Control Volume-Based Finite Difference Method

Initial modelling on predicting velocity profiles in pultrusion dies was carried out by Gorthala et al. (1994). Here a two-dimensional mathematical model in cylindrical co-ordinates with a control-volume-based finite-difference method was developed for resin fiow, cure and heat transfer associated with the pultrusion process. Raper et al. 

To numerically solve equations of the above mathematical models, the general computational gas dynamics is adopted in the present work. The general differential equations (2.7) and (2.31) are then discretized by the control volume-based finite difference method, and the resulting set of algebraic equations is iteratively solved. The numerical solver for the general differential equations can be repeatedly appUed for each scale variable over a controlled volume mesh. This process must be conducted extremely carefully to avoid the influence of slight changes in the accuracy of discretization. 

Computational fluid dynamics (CFD) Control volume method Control volume-based finite difference method... 

The study for predicting the velocity profiles in pultrusion by Gorthala et aL (1994) used a variable viscosity model. A comprehensive two-dimensional mathematical model in cylindrical coordinates was developed for resin flow, cure and heat transfer. A control-volume-based finite difference method (FDM) (Patankar method) was used for solving the governing equations. The use of artificial neural networks (ANNs) for pultrusion modelling in terms of the real process data and their potential for intelligent machine control was proposed by Wilcox and Wright (1998). Liu et al. (2000 Liu, 2001 Liu and Hillier, 1999) implemented a finite element/control volume... 

Control Volume-Based Finite Difference Method... 

A novel solution procedure has been developed for examining two-dimensional Newtonian fluid flow in thin lubricant films. This technique Is based on a control volume formulation which Is capable of describing fluid property variations In three dimensions. Due to the nature of this formulation, conservation of mass Is ensured for each fluid column, while this Is not the case for common non-conservative finite difference methods. 

For most numerically solved models, a control-volume approach is used. This approach is based on dividing the modeling domain into a mesh. Between mesh points, there are finite elements or boxes. Using Taylor series expansions, the governing equations are cast in finite-difference form. Next, the equations for the two half-boxes on either side of a mesh point are set equal to each other hence, mass is rigorously conserved. This approach requires that all vectors be defined at half-mesh points, all scalars at full-mesh points, and all reaction rates at quarter-mesh points. The exact details of the numerical methods can be found elsewhere (for example, see ref 273) and are not the purview of this review article. The above approach is essentially the same as that used in CFD packages (e.g.. Fluent) or discussed in Appendix C of ref 139 and is related to other numerical methods applied to fuel-cell modeling. ... 

Understanding the free surface flow of viscoelastic fluids in micro-channels is important for the design and optimization of micro-injection molding processes. In this paper, flow visualization of a non-Newtonian polyacrylamide (PA) aqueous solution in a transparent polymethylmethacrylate (PMMA) channel with microfeatures was carried out to study the flow dynamics in micro-injection molding. The transient flow near the flow front and vortex formation in microfeatures were observed. Simulations based on the control volume finite element method (CVFEM) and the volume of fluid (VOF) technique were carried out to investigate the velocity field, pressure, and shear stress distributions. The mesoscopic CONNFFESSIT (Calculation of Non-Newtonian How Finite Elements and Stochastic Simulation Technique) method was also used to calculate the normal stress difference, the orientation of the polymer molecules and the vortex formation at steady state. 

Based on the finite volume method, the control equation can be converted to a numerical method for solving algebraic equations. Convection of equation use second-order upwind difference during the discrete process, the solver is based on the pressure, the pressure-velocity coupling adopt the SIMPLE algorithm, pressure interpolation scheme use PRESTO Format. 

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