Least-squares finite element methods for the Navier-Stokes equations for generalized Newtonian fluids

In this contribution we present the least-squares finite element method (LSFEM) for the incompressible Navier-Stokes equations. In detail, we consider a non-Newtonian fluid flow, which is described by a power-law model, see [1]. The second-order problem is reformulated by introducing a first-order div-grad system consisting of the equilibrium condition, the incompressibility condition and the constitutive equation, which are written in residual forms, see [2]. Here, higher-order finite elements which are an important aspect regarding accuracy for the present formulation are investigated. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical solution of volterra functional integral equation by using cubic B‐spline scaling functions

In this article, we consider a class of nonlinear functional integral equations which has rather general form and contains a lot of particular cases such as functional equations and nonlinear integral equations of Volterra type. We use a combination of a fixed point method and cubic semiorthogonal B‐spline scaling functions to solve the integral equation numerically. We provide an error analysis for the method which shows that the approximate solution converges to the exact solution. Some numerical results for several test problems are given to confirm the accuracy and the ease of implementation of the method. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 699–722, 2014     

Rapid production of monodisperse cross-linked red blood corpuscle-like particles via scalable one-pot dispersion polymerization

Cross-linked polystyrene (PS) particles having red blood corpuscle (RBC)-like shape were synthesized by one-pot dispersion polymerization of styrene with ethanol/water mixture and ethylene glycol dimethacrylate (EGDMA) as the reaction medium and cross-linker, respectively. Monitoring of the reaction showed that RBC-like shape forms due to asymmetric shrinkage of a cross-linked network during the phase separation. In addition, three dimensional phase diagram was generated based on the yielded data that showed that the formation of such unique shape extremely depends on the polarity of the medium and injection time of the cross-linker. In situ synthesis of RBC-like particles, as promising biomaterials in targeted drug delivery and a model for the understanding of the cell behavior, via such fast and high solid content approach makes it to be conducive to subsequent scale up, i.e. potential commercial adoption.     

Diffusion bonding in multi-layers systems

 A mathematical model is presented to simulate the diffusion bonding in multi-layers systems. The model is solved analytically using Green's function method. The time required by the bonding material to attain its maximum solvability in the other two layers is estimated. Received on 4 January 2000     

A hybrid DSMC/Navier–Stokes frame to solve mixed rarefied/nonrarefied hypersonic flows over nano‐plate and micro‐cylinder

We extend a hybrid DSMC/Navier–Stokes (NS) approach to unify the DSMC and the NS simulators in one framework capable of solving the mixed non‐equilibrium and near‐equilibrium flow regions efficiently. Furthermore, we use a one‐way state‐based coupling (Dirichlet–Dirichlet boundary‐condition coupling) to transfer the required information from the continuum region to the rarefied one. The current hybrid DSMC–NS frame is applied to the hypersonic flows over nanoflat plate and microcylinder cases. The achieved solutions are compared with the pure DSMC and NS solutions. The results show that the current hybrid approach predicts the surface heat transfer rate and shear stress magnitudes very accurately. Some important conclusions can be drawn from this study. For example, although the shock wave region would be a non‐equilibrium region, it is not necessary to use a pure DSMC simulator to solve it entirely. This is important when the researchers wish to predict the surface properties such as velocity slip, temperature jump, wall heat flux rate, and friction drag magnitudes accurately. Our investigation showed that our hybrid solution time would be at least 40% (for the flat plate) and 35% (for the cylinder) of the time that must be spent by a pure DSMC solver to attain the same accuracy.Copyright © 2013 John Wiley & Sons, Ltd.