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

Investigation of particles size effects in Dissipative Particle Dynamics (DPD) modelling of colloidal suspensions

In the Dissipative Particle Dynamics (DPD) simulation of suspension, the fluid (solvent) and colloidal particles are replaced by a set of DPD particles and therefore their relative sizes (as measured by their exclusion zones) can affect the maximal packing fraction of the colloidal particles. In this study, we investigate roles of the conservative, dissipative and random forces in this relative size ratio (colloidal/solvent). We propose a mechanism of adjusting the DPD parameters to properly model the solvent phase (the solvent here is supposed to have the same isothermal compressibility to that of water)

A dissipative particle dynamics model for thixotropic materials exhibiting pseudo-yield stress behaviour

Many materials (e.g., gels, colloids, concentrated cohesive sediments, etc.) exhibit a stable solid form at rest, and liquify once subjected to an applied stress exceeding a critical value – a yield-stress behaviour. This can be qualitatively explained by the forming and destruction of the fluid microstructure [1], and it may be modelled as a thixotropic and yield stress material. In this paper, we propose a mesoscopic model which is able to mimic a thixotropic and yield stress behaviour using a particle-based technique known as dissipative particle dynamics (DPD). The DPD technique satisfies conservation of mass and momentum and it has been applied successfully for a number of problems involving complex-structure fluids, such as polymer solutions, suspensions of rigid particles, droplets, biological fluids, etc. In this work, an indirect linkage dissipative particle model (ILDP) is proposed based on qualitative microstructural physics, which results in a non-Newtonian fluid with observed yield stress and thixotropic properties. The model comprises of two types, or species, of DPD particles – with only repulsive conservative force between the same species, and with repulsive force at short range and attractive force at long range between different species. Numerical results show that the proposed DPD fluid can represent some observed complex behaviours, such as yield stress and thixotropic effects

Strongly overdamped dissipative particle dynamics for fluid-solid systems

In this paper, a numerical scheme is used to study strongly-overdamped Dissipative Particles Dynamics (DPD) systems for the modelling of fluid-solid systems. In the scheme, the resultant set of algebraic equations for the velocities are directly solved in an iterative manner. Different test problems, e.g., viscometric flows, particulate suspensions and flows past a periodic square array of cylinders, are used to verify the proposed method. In the simulation of particulate suspensions, a new simple model for massless suspended particles is presented. A DPD fluid in the overdamped limit is shown to possess several attractive properties including much faster dynamic response and near-incompressibility

A numerical study of compact approximations based on flat integrated radial basis functions for second-order differential equations

In this paper, we propose a simple but effective preconditioning technique to improve the numerical stability of Integrated Radial Basis Function (IRBF) methods. The proposed preconditioner is simply the inverse of a well-conditioned matrix that is constructed using non-flat IRBFs. Much larger values of the free shape parameter of IRBFs can thus be employed and better accuracy for smooth solution problems can be achieved. Furthermore, to improve the accuracy of local IRBF methods, we propose a new stencil, namely Combined Compact IRBF (CCIRBF), in which (i) the starting point is the fourth-order derivative; and (ii) nodal values of first- and second-order derivatives at side nodes of the stencil are included in the computation of first- and second-order derivatives at the middle node in a natural way. The proposed stencil can be employed in uniform/nonuniform Cartesian grids. The preconditioning technique in combination with the CCIRBF scheme employed with large values of the shape parameter are tested with elliptic equations and then applied to simulate several fluid flow problems governed by Poisson, Burgers, convection-diffusion, and Navier-Stokes equations. Highly accurate and stable solutions are obtained. In some cases, the preconditioned schemes are shown to be several orders of magnitude more accurate than those without preconditioning

The burden and characteristics of enteric fever at a healthcare facility in a densely populated area of Kathmandu

Enteric fever, caused by Salmonella enterica serovars Typhi and Paratyphi A (S. Typhi and S. Paratyphi A) remains a major public health problem in many settings. The disease is limited to locations with poor sanitation which facilitates the transmission of the infecting organisms. Efficacious and inexpensive vaccines are available for S. Typhi, yet are not commonly deployed to control the disease. Lack of vaccination is due partly to uncertainty of the disease burden arising from a paucity of epidemiological information in key locations. We have collected and analyzed data from 3,898 cases of blood culture-confirmed enteric fever from Patan Hospital in Lalitpur Sub-Metropolitan City (LSMC), between June 2005 and May 2009. Demographic data was available for a subset of these patients (n = 527) that were resident in LSMC and who were enrolled in trials. We show a considerable burden of enteric fever caused by S. Typhi (2,672; 68.5%) and S. Paratyphi A (1,226; 31.5%) at this Hospital over a four year period, which correlate with seasonal fluctuations in rainfall. We found that local population density was not related to incidence and we identified a focus of infections in the east of LSMC. With data from patients resident in LSMC we found that the median age of those with S. Typhi (16 years) was significantly less than S. Paratyphi A (20 years) and that males aged 15 to 25 were disproportionately infected. Our findings provide a snapshot into the epidemiological patterns of enteric fever in Kathmandu. The uneven distribution of enteric fever patients within the population suggests local variation in risk factors, such as contaminated drinking water. These findings are important for initiating a vaccination scheme and improvements in sanitation. We suggest any such intervention should be implemented throughout the LSMC area.This work was supported by The Wellcome Trust, Euston Road, London, United Kingdom. MFB is supported by the Medical Research Council (grant G0600718). SB is supported by an OAK foundation fellowship through Oxford University

A microstructure model for viscoelastic–thixotropic fluids

A microstructure model to describe the viscoelasticity and thixotropy properties of complex fluids is proposed. The model is based on the Lodge–Yamamoto network theory and is an extension of the Phan-Thien–Tanner model, with a kinetic process in which specific forms of creation and destruction rates are assumed. The final equation is simple with a small number of empirical parameters required and can be conveniently employed in engineering simulations. The predictions based on the model in a variety of shear and oscillatory shear flows are given. The stress response obtained from the model prediction agrees well with experiments on both shear and oscillatory flow histories

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