A natural extension of the conventional finite volume method into polygonal unstructured meshes for CFD application.

A new general cell-centered solution procedure based upon the conventional control or finite volume (CV or FV) approach has been developed for numerical heat transfer and fluid flow which encompasses both structured and unstructured meshes for any kind of mixed polygon cell. Unlike conventional FV methods for structured and block structured meshes and both FV and FE methods for unstructured meshes, the irregular control volume (ICV) method does not require the shape of the element or cell to be predefined because it simply exploits the concept of fluxes across cell faces. That is, the ICV method enables meshes employing mixtures of triangular, quadrilateral, and any other higher order polygonal cells to be exploited using a single solution procedure. The ICV approach otherwise preserves all the desirable features of conventional FV procedures for a structured mesh; in the current implementation, collocation of variables at cell centers is used with a Rhie and Chow interpolation (to suppress pressure oscillation in the flow field) in the context of the SIMPLE pressure correction solution procedure. In fact all other FV structured mesh-based methods may be perceived as a subset of the ICV formulation. The new ICV formulation is benchmarked using two standard computational fluid dynamics (CFD) problems i.e., the moving lid cavity and the natural convection driven cavity. Both cases were solved with a variety of structured and unstructured meshes, the latter exploiting mixed polygonal cell meshes. The polygonal mesh experiments show a higher degree of accuracy for equivalent meshes (in nodal density terms) using triangular or quadrilateral cells; these results may be interpreted in a manner similar to the CUPID scheme used in structured meshes for reducing numerical diffusion for flows with changing direction.

Numerical modelling and validation of Marangoni and surface tension phenomena using the finite volume method

Surface tension induced flow is implemented into a numerical modelling framework and validated for a number of test cases. Finite volume unstructured mesh techniques are used to discretize the mass, momentum and energy conservation equations in three dimensions. An explicit approach is used to include the effect of surface tension forces on the flow profile and final shape of a liquid domain. Validation of this approach is made against both analytical and experimental data. Finally, the method is used to model the wetting balance test for solder alloy material, where model predictions are used to gain a greater insight into this process. Copyright © 2000 John Wiley & Sons, Ltd.

Viscoelastic flow through a planar contraction using a semi-Lagrangian finite volume method

A semi-Lagrangian finite volume scheme for solving viscoelastic flow problems is presented. A staggered grid arrangement is used in which the dependent variables are located at different mesh points in the computational domain. The convection terms in the momentum and constitutive equations are treated using a semi-Lagrangian approach in which particles on a regular grid are traced backwards over a single time-step. The method is applied to the 4 : 1 planar contraction problem for an Oldroyd B fluid for both creeping and inertial flow conditions. The development of vortex behaviour with increasing values of We is analyzed.

Domain decomposition using a 2-level correction scheme

The PHYSICA software was developed to enable multiphysics modelling allowing for interaction between Computational Fluid Dynamics (CFD) and Computational Solid Mechanics (CSM) and Computational Aeroacoustics (CAA). PHYSICA uses the finite volume method with 3-D unstructured meshes to enable the modelling of complex geometries. Many engineering applications involve significant computational time which needs to be reduced by means of a faster solution method or parallel and high performance algorithms. It is well known that multigrid methods serve as a fast iterative scheme for linear and nonlinear diffusion problems. This papers attempts to address two major issues of this iterative solver, including parallelisation of multigrid methods and their applications to time dependent multiscale problems.

A hybrid Laplace transform/finite difference boundary element method for diffusion problems

The solution process for diffusion problems usually involves the time development separately from the space solution. A finite difference algorithm in time requires a sequential time development in which all previous values must be determined prior to the current value. The Stehfest Laplace transform algorithm, however, allows time solutions without the knowledge of prior values. It is of interest to be able to develop a time-domain decomposition suitable for implementation in a parallel environment. One such possibility is to use the Laplace transform to develop coarse-grained solutions which act as the initial values for a set of fine-grained solutions. The independence of the Laplace transform solutions means that we do indeed have a time-domain decomposition process. Any suitable time solver can be used for the fine-grained solution. To illustrate the technique we shall use an Euler solver in time together with the dual reciprocity boundary element method for the space solution

Numerical investigation of a source extraction technique based on an acoustic correction method

An aerodynamic sound source extraction from a general flow field is applied to a number of model problems and to a problem of engineering interest. The extraction technique is based on a variable decomposition, which results to an acoustic correction method, of each of the flow variables into a dominant flow component and a perturbation component. The dominant flow component is obtained with a general-purpose Computational Fluid Dynamics (CFD) code which uses a cell-centred finite volume method to solve the Reynolds-averaged Navier–Stokes equations. The perturbations are calculated from a set of acoustic perturbation equations with source terms extracted from unsteady CFD solutions at each time step via the use of a staggered dispersion-relation-preserving (DRP) finite-difference scheme. Numerical experiments include (1) propagation of a 1-D acoustic pulse without mean flow, (2) propagation of a 2-D acoustic pulse with/without mean flow, (3) reflection of an acoustic pulse from a flat plate with mean flow, and (4) flow-induced noise generated by the an unsteady laminar flow past a 2-D cavity. The computational results demonstrate the accuracy for model problems and illustrate the feasibility for more complex aeroacoustic problems of the source extraction technique.

A fast, streaming SIMD extensions 2, logistic squashing function

Schraudolph proposed an excellent exponential approximation providing increased performance particularly suited to the logistic squashing function used within many neural networking applications. This note applies Intel's streaming SIMD Extensions 2 (SSE2), where SIMD is single instruction multiple data, of the Pentum IV class processor to Schraudolph's technique, further increasing the performance of the logistic squashing function. It was found that the calculation of the new 32-bit SSE2 logistic squashing function described here was up to 38 times faster than the conventional exponential function and up to 16 times faster than a Schraudolph-style 32-bit method on an Intel Pentum D 3.6 GHz CPU.

HPLC-ESI-MS method development for the elucidation of nicardipine degradation products

Purpose: Nicardipine is a member of a family of calcium channel blockers named dihydropiridines that are known to be photolabile and may cause phototoxicity. It is therefore vital to develop analytical method which can study the photodegradation of nicardipine. Method: Forced acid degradation of nicardipine was conducted by heating 12 ml of 1 mg/ml nicardipine with 3 ml of 2.5 M HCl for two hours. A gradient HPLC medthod was developed using Agilent Technologies 1200 series quaternary system. Separation was achieved with a Hichrome (250 x 4.6 mm) 5 μm C18 reversed phase column and mobile phase composition of 70% A(100%v/v water) and 30% B(99%v/v acetonitrile + 1%v/v formic acid) at time zero, composition of A and B was then charged to 60%v/v A;40%v/v B at 10minutes, 50%v/v A; 50%v/v B at 30minutes and 70%v/v A; 30%v/v B at 35minutes. 20μl of 0.8mg/ml of nicardipine degradation was injected at room temperature (25oC). The gradient method was transferred onto a HPLC-ESI-MS system (HP 1050 series - AQUAMAX mass detector) and analysis conducted with an acid degradation concentration of 0.25mg/ml and 20μl injection volume. ESI spectra were acquired in positive ionisation mode with MRM 0-600 m/z. Results: Eleven nicardipine degradation products were detected in the HPLC analysis and the resolution (RS) between the respective degradants where 1.0, 1.2, 6.0, 0.4, 1.7, 3.7, 1.8, 1.0, and 1.7 respectively. Nine degradation products were identified in the ESI spectra with the respective m/z ratio; 171.0, 166.1, 441.2, 423.2, 455.2, 455.2, 331.1, 273.1, and 290.1. The possible molecular formulae for each degradants were ambiguously determined. Conclusion: A sensitive and specific method was developed for the analysis of nicardipine degradants. Method enables detection and quantification of nicardipine degradation products that can be used for the study of the kinetics of nicardipine degradation processes.

Using a modified shepards method for optimization of a nanoparticulate cyclosporine a formulation prepared by a static mixer technique

An innovative methodology has been used for the formulation development of Cyclosporine A (CyA) nanoparticles. In the present study the static mixer technique, which is a novel method for producing nanoparticles, was employed. The formulation optimum was calculated by the modified Shepard's method (MSM), an advanced data analysis technique not adopted so far in pharmaceutical applications. Controlled precipitation was achieved injecting the organic CyA solution rapidly into an aqueous protective solution by means of a static mixer. Furthermore the computer based MSM was implemented for data analysis, visualization, and application development. For the optimization studies, the gelatin/lipoid S75 amounts and the organic/aqueous phase were selected as independent variables while the obtained particle size as a dependent variable. The optimum predicted formulation was characterized by cryo-TEM microscopy, particle size measurements, stability, and in vitro release. The produced nanoparticles contain drug in amorphous state and decreased amounts of stabilizing agents. The dissolution rate of the lyophilized powder was significantly enhanced in the first 2 h. MSM was proved capable to interpret in detail and to predict with high accuracy the optimum formulation. The mixer technique was proved capable to develop CyA nanoparticulate formulations.