A stable and accurate control-volume technique based on integrated radial basis function networks for fluid-flow problems

Radial basis function networks (RBFNs) have been widely used in solving partial differential equations as they are able to provide fast convergence. Integrated RBFNs have the ability to avoid the problem of reduced convergence-rate caused by differentiation. This paper is concerned with the use of integrated RBFNs in the context of control-volume discretisations for the simulation of fluid-flow problems. Special attention is given to (i) the development of a stable high-order upwind scheme for the convection term and (ii) the development of a local high-order approximation scheme for the diffusion term. Benchmark problems including the lid-driven triangular-cavity flow are employed to validate the present technique. Accurate results at high values of the Reynolds number are obtained using relatively-coarse grids

A continuum-microscopic method based on IRBFs and control volume scheme for viscoelastic fluid flows

A numerical computation of continuum-microscopic model for visco-elastic flows based on the Integrated Radial Basis Function (IRBF) Control Volume and the Stochastic Simulation Techniques (SST) is reported in this paper. The macroscopic flow equations are closed by a stochastic equation for the extra stress at the microscopic level. The former are discretised by a 1D-IRBF-CV method while the latter is integrated with Euler explicit or Predictor-Corrector schemes. Modelling is very efficient as it is based on Cartesian grid, while the integrated RBF approach enhances both the stability of the procedure and the accuracy of the solution. The proposed method is demonstrated with the solution of the start-up Couette flow of the Hookean and FENE dumbbell model fluids

Institutional Inconsistencies and Microentrepreneurial Intent to Quit a Business: Street Vendors in Vietnam

Beyond actual institutional influences, entrepreneurs’ perceptions of institutions and their potential inconsistencies in interpreting institutional change may influence entrepreneurial intent to quit a business. Especially at the microentrepreneurial level, inconsistencies in perceptions of institutional change may variously affect individuals’ intent to abandon their business, seek jobs in other sectors, or even continue in business despite regulatory institutional changes making their business legally untenable. Our goal in this research is to empirically measure these intents in the face of inconsistent perceptions of institutional change with a sample of 660 street vendors from different cities in Vietnam. We find that perception of the two theoretical constructs, actions as rules and diminished utility of regulatory control, are negatively correlated with intent to quit a business, which is consistent with our hypotheses. Contrary to what we hypothesized, however, microentrepreneurial intent to exit their business is positively correlated with perceptions of retrospective legitimization. Implications for future research and public policy are also discussed

Imposition of physical parameters in dissipative particle dynamics

In the mesoscale simulations by the dissipative particle dynamics (DPD), the motion of a fluid is modelled by a set of particles interacting in a pairwise manner, and it has been shown to be governed by the Navier–Stokes equation, with its physical properties, such as viscosity, Schmidt number, isothermal compressibility, relaxation and inertia time scales, in fact its whole rheology resulted from the choice of the DPD model parameters. In this work, we will explore the response of a DPD fluid with respect to its parameter space, where the model input parameters can be chosen in advance so that (i) the ratio between the relaxation and inertia time scales is fixed; (ii) the isothermal compressibility of water at room temperature is enforced; and (iii) the viscosity and Schmidt number can be specified as inputs. These impositions are possible with some extra degrees of freedom in the weighting functions for the conservative and dissipative forces. Numerical experiments show an improvement in the solution quality over conventional DPD parameters/weighting functions, particularly for the number density distribution and computed stresses

BEM-RBF approach for viscoelastic flow analysis

A new BE-only method is achieved for the numerical solution of viscoelastic flows. A decoupled algorithm is chosen where the fluid is considered as being composed of an artificial Newtonian component and the remaining component is accordingly defined from the original constitutive equation. As a result the problem is viewed as that of solving for the flow of a Newtonian liquid with the non-linear viscoelastic effects acting as a pseudo body force. Thus the general solution is obtained by adding a particular solution to the homogeneous one. The former is obtained by a BEM for the base Newtonian fluid and the latter is obtained analytically by approximating the pseudo body force in terms of suitable radial basis functions (RBFs). Embedded in the approximation of the pseudo body force is the calculation of the polymer stress. This is achieved by solving the constitutive equation using RBF networks (RBFNs). Both the calculations of the particular solution and the polymer stress are therefore meshless and the resultant BEM-RBF method is a BE-only method. The complete elimination of any structured domain discretisation is demonstrated with a number of flow problems involving the Upper Convected Maxwell (UCM) and the Oldroyd-B fluids

A simple, effective, green method for regioselective 3-acylation of unprotected indoles

A fast and green method is developed for regioselective acylation of indoles in the 3-position without the need for protection of the NH position. The method is based on Friedel-Crafts acylation using acid anhydrides. The method has been optimized, and Y(OTf)3 in catalytic amounts is found to be the best catalyst together with the commercially available ionic liquid [BMI]BF4 (1-butyl-3-methylimidazolium tetrafluoro-borate) as solvent. The reaction is completed in a very short time using monomode microwave irradiation. The catalyst can be reused up to four times without significant loss of activity. A range of substituted indoles are investigated as substrates, and thirteen new compounds have been synthesized

Free vibration analysis of laminated composite plates based on FSDT using one-dimensional IRBFN method

This paper presents a new effective radial basis function (RBF) collocation technique for the free vibration analysis of laminated composite plates using the first order shear deformation theory (FSDT). The plates, which can be rectangular or non-rectangular, are simply discretised by means of Cartesian grids. Instead of using conventional differentiated RBF networks, one-dimensional integrated RBF networks (1D-IRBFN) are employed on grid lines to approximate the field variables. A number of examples concerning various thickness-to-span ratios, material properties and boundary conditions are considered. Results obtained are compared with the exact solutions and numerical results by other techniques in the literature to investigate the performance of the proposed method

An improved dissipative particle dynamics scheme

Dissipative particle dynamics (DPD) and smoothed dissipative particle dynamics (sDPD) have become most popular numerical techniques for simulating mesoscopic flow phenomena in fluid systems. Several DPD/sDPD simulations in the literature indicate that \textcolor{red}{the model fluids} should be designed with their dynamic response, measured by the Schmidt number, in a relevant range in order to reach a good agreement with the experimental results. In this paper, we propose a new dissipative weighting function (or a new kernel) for the DPD (or the sDPD) formulation, which allows both the viscosity and the Schmidt number to be independently specified as input parameters. We also show that some existing dissipative functions/kernels are special cases of the proposed one, and the imposed viscosity of the present DPD/sDPD system has a lower and upper limit. Numerical verification of the proposed function/kernel is conducted in viscometric flows

ADI method based on C2-continuous two-node integrated-RBF elements for viscous flows

We propose a C2-continuous alternating direction implicit (ADI) method for the solution of the streamfunction-vorticity equations governing steady 2D incompressible viscous fluid flows. Discretisation is simply achieved with Cartesian grids. Local two-node integrated radial basis function elements (IRBFEs) [D.-A. An-Vo, N. Mai-Duy, T. Tran-Cong, A C2-continuous control-volume technique based on Cartesian grids and two-node integrated-RBF elements for second-order elliptic problems, CMES: Computer Modeling in Engineering & Sciences 72 (2011) 299-334] are used for the discretisation of the diffusion terms, and then the convection terms are incorporated into system matrices by treating nodal derivatives as unknowns. ADI procedure is applied for the time integration. Following ADI factorisation, the two-dimensional problem becomes a sequence of one-dimensional problems. The solution strategy consists of multiple use of a one-dimensional sparse matrix algorithm that helps saving the computational cost. High levels of accuracy and efficiency of the present methods are demonstrated with solutions of several benchmark problems defined on rectangular and non-rectangular domains

Analysis of viscoelastic flow by a radial basis function networks method

This paper presents a new mesh-free method based on MultiQuadric (MQ) Radial Basis Function Networks (RBFNs) for the analysis of visoelastic flows. The method uses universal approximation RBFNs to represent the numerical solution of Partial Differential Equations (PDEs) governing visoelastic flows. The main advantages of the method are its mesh-free nature and ease of implementation. The working of the method is demonstrated in detail with the simulation of the visoelastic flow through straight (Poiseuille flow) and corrugated tubes. In the case of corrugated tube flow, the irregularly shaped domain is extended to a regularly shaped one in order to simplify the pre-processing. The method achieves the Weissenberg number of at least up to 100 for the poiseuille flow of UCM and Oldroyd-B fluids using a collocation density of 6 x 6 and about 4 for the corrugated tube flow of Oldroyd-B fluid using a collocation density of 13 x 25