Home About us Contact
|
Home About us Contact | ||
|
|
||
Finite-volume Method (finite-volume + method)
Selected AbstractsSimulations of IEF in microchannel with variable cross-sectional areaELECTROPHORESIS, Issue 5 2009Yin Chou Abstract This study develops a 1-D mass transport model to describe the electrophoresis transport behavior within a microchannel with a variable cross-sectional area. Utilizing three different numerical schemes, simulations are performed to investigate the IEF of proteins in ampholyte-based pH gradients within both a planar microchannel and a contraction,expansion microchannel, respectively. The simulation results obtained using the modified 1-D mass transport model and the finite-volume method (FVM) for the IEF separation of a single protein sample in a ten-ampholyte-based pH gradient within a planar microchannel are consistent with those presented by Shim et al. [Electrophoresis 2007, 28, 572,586] using a 2-D FVM scheme. In addition, the Courant,Friedrichs,Lewy number insensitive conservation element and solution element (CNI-CESE) method is found to be both more robust and more computationally efficient than the conventional CESE scheme when modeling IEF phenomena within a contraction,expansion microchannel. In modeling the IEF separation of four sample ampholytes in a 20-ampholtye-based pH gradient within a contraction,expansion microchannel, the results obtained using the CNI-CESE scheme are in good agreement with those published in literature. Moreover, the simulations can be performed significantly faster with the new 1-D model and the CNI-CESE scheme. Finally, the results obtained using the modified 1-D mass transport model and the CNI-CESE scheme demonstrate that the concentration of the focused test sample and the resolution of the pH gradient within the microchannel increase as the number of ampholytes used to accomplish the IEF separation process is increased. [source] Assessment of Joule heating and its effects on electroosmotic flow and electrophoretic transport of solutes in microfluidic channelsELECTROPHORESIS, Issue 3 2006Gongyue Tang Abstract Joule heating is inevitable when an electric field is applied across a conducting medium. It would impose limitations on the performance of electrokinetic microfluidic devices. This article presents a 3-D mathematical model for Joule heating and its effects on the EOF and electrophoretic transport of solutes in microfluidic channels. The governing equations were numerically solved using the finite-volume method. Experiments were carried out to investigate the Joule heating associated phenomena and to verify the numerical models. A rhodamine,B-based thermometry technique was employed to measure the solution temperature distributions in microfluidic channels. The microparticle image velocimetry technique was used to measure the velocity profiles of EOF under the influence of Joule heating. The numerical solutions were compared with experimental results, and reasonable agreement was found. It is found that with the presence of Joule heating, the EOF velocity deviates from its normal "plug-like" profile. The numerical simulations show that Joule heating not only accelerates the sample transport but also distorts the shape of the sample band. [source] Parsimonious finite-volume frequency-domain method for 2-D P,SV -wave modellingGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2008R. Brossier SUMMARY A new numerical technique for solving 2-D elastodynamic equations based on a finite-volume frequency-domain approach is proposed. This method has been developed as a tool to perform 2-D elastic frequency-domain full-waveform inversion. In this context, the system of linear equations that results from the discretization of the elastodynamic equations is solved with a direct solver, allowing efficient multiple-source simulations at the partial expense of the memory requirement. The discretization of the finite-volume approach is through triangles. Only fluxes with the required quantities are shared between the cells, relaxing the meshing conditions, as compared to finite-element methods. The free surface is described along the edges of the triangles, which can have different slopes. By applying a parsimonious strategy, the stress components are eliminated from the discrete equations and only the velocities are left as unknowns in the triangles. Together with the local support of the P0 finite-volume stencil, the parsimonious approach allows the minimizing of core memory requirements for the simulation. Efficient perfectly matched layer absorbing conditions have been designed for damping the waves around the grid. The numerical dispersion of this FV formulation is similar to that of O(,x2) staggered-grid finite-difference (FD) formulations when considering structured triangular meshes. The validation has been performed with analytical solutions of several canonical problems and with numerical solutions computed with a well-established FD time-domain method in heterogeneous media. In the presence of a free surface, the finite-volume method requires 10 triangles per wavelength for a flat topography, and fifteen triangles per wavelength for more complex shapes, well below the criteria required by the staircase approximation of O(,x2) FD methods. Comparisons between the frequency-domain finite-volume and the O(,x2) rotated FD methods also show that the former is faster and less memory demanding for a given accuracy level, an attractive feature for frequency-domain seismic inversion. We have thus developed an efficient method for 2-D P,SV -wave modelling on structured triangular meshes as a tool for frequency-domain full-waveform inversion. Further work is required to improve the accuracy of the method on unstructured meshes. [source] Simulating the hydraulic characteristics of the lower Yellow River by the finite-volume techniqueHYDROLOGICAL PROCESSES, Issue 14 2002Qing Wan Abstract The finite-volume technique is used to solve the two-dimensional shallow-water equations on unstructured mesh consisting of quadrilateral elements. In this paper the algorithm of the finite-volume method is discussed in detail and particular attention is paid to accurately representing the complex irregular computational domain. The lower Yellow River reach from Huayuankou to Jiahetan is a typical meandering river. The generation of the computational mesh, which is used to simulate the flood, is affected by the distribution of water works in the river channel. The spatial information about the two Yellow River levee, the protecting dykes, and those roads that are obviously higher than the ground, need to be used to generate the computational mesh. As a result these dykes and roads locate the element interfaces of the computational mesh. In the model the finite-volume method is used to solve the shallow-wave equations, and the Osher scheme of the empirical function is used to calculate the flux through the interface between the neighbouring elements. The finite-volume method has the advantage of using computational domain with complex geometry, and the Osher scheme is a method based on characteristic theory and is a monotone upwind numerical scheme with high resolution. The flood event with peak discharge of 15 300 m3/s, occurring in the period from 30 July to 10 August 1982, is simulated. The estimated result indicates that the simulation method is good for routing the flood in a region with complex geometry. Copyright © 2002 John Wiley & Sons, Ltd. [source] A moving-mesh finite-volume method to solve free-surface seepage problem in arbitrary geometriesINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 14 2007M. Darbandi Abstract The main objective of this work is to develop a novel moving-mesh finite-volume method capable of solving the seepage problem in domains with arbitrary geometries. One major difficulty in analysing the seepage problem is the position of phreatic boundary which is unknown at the beginning of solution. In the current algorithm, we first choose an arbitrary solution domain with a hypothetical phreatic boundary and distribute the finite volumes therein. Then, we derive the conservative statement on a curvilinear co-ordinate system for each cell and implement the known boundary conditions all over the solution domain. Defining a consistency factor, the inconsistency between the hypothesis boundary and the known boundary conditions is measured at the phreatic boundary. Subsequently, the preceding mesh is suitably deformed so that its upper boundary matches the new location of the phreatic surface. This tactic results in a moving-mesh procedure which is continued until the nonlinear boundary conditions are fully satisfied at the phreatic boundary. To validate the developed algorithm, a number of seepage models, which have been previously targeted by the other investigators, are solved. Comparisons between the current results and those of other numerical methods as well as the experimental data show that the current moving-grid finite-volume method is highly robust and it provides sufficient accuracy and reliability. Copyright © 2007 John Wiley & Sons, Ltd. [source] Coupled solution of the species conservation equations using unstructured finite-volume methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2010Ankan Kumar Abstract A coupled solver was developed to solve the species conservation equations on an unstructured mesh with implicit spatial as well as species-to-species coupling. First, the computational domain was decomposed into sub-domains comprised of geometrically contiguous cells,a process similar to additive Schwarz decomposition. This was done using the binary spatial partitioning algorithm. Following this step, for each sub-domain, the discretized equations were developed using the finite-volume method, and solved using an iterative solver based on Krylov sub-space iterations, that is, the pre-conditioned generalized minimum residual solver. Overall (outer) iterations were then performed to treat explicitness at sub-domain interfaces and nonlinearities in the governing equations. The solver is demonstrated for both two-dimensional and three-dimensional geometries for laminar methane,air flame calculations with 6 species and 2 reaction steps, and for catalytic methane,air combustion with 19 species and 24 reaction steps. It was found that the best performance is manifested for sub-domain size of 2000 cells or more, the exact number depending on the problem at hand. The overall gain in computational efficiency was found to be a factor of 2,5 over the block (coupled) Gauss,Seidel procedure. All calculations were performed on a single processor machine. The largest calculations were performed for about 355 000 cells (4.6 million unknowns) and required 900,MB of peak runtime memory and 19,h of CPU on a single processor. Copyright © 2009 John Wiley & Sons, Ltd. [source] An enhanced polygonal finite-volume method for unstructured hybrid meshesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2007Hyung Taek Ahn Abstract Irregular hybrid meshes may excessively distort the node-dual finite-volume discretization. A new scheme is formulated that uses a different type of polygonal control volume. Superior stability of the polygonal scheme over the conventional node-dual scheme is demonstrated on representative irregular hybrid meshes for incompressible viscous flow past a circular cylinder. Copyright © 2006 John Wiley & Sons, Ltd. [source] Finite volume method with zonal-embedded grids for cylindrical coordinatesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2006Yong Kweon Suh Abstract A zonal-embedded-grid technique has been developed for computation of the two-dimensional Navier,Stokes equations with cylindrical coordinates. As is well known, the conventional regular grid system gives very small grid spacings in the azimuthal direction so it requires a very small time step for a stable numerical solution when the explicit method is used. The fundamental idea of the zonal-embedded-grid technique is that the number of azimuthal grids can be made small near the origin of the coordinates so that the grid size is more uniformly distributed over the domain than with the conventional regular-grid system. The code developed using this technique combined with the explicit, finite-volume method was then applied to calculation of the asymmetric swirl flows and Lamb's multi-polar vortex flows within a full circle and the spin-up flows within a semi-circle. It was shown that the zonal-embedded grids allow a time step far larger than the conventional regular grids. For the case of the Lamb's multi-polar vortex flows, the code was validated by comparing the calculated results with the exact solutions. For the case of the semi-circle spin-up flows, the experimental results were used for the verification. It was seen that the numerical results were in good agreement with the experimental results both qualitatively and quantitatively. Copyright © 2006 John Wiley & Sons, Ltd. [source] Hybrid finite-volume finite-difference scheme for the solution of Boussinesq equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2005K. S. Erduran Abstract A hybrid scheme composed of finite-volume and finite-difference methods is introduced for the solution of the Boussinesq equations. While the finite-volume method with a Riemann solver is applied to the conservative part of the equations, the higher-order Boussinesq terms are discretized using the finite-difference scheme. Fourth-order accuracy in space for the finite-volume solution is achieved using the MUSCL-TVD scheme. Within this, four limiters have been tested, of which van-Leer limiter is found to be the most suitable. The Adams,Basforth third-order predictor and Adams,Moulton fourth-order corrector methods are used to obtain fourth-order accuracy in time. A recently introduced surface gradient technique is employed for the treatment of the bottom slope. A new model ,HYWAVE', based on this hybrid solution, has been applied to a number of wave propagation examples, most of which are taken from previous studies. Examples include sinusoidal waves and bi-chromatic wave propagation in deep water, sinusoidal wave propagation in shallow water and sinusoidal wave propagation from deep to shallow water demonstrating the linear shoaling properties of the model. Finally, sinusoidal wave propagation over a bar is simulated. The results are in good agreement with the theoretical expectations and published experimental results. Copyright © 2005 John Wiley & Sons, Ltd. [source] Progressive optimization on unstructured grids using multigrid-aided finite-difference sensitivitiesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10-11 2005L. A. Catalano Abstract This paper proposes an efficient and robust progressive-optimization procedure, employing cheap, flexible and easy-to-program multigrid-aided finite-differences for the computation of the sensitivity derivatives. The entire approach is combined with an upwind finite-volume method for the Euler and the Navier,Stokes equations on cell-vertex unstructured (triangular) grids, and validated versus the inverse design of an airfoil, under inviscid (subsonic and transonic) and laminar flow conditions. The methodology turns out to be robust and highly efficient, the converged design optimization being obtained in a computational time equal to that required by 11,17 (depending on the application) multigrid flow analyses on the finest grid. Copyright © 2004 John Wiley & Sons, Ltd. [source] Evaluation of Smagorinsky-based subgrid-scale models in a finite-volume computationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2002Petri Majander Abstract Smagorinsky-based models are assessed in a turbulent channel flow simulation at Reb=2800 and Reb=12500. The Navier,Stokes equations are solved with three different grid resolutions by using a co-located finite-volume method. Computations are repeated with Smagorinsky-based subgrid-scale models. A traditional Smagorinsky model is implemented with a van Driest damping function. A dynamic model assumes a similarity of the subgrid and the subtest Reynolds stresses and an explicit filtering operation is required. A top-hat test filter is implemented with a trapezoidal and a Simpson rule. At the low Reynolds number computation none of the tested models improves the results at any grid level compared to the calculations with no model. The effect of the subgrid-scale model is reduced as the grid is refined. The numerical implementation of the test filter influences on the result. At the higher Reynolds number the subgrid-scale models stabilize the computation. An analysis of an accurately resolved flow field reveals that the discretization error overwhelms the subgrid term at Reb=2800 in the most part of the computational domain. Copyright © 2002 John Wiley & Sons, Ltd. [source] Thermal performance of the exhausting and the semi-exhausting triple-glazed airflow windowsINTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 3 2006Moo-Hyun Kim Abstract The thermal performance of the airflow window systems was studied numerically using the finite-volume method. Effort was directed towards the reduction in space cooling load for the exhausting and the semi-exhausting triple-glazed airflow windows. The effects of various parameters such as exhausting airflow rate, solar insolation, and aspect ratio were presented. Some qualitative and quantitative comparisons between two systems were made. It was disclosed that the space-heat gain was considerably reduced by increasing the exhausting airflow rate, and the decrease in the space-heat gain of the semi-exhausting airflow window was larger than that of the exhausting airflow window by about 10 W throughout most of the Re range (except the range of near Re = 0) of this numerical work. Copyright © 2005 John Wiley & Sons, Ltd. [source] | ||||||||||