A point implicit unstructured grid solver for the euler and Navier–Stokes equations

An upwind finite element technique that uses cell-centred quantities and implicit and/or explicit time marching has been developed for computing hypersonic laminar viscous flows using adaptive triangular grids. The approach is an extension to unstructured grids of the LAURA algorithm due to Gnoffo. A structured grid of quadrilaterals is laid out near a solid surface. For inviscid flows the method is stable at Courant numbers of over 100000. A first-order basic scheme and a higher-order flux-corrected transport (FCT) scheme have been implemented. This technique has been applied to the problem of predicting type III and IV shock wave interactions on a cylinder, with a view to simulating the pressure and heating rate augmentation caused by an impinging shock on the leading edge of a cowl lip of an engine inlet. The predictions of wall pressure and heating rates compare very well with experimental data. The flow features are distinctly captured with a sequence of adaptively generated grids.     

Numerical studies of slow viscous rotating flow past a sphere. III

The flow of steady incompressible viscous fluid rotating about the z-axis with angular velocity ω and moving with velocity u past a sphere of radius a which is kept fixed at the origin is investigated by means of a numerical method for small values of the Reynolds number Re_ω. The Navier–Stokes equations governing the axisymmetric flow can be written as three coupled non-linear partial differential equations for the streamfunction, vorticity and rotational velocity component. Central differences are applied to the partial differential equations for solution by the Peaceman–Rachford ADI method, and the resulting algebraic equations are solved by the ‘method of sweeps’. The results obtained by solving the non-linear partial differential equations are compared with the results obtained by linearizing the equations for very small values of Re_ω. Streamlines are plotted for Ψ = 0·05, 0·2, 0·5 for both linear and non-linear cases. The magnitude of the vorticity vector near the body, i.e. at z = 0·2, is plotted for Re_ω = 0·05, 0·24, 0·5. The correction to the Stokes drag as a result of rotation of the fluid is calculated.     

非绝热壁叶栅的粘性流动

非绝热壁叶栅的粘性流动王正明（中国科学院工程热物理研究所北京１０００８０）关键词非绝热壁；叶栅；粘性流动１引言近年来，随着计算机运算速度的提高，叶轮机械内部粘性流动的数值解法发展很快，对于动量方程，已广泛采用亘接求解不作简化的完全的Ｎ－Ｓ方程，以便更...     

Effect of the Hydrodynamic Interaction of a Large Number of Particles on Their Sedimentation Rate in a Viscous Fluid

The gravity-induced sedimentation of a large number of identical spherical particles in a viscous fluid is considered. The hydrodynamic interaction of all the particles is taken into account. The problem is modeled numerically for random locations of 1–100 particles forming different configurations. A dependence of the mean sedimentation rate on the particle number and concentration in the cloud is obtained and compared with previous results.     

Three‐dimensional transient free‐surface flow of viscous fluids inside cavities of arbitrary shape

The three‐dimensional transient free‐surface flow inside cavities of arbitrary shape is examined in this study. An adaptive (Lagrangian) boundary‐element approach is proposed for the general three‐dimensional simulation of confined free‐surface flow of viscous incompressible fluids. The method is stable as it includes remeshing capabilities of the deforming free‐surface, and thus can handle large deformations. A simple algorithm is developed for mesh refinement of the deforming free‐surface mesh. Smooth transition between large and small elements is achieved without significant degradation of the aspect ratio of the elements in the mesh. The method is used to determine the flow field and free‐surface evolution inside cubic, rectangular and cylindrical containers. These problems illustrate the transient nature of the flow during the mixing process. Surface tension effects are also explored. Copyright © 2003 John Wiley & Sons, Ltd.     

On the minimum of extended dissipation in viscous nematodynamics

This paper develops the variational principle of minimum extended dissipation for slow (low Reynolds number) flows of nematic liquids as described by the five parametric Leslie–Ericksen–Parodi (LEP) constitutive equations. It is shown that the Eulers equations for minimizer of the extended dissipative functional are the Stokes equations for the LEP fluid. When the molecular (including magnetic) field is absent, the extended dissipative functional coincides with the true dissipative functional, whose Euler equations are the Stokes equations for the Ericksen fluid.     

Optical studies of local flow behaviour of a non-Newtonian fluid inside a porous medium

In this study the local flow of a polymeric solution inside a porous medium is studied visually. While the flow is quite uniform for low volume flow rates it shows pronounced nonuniformity for higher volume flow rates. That is to say, only certain preferred passages are taken and these passages change in time (they fluctuate). This flow irregularity is the reason for increased resistance. Received: 28 April 1997 Accepted: 30 December 1997     

Aggregation equations with gradient potential as Radon measure and initial data in Besov-Morrey spaces

In this work, we present conditions to obtain a global-in-time existence of solutions to a class of nonlinear viscous transport equations describing aggregation phenomena in biology with sufficiently small initial data in Besov-Morrey spaces and gradient potential as a Radon measure. We also study the self-similarity and asymptotic stability of solutions at large times.     

Mechanical Properties of Bacterially Synthesized Nanocellulose Hydrogels

The mechanical characteristics of bacterially synthesized nano-cellulose (BNC) were studied with uniaxial compression and tensile tests. Compressive loads result in a release of water and the deformation of the water-saturated network corresponds approximately to the volume of released water. The BNC hydrogel exhibits a mainly viscous response under compression. The strain response under tensile loads has an elastic and a viscous component. This can be described with a Maxwell model, where the viscosity is strain rate-dependent. When the aqueous phase of the BNC hydrogel is stabilized with an additional alginate hydrogel matrix, the system exhibits an elastic response under compressive loads. The analysis of the ‘alginated’ BNC network with the Maxwell model shows that the alginate matrix increases the viscosity of the composite system. The results of the mechanical tests show that the water absorbed in the BNC hydrogel strongly influences its mechanical behavior.     

On modified block SSOR iteration methods for linear systems from steady incompressible viscous flow problems

In order to solve the large sparse systems of linear equations arising from numerical solutions of two-dimensional steady incompressible viscous flow problems in primitive variable formulation, we present block SSOR and modified block SSOR iteration methods based on the special structures of the coefficient matrices. In each step of the block SSOR iteration, we employ the block LU factorization to solve the sub-systems of linear equations. We show that the block LU factorization is existent and stable when the coefficient matrices are block diagonally dominant of type-II by columns. Under suitable conditions, we establish convergence theorems for both block SSOR and modified block SSOR iteration methods. In addition, the block SSOR iteration and AF-ADI method are considered as preconditioners for the nonsymmetric systems of linear equations. Numerical experiments show that both block SSOR and modified block SSOR iterations are feasible iterative solvers and they are also effective for preconditioning Krylov subspace methods such as GMRES and BiCGSTAB when used to solve this class of systems of linear equations.