Different types of solutions to a multivalued model of granular flow

We deal with a modification of the Savage–Hutter model describing granular material with multivalued friction force. The multivalued structure of this model requires a modification of known definitions of a solution. The connections between definitions of three different types of solutions: entropy, measure‐valued and kinetic are shown. Copyright © 2013 John Wiley & Sons, Ltd.     

Modeling methods and a branch and cut algorithm for pharmaceutical clinical trial planning using stochastic programming

We discuss methods for the solution of a multi-stage stochastic programming formulation for the resource-constrained scheduling of clinical trials in the pharmaceutical research and development pipeline. First, we present a number of theoretical properties to reduce the size and improve the tightness of the formulation, focusing primarily on non-anticipativity constraints. Second, we develop a novel branch and cut algorithm where necessary non-anticipativity constraints that are unlikely to be active are removed from the initial formulation and only added if they are violated within the search tree. We improve the performance of our algorithm by combining different node selection strategies and exploring different approaches to constraint violation checking.     

A kinetic scheme for unsteady pressurised flows in closed water pipes

The aim of this paper is to present a kinetic numerical scheme for the computations of transient pressurised flows in closed water pipes. Firstly, we detail the mathematical model written as a conservative hyperbolic partial differentiel system of equations, and then we recall how to obtain the corresponding kinetic formulation. Then we build the kinetic scheme ensuring an upwinding of the source term due to the topography performed in a close manner described by Perthame and Simeoni (2001) [1] and Botchorishvili et al. (2003) [2] using an energetic balance at microscopic level. The validation is lastly performed in the case of a water hammer in an uniform pipe: we compare the numerical results provided by an industrial code used at EDF-CIH (France), which solves the Allievi equation (the commonly used equation for pressurised flows in pipes) by the method of characteristics, with those of the kinetic scheme. It appears that they are in a very good agreement.     

A high-order compact scheme for solving the 2D steady incompressible Navier-Stokes equations in general curvilinear coordinates

In this paper, a high-order compact finite difference algorithm is established for the stream function-velocity formulation of the two-dimensional steady incompressible Navier-Stokes equations in general curvilinear coordinates. Different from the previous work, not only the stream function and its first-order partial derivatives but also the second-order mixed partial derivative is treated as unknown variable in this work. Numerical examples, including a test problem with an analytical solution, three types of lid-driven cavity flow problems with unusual shapes and steady flow past a circular cylinder as well as an elliptic cylinder with angle of attack, are solved numerically by the newly proposed scheme. For two types of the lid-driven trapezoidal cavity flow, we provide the detailed data using the fine grid sizes, which can be considered the benchmark solutions. The results obtained prove that the present numerical method has the ability to solve the incompressible flow for complex geometry in engineering applications, especially by using a nonorthogonal coordinate transformation, with high accuracy.     

Adaptive numerical modeling using the hierarchical Fup basis functions and control volume isogeometric analysis

A novel adaptive algorithm that is based on new hierarchical Fup (HF) basis functions and a control volume formulation is presented. Because of its similarity to the concept of isogeometric analysis (IGA), we refer to it as control volume isogeometric analysis (CV-IGA). Among other interesting properties, the IGA introduced k-refinement as advanced version of hp-refinement, where every basis function of the nth order from one resolution level are replaced by a linear combination of more basis functions of the n+1th order at the next resolution level. However, k-refinement can be performed only on whole domain, while local adaptive k-refinement is not possible with classical B-spline basis functions. HF basis functions (infinitely differentiable splines) satisfy partition of unity, and they are linearly independent and locally refinable. Their main feature is execution of the adaptive local hp-refinement because any basis function of the nth order from one resolution level can be replaced by a linear combination of more basis functions of the n+1th order at the next resolution level providing spectral convergence order. The comparison between uniform vs hierarchical adaptive solutions is demonstrated, and it is shown that our adaptive algorithm returns the desired accuracy while strongly improving the efficiency and controlling the numerical error. In addition to the adaptive methodology, a stabilization procedure is applied for advection-dominated problems whose numerical solutions “suffer” from spurious oscillations. Stabilization is added only on lower resolution levels, while higher resolution levels ensure an accurate solution and produce a higher convergence order. Since the focus of this article is on developing HF basis functions and adaptive CV-IGA, verification is performed on the stationary one-dimensional boundary value problems.     

Interaction of a deformable solid with two-phase flows: An Eulerian-based numerical model for fluid-structure interaction using the level contour reconstruction method

We describe the formulation of a method for fluid-structure interaction involving the coupling of moving and/or flexible solid structures with multiphase flows in the framework of the Level Contour Reconstruction Method. We present an Eulerian-based numerical procedure for tracking the motion and interaction of a liquid-gas interface with a fluid-solid interface in the Lagrangian frame together with the evaluation of the fluid transport equations coupled to those for the solid transport, namely the left Cauchy-Green strain tensor field, in the Eulerian frame. To prevent excessive dissipation due to the convective nature of the solid transport equation, a simple incompressibility constraint for the strain field is enforced. A single grid structure is used for both the fluid and solid phases which allows for a simple and natural coupling of the fluid and solid dynamics. Several benchmark tests are performed to show the accuracy of the numerical method and which demonstrate accurate results compared to several of those in the existing literature. In particular we show that surface tension effects including contact line dynamics on the deforming solid phase can be properly simulated. The three-phase interaction of a droplet impacting on a flexible cantilever is investigated in detail. The simulations follow the detailed motion of the droplet impact (and subsequent deformation, breakup, and fall trajectory) along with the motion of the deformable solid cantilever due to its own weight as well as due to the force of the droplet impact.     

High-throughput measurements of ciprofloxacin,clomipramine and fexofenadine hydrochlorides with an 8-channel electrical titrator

By employing a developed automatic eight-channel electrical titrator, ciprofloxacin, clomipramine and fexofenadine hydrochlorides are determined in batch, respectively, with satisfactory accuracy and precision. It shows a higher efficiency superior to traditional titration method, and maximally 30 measurements per minute can be completed.     

Unified one‐fluid formulation for incompressible flexible solids and multiphase flows: Application to hydrodynamics using the immersed structural potential method (ISPM)

In this paper, we present a two‐dimensional computational framework for the simulation of fluid‐structure interaction problems involving incompressible flexible solids and multiphase flows, further extending the application range of classical immersed computational approaches to the context of hydrodynamics. The proposed method aims to overcome shortcomings such as the restriction of having to deal with similar density ratios among different phases or the restriction to solve single‐phase flows. First, a variation of classical immersed techniques, pioneered with the immersed boundary method (IBM), is presented by rearranging the governing equations, which define the behaviour of the multiple physics involved. The formulation is compatible with the “one‐fluid” formulation for two‐phase flows and can deal with large density ratios with the help of an anisotropic Poisson solver. Second, immersed deformable structures and fluid phases are modelled in an identical manner except for the computation of the deviatoric stresses. The numerical technique followed in this paper builds upon the immersed structural potential method developed by the authors, by adding a level set–based method for the capturing of the fluid‐fluid interfaces and an interface Lagrangian‐based meshless technique for the tracking of the fluid‐structure interface. The spatial discretisation is based on the standard marker‐and‐cell method used in conjunction with a fractional step approach for the pressure/velocity decoupling, a second‐order time integrator, and a fixed‐point iterative scheme. The paper presents a wide d range of two‐dimensional applications involving multiphase flows interacting with immersed deformable solids, including benchmarking against both experimental and alternative numerical schemes.     

基于IB-LBFS和绝对节点坐标法的降落伞柔性结构流固耦合数值模拟

在空气动力学、水动力学和生物流体力学领域中,大变形柔性结构的流固耦合现象是一个重要的非线性力学问题.对该系统的数值模拟是分析这一问题的有效手段.将近年提出的一种Descartes流场求解器,即浸润边界-格子Boltzmann通量求解器(immersed boundary-lattice Boltzmann flux solver,IB-LBFS)作为流场求解方法,并引入绝对节点坐标法(absolute nodal coordinate formulation,ANCF)作为大变形结构分析手段,构建了流固耦合求解器以模拟三维流场中的大变形柔性体运动.使用三维来流中的旗帜摆动算例对该流固耦合求解器进行了验证计算.基于该流固耦合求解器对三维不可压流场中的矩形降落伞和十字形降落伞的展开过程进行了非定常流固耦合数值模拟.     

HPLC‐DAD method for the simultaneous determination of zofenopril and hydrochlorothiazide in oral pharmaceutical formulations

An HPLC method with DAD detection was developed and validated for the simultaneous determination of zofenopril and hydrochlorothiazide in tablets. The separation was carried out through a gradient elution using an Agilent LiChrospher C18 column (250×4.0 mm id, 5 μm) and a mobile phase consisting of (A) water–TFA (99.9:0.1 v/v) and (B) acetonitrile–TFA (99.1:0.1 v/v) delivered at a flow‐rate of 1.0 mL/min. 8‐Chlorotheophylline was used as internal standard. Calibration curves were found to be linear for the two drugs over the concentration ranges of 5.0–40 and 1.0–20 μg/mL for zofenopril and hydrochlorothiazide, respectively. Linearity, precision, accuracy, specificity and robustness were determined in order to validate the proposed method, which was further applied to the analysis of commercial tablets. The proposed method is simple and rapid, and gives accurate and precise results.