When the Galerkin finite-element method with a nine-node isoparametric Lagrangian element is applied to solve non-Newtonian fluid flow problems, a considerable amount of computing time is required to solve the discretized non-linear system of equations by Newton's method. A method proposed by Broyden has been modified to compute the Jacobian matrix associated with Newton's method. This modified Broyden's method can be combined with the frontal method to efficiently solve the linearized finite-element equations during the iteration. Numerical results of a sample problem concerning the determination of the pressure-drop/flow-rate relationship for power-law fluids in rectangular ducts show that the application of this new method can reduce computing time substantially. 相似文献
A 3-D nonlinear problem of supercavitating flow past an axisymmetric body at a small angle of attack is investigated by means
of the perturbation method and Fourier-cosine-expansion method. The first three order perturbation equations are derived in
detail and solved numerically using the boundary integral equation method and iterative techniques. Computational results
of the hydrodynamic characteristics and cavity shapes of each order are presented for nonaxisymmetric supercavitating flow
past cones with various apex-angles at different cavitation numbers. The numerical results are found in good agreement with
experimental data.
The project supported by the National Natural Science Foundation of China 相似文献
In this paper a constitutive equation for the extra stress tensor τ is considered, which can be used for steady axisymmetric
flows when uϕ=0 (non-swirling). It is explicit with coefficients which, in case of incompressibility, depend only upon three invariants.
As such it should prove useful in numerical calculations, especially so if used in its simplest form, namely the quasi-Newtonian
fluid. Here, a purely viscous code can be used. The constitutive equation is self-consistent and receives additional justification
from the fact that any constitutive equation is bound to result in the form proposed if the flow is a constant stretch history
flow.
Received: 30 March 1998 Accepted: 6 August 1998 相似文献
Fundamental concepts underlying spectral collocation methods, especially pertaining to their use in the solution of partial differential equations, are outlined. Theoretical accuracy results are reviewed and compared with results from test problems. A number of practical aspects of the construction and use of spectral methods are detailed, along with several solution schemes which have found utility in applications of spectral methods to practical problems. Results from a few of the successful applications of spectral methods to problems of aerodynamic and fluid mechanic interest are then outlined, followed by a discussion of the problem areas in spectral methods and the current research under way to overcome these difficulties. 相似文献
The study of viscous flow in tubes with deformable walls is of specific interest in industry and biomedical technology and
in understanding various phenomena in medicine and biology (atherosclerosis, artery replacement by a graft, etc) as well.
The present work describes numerically the behavior of a viscous incompressible fluid through a tube with a non-linear elastic
membrane insertion. The membrane insertion in the solid tube is composed by non-linear elastic material, following Fung’s
(Biomechanics: mechanical properties of living tissue, 2nd edn. Springer, New York, 1993) type strain–energy density function.
The fluid is described through a Navier–Stokes code coupled with a system of non linear equations, governing the interaction
with the membrane deformation. The objective of this work is the study of the deformation of a non-linear elastic membrane
insertion interacting with the fluid flow. The case of the linear elastic material of the membrane is also considered. These
two cases are compared and the results are evaluated. The advantages of considering membrane nonlinear elastic material are
well established. Finally, the case of an axisymmetric elastic tube with variable stiffness along the tube and membrane sections
is studied, trying to substitute the solid tube with a membrane of high stiffness, exhibiting more realistic response. 相似文献
The present paper reports on a modified pressure implicit predictor corrector type scheme for solving the flow governing equations, in which a consistent formulation is combined with a multi-grid solver for the pressure correction. In addition a parabolic sublayer (PSL) approach for the treatment of the flow in the vicinity of solid walls is critically evaluated in terms of accuracy and computational efficiency. The lid-driven cavity flow is chosen as the test case and results are presented for Reynolds numbers ranging from 100 to 1000. Predictions with the proposed scheme indicate substantial computational savings and fairly good agreement when compared with previous work. The PSL approach reduces the computing time, but with increasing Reynolds numbers the accuracy of the solutions tends to deteriorate. 相似文献
An Uzawa-type algorithm is designed for the coupled Stokes equations discretized by the mixed finite element method. The velocity solved by the presented algorithm is weakly divergence-free, which is different from the one solved by the common Uzawa method. Besides, an optimal relaxation parameter of the presented algorithm is provided. 相似文献
In this paper, a parallel algorithm with iterative form for solving finite element equation is presented. Based on the iterative solution of linear algebra equations, the parallel computational steps are introduced in this method. Also by using the weighted residual method and choosing the appropriate weighting functions, the finite element basic form of parallel algorithm is deduced. The program of this algorithm has been realized on the ELXSI-6400 parallel computer of Xi'an Jiaotong University. The computational results show the operational speed will be raised and the CPU time will be cut down effectively. So this method is one kind of effective parallel algorithm for solving the finite element equations of large-scale structures. 相似文献
Preconditioned conjugate gradient algorithms for solving 3D Stokes problems by stable piecewise discontinuous pressure finite elements are presented. The emphasis is on the preconditioning schemes and their numerical implementation for use with Hermitian based discontinuous pressure elements. For the piecewise constant discontinuous pressure elements, a variant implementation of the preconditioner proposed by Cahouet and Chabard for the continuous pressure elements is employed. For the piecewise linear discontinuous pressure elements, a new preconditioner is presented. Numerical examples are presented for the cubic lid-driven cavity problem with two representative elements, i.e. the Q2-PO and the Q2-P1 brick elements. Numerical results show that the preconditioning schemes are very effective in reducing the number of pressure iterations at very reasonable costs. It is also shown that they are insensitive to the mesh Reynolds number except for nearly steady flows (Rem → 0) and are almost independent of mesh sizes. It is demonstrated that the schemes perform reasonably well on non-uniform meshes. 相似文献
This paper presents a theoretical formulation in which the stream-tube method (STM) is examined through a variational approach for solving solid strain and fluid flow problems with finite elements. The analysis considers a reference domain, used as computational domain, related to the physical domain by an unknown transformation function to be determined numerically. Mass conservation is automatically verified by STM. The variational approach leads to eliminate the pressure in fluid problems and avoids to set up a mixed displacement–pressure procedure in the case of incompressible solids. Examples are given for fluid flows, applications and comparisons are also provided in the bending problem in elasticity. 相似文献
The boundary value problem arises in boundary layer equations for the steady flow of a power-law fluid over an impermeable, semi-infinite flat plane. The parameter μ is equal to where n is the exponent of the strain rate in the expression for the shear stress. We develop and prove the convergence of an iterative method for the solution of the given boundary value broblem for dilatant fluids (0 < μ <1). The iterative method can be easily implemented computationally. An added feature of our technique is that it accurately yields y(0), an important parameter which is related to the drag at the plate. The iterative method works well computationally not only for 0 < μ < 1 but for the range 1 < μ < 4 (pseudoplastic fluids with 1 > n > ), as well. 相似文献
In this paper the generation of general curvilinear co-ordinate systems for use in selected two-dimensional fluid flow problems is presented. The curvilinear co-ordinate systems are obtained from the numerical solution of a system of Poisson equations. The computational grids obtained by this technique allow for curved grid lines such that the boundary of the solution domain coincides with a grid line. Hence, these meshes are called boundary fitted grids (BFG). The physical solution area is mapped onto a set of connected rectangles in the transformed (computational) plane which form a composite mesh. All numerical calculations are performed in the transformed plane. Since the computational domain is a rectangle and a uniform grid with mesh spacings Δξ = Δη = 1 (in two-dimensions) is used, the computer programming is substantially facilitated. By means of control functions, which form the r.h.s. of the Poisson equations, the clustering of grid lines or grid points is governed. This allows a very fine resolution at certain specified locations and includes adaptive grid generation. The first two sections outline the general features of BFGs, and in section 3 the general transformation rules along with the necessary concepts of differential geometry are given. In section 4 the transformed grid generation equations are derived and control functions are specified. Expressions for grid adaptation arc also presented. Section 5 briefly discusses the numerical solution of the transformed grid generation equations using sucessive overrelaxation and shows a sample calculation where the FAS (full approximation scheme) multigrid technique was employed. In the companion paper (Part II), the application of the BFG method to selected fluid flow problems is addressed. 相似文献