Consequently, numerical solution of the equations of change has been an important research topic for many decades, both in solid mechanics and in fluid mechanics. Solid mechanics is significantly simpler than fluid mechanics because of the absence of the nonlinear convection term, and the finite element method has become the standard method. In fluid mechanics, however, the finite element method is primarily used for laminar flows, and other methods, such as the finite difference and finite volume methods, are used for both laminar and turbulent flows. The recently developed lattice-Boltzmann method is also being used, primarily in academic circles. All of these methods involve the approximation of the field equations defined over a continuous domain by discrete eqnalions associated with a finite set of discrete points within the domain and specified by the user, directly or through an antomated algorithm. Regardless of the method, the numerical solution of the conservation equations for fluid flow is known as computational fluid dynamics (CFD). 

In general, simulation methods can be divided into those that use a computer and those that do not, as shown in Fig. 14.1. Those simulations without computer can be separated into destructive and nondestructive methods. Simulations that use a computer can either be based on technical models (for example, finite element method for structural composites, computational fluid dynamics for polymer flows), on examples taken from nature (for example, artificial neural networks, evolutionary algorithms for machine setting optimization), and those based on analytical equations (for example, warp tension during weaving). 

D. C. Rapaport, Hardware Issues in Molecular Dynamics Algorithm Design, in Computer Modelling of Fluids Polymers and Solids, C. R. A. Cat-low et al., eds., Kluwer Academic Publishers Group, 1990, 249-267. 

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