共查询到20条相似文献,搜索用时 234 毫秒
1.
David P. Young Robin G. Melvin Michael B. Bieterman Forrester T. Johnson Satish S. Samant 《国际流体数值方法杂志》1990,11(8):1075-1095
In computational fluid dynamics, non-linear differential equations are essential to represent important effects such as shock waves in transonic flow. Discretized versions of these non-linear equations are solved using iterative methods. In this paper an inexact Newton method using the GMRES algorithm of Saad and Schultz is examined in the context of the full potential equation of aerodynamics. In this setting, reliable and efficient convergence of Newton methods is difficult to achieve. A poor initial solution guess often leads to divergence or very slow convergence. This paper examines several possible solutions to these problems, including a standard local damping strategy for Newton's method and two continuation methods, one of which utilizes interpolation from a coarse grid solution to obtain the initial guess on a finer grid. It is shown that the continuation methods can be used to augment the local damping strategy to achieve convergence for difficult transonic flow problems. These include simple wings with shock waves as well as problems involving engine power effects. These latter cases are modelled using the assumption that each exhaust plume is isentropic but has a different total pressure and/or temperature than the freestream. 相似文献
2.
Björn Johannesson 《Transport in Porous Media》2010,85(2):565-592
A numerical scheme for the transient solution of a generalized version of the Poisson–Nernst–Planck (PNP) equations is presented.
The finite element method is used to establish the coupled non-linear matrix system of equations capable of solving the present
problem iteratively. The PNP equations represent a set of diffusion equations for charged species, i.e. dissolved ions, present
in the pore solution of a rigid porous material in which the surface charge can be assumed neglectable. These equations are
coupled to the ‘internally’ induced electrical field and to the velocity field of the fluid. The Nernst–Planck equations describing
the diffusion of the ionic species and Gauss’ law in use are, however, coupled in both directions. The governing set of equations
is derived from a simplified version of the so-called hybrid mixture theory (HMT). The simplifications used here mainly concerns
ignoring the deformation and stresses in the porous material in which the ionic diffusion occurs. The HMT is a special version
of the more ‘classical’ continuum mixture theories in the sense that it works with averaged equations at macroscale and that
it includes the volume fractions of phases in its structure. The background to the PNP equations can by the HMT approach be
described by using the postulates of mass conservation of constituents together with Gauss’ law used together with consistent
constitutive laws. The HMT theory includes the constituent forms of the quasistatic version of Maxwell’s equations making
it suitable for analyses of the kind addressed in this work. Within the framework of HTM, constitutive equations have been
derived using the postulate of entropy inequality together with the technique of identifying properties by Lagrange multipliers.
These results will be used in obtaining a closed set of equations for the present problem. 相似文献
3.
S. Mizzi R. W. Barber D. R. Emerson J. M. Reese S. K. Stefanov 《Continuum Mechanics and Thermodynamics》2007,19(5):273-283
This paper presents a new technique that combines Grad’s 13-moment equations (G13) with a phenomenological approach to rarefied
gas flows. This combination and the proposed solution technique capture some important non-equilibrium phenomena that appear
in the early continuum-transition flow regime. In contrast to the fully coupled 13-moment equation set, a significant advantage
of the present solution technique is that it does not require extra boundary conditions explicitly; Grad’s equations for viscous
stress and heat flux are used as constitutive relations for the conservation equations instead of being solved as equations
of transport. The relative computational cost of this novel technique is low in comparison to other methods, such as fully
coupled solutions involving many moments or discrete methods. In this study, the proposed numerical procedure is tested on
a planar Couette flow case, and the results are compared to predictions obtained from the direct simulation Monte Carlo method.
This test case highlights the presence of normal viscous stresses and tangential heat fluxes that arise from non-equilibrium
phenomena, which cannot be captured by the Navier–Stokes–Fourier constitutive equations or phenomenological modifications.
相似文献
4.
H. Salt 《Transport in Porous Media》1988,3(4):325-341
The ‘power integral method’ of calculating heat transfer across a convecting porous layer is extended to flux and porous boundaries.
Convection starts at lower Rayleigh numbers for constant flux than for isothermal impervious boundaries and the flux is much
greater. At higher Rayleigh numbers, as more of the higher modes contribute to the flux, the type of boundary has less influence
on the heat transfer across the layer. For constant flux boundaries, simplified equations are developed to determine critical
values for the second and higher modes and these values can be related simply to those for isothermal impervious boundaries. 相似文献
5.
混沌分形是动力系统普遍出现的一种现象,牛顿-拉夫森NR(Newton-Raphson)方法是重要的一维及多维迭代技术,其迭代本身对初始点非常敏感,该敏感区是牛顿-拉夫森法所构成的非线性离散动力系统Julia集,在Julia集中迭代函数会呈现出混沌分形现象,提出了一种寻找牛顿-拉夫森函数的Julia点的求解方法,利用非线性离散动力系统在其Julia集出现混沌分形现象的特点,提出了一种基于牛顿-拉夫森法的非线性方程组求解的新方法,计算实例表明了该方法的有效性和正确性. 相似文献
6.
G. V. Alekseev D. A. Tereshko 《Journal of Applied Mechanics and Technical Physics》2010,51(4):510-520
An inverse extremum problem of boundary control for steady equations of thermal convection is considered. The cost functional
in this problem is chosen to be the root-mean-square deviation of flow velocity or vorticity from the velocity or vorticity
field given in a certain part of the flow domain; the control parameter is the heat flux through a part of the boundary. A
theorem on sufficient conditions on initial data providing the existence, uniqueness, and stability of the solution is given.
A numerical algorithm of solving this problem, based on Newton’s method and on the finite element method of discretization
of linear boundary-value problems, is proposed. Results of computational experiments on solving extremum problems, which confirm
the efficiency of the method developed, are discussed. 相似文献
7.
In the present paper, a plate and frame heat exchanger is considered. Multi-objective optimization using genetic algorithm
is developed in order to obtain a set of geometric design parameters, which lead to minimum pressure drop and the maximum
overall heat transfer coefficient. Vividly, considered objective functions are conflicting and no single solution can satisfy
both objectives simultaneously. Multi-objective optimization procedure yields a set of optimal solutions, called Pareto front,
each of which is a trade-off between objectives and can be selected by the user, regarding the application and the project’s
limits. The presented work takes care of numerous geometric parameters in the presence of logical constraints. A sensitivity
analysis is also carried out to study the effects of different geometric parameters on the considered objective functions.
Modeling the system and implementing the multi-objective optimization via genetic algorithm has been performed by MATLAB. 相似文献
8.
We consider the Navier–Stokes equations in a thin domain of which the top and bottom surfaces are not flat. The velocity fields
are subject to the Navier conditions on those boundaries and the periodicity condition on the other sides of the domain. This
toy model arises from studies of climate and oceanic flows. We show that the strong solutions exist for all time provided
the initial data belong to a “large” set in the Sobolev space H
1. Furthermore we show, for both the autonomous and the nonautonomous problems, the existence of a global attractor for the
class of all strong solutions. This attractor is proved to be also the global attractor for the Leray–Hopf weak solutions
of the Navier–Stokes equations. One issue that arises here is a nontrivial contribution due to the boundary terms. We show
how the boundary conditions imposed on the velocity fields affect the estimates of the Stokes operator and the (nonlinear)
inertial term in the Navier–Stokes equations. This results in a new estimate of the trilinear term, which in turn permits
a short and simple proof of the existence of strong solutions for all time. 相似文献
9.
求解非线性方程组的混合遗传算法 总被引:27,自引:2,他引:25
非线性方程组的求解是数值计算领域中最困难的问题。大多数的数值求解算法例如牛顿法的收敛性和性能特征在很大程度上依赖于初始点。但是对于很多非线性方程组,选择好的初始点是一件非常困难的事情。本文结合遗传算法和经典算法的优点,提出了一种用于求解非线性方程组的混合遗传算法。该混合算法充分发挥了遗传算法的群体搜索和全局收敛性,有效地克服了经典算法的初始点敏感问题;同时在遗传算法中引入经典算法(Powell法、拟牛顿迭代法)作局部搜索,克服了遗传算法收敛速度慢和精度差的缺点。选择了几个典型非线性方程组,从收敛可靠性、计算成本和适用性等指标分析对比了不同算法。计算结果表明所设计的混合遗传算法有着可靠的收敛性和较高的收敛速度和精度,是求解非线性方程组的一种成功算法。 相似文献
10.
The interfacial heat transfer coefficient (IHTC) is necessary for accurate simulation of the casting process. In this study,
a cylindrical geometry is selected for the determination of the IHTC between aluminum alloy casting and the surrounding sand
mold. The mold surface heat flux and temperature are estimated by two inverse heat conduction techniques, namely Beck’s algorithm
and control volume technique. The instantaneous cast and mold temperatures are measured experimentally and these values are
used in the theoretical investigations. In the control volume technique, partial differential heat conduction equation is
reduced to ordinary differential equations in time, which are then solved sequentially. In Beck’s method, solution algorithm
is developed under the function specification method to solve the inverse heat conduction equations. The IHTC was determined
from the surface heat flux and the mold surface temperature by both the techniques and the results are compared. 相似文献
11.
El?in?Yusufo?lu 《Nonlinear dynamics》2008,52(4):395-402
This paper deals with obtaining explicit solutions of a generalized non-linear Boussinesq equation using He’s variational
iteration method. Both finite and blow-up solutions can be obtained. 相似文献
12.
An analytical approximate method for strongly nonlinear damped oscillators is proposed. By introducing phase and amplitude
of oscillation as well as a bookkeeping parameter, we rewrite the governing equation into a partial differential equation
with solution being a periodic function of the phase. Based on combination of the Newton’s method with the harmonic balance
method, the partial differential equation is transformed into a set of linear ordinary differential equations in terms of
harmonic coefficients, which can further be converted into systems of linear algebraic equations by using the bookkeeping
parameter expansion. Only a few iterations can provide very accurate approximate analytical solutions even if the nonlinearity
and damping are significant. The method can be applied to general oscillators with odd nonlinearities as well as even ones
even without linear restoring force. Three examples are presented to illustrate the usefulness and effectiveness of the proposed
method. 相似文献
13.
Highly nonlinear advection–dispersion-reaction equations govern numerous transport phenomena. Robust, accurate, and efficient
algorithms to solve these equations hold the key to the success of applying numerical models to field problems. This paper
presents the development and verification of a computational algorithm to approximate the highly nonlinear transport equations
of reactive chemical transport and multiphase flow. The algorithm was developed based on the Lagrangian-Eulerian decoupling method with an adaptive ZOOMing and Peak/valley Capture (LEZOOMPC) scheme. It consists of both backward and forward node tracking, rough element determination, peak/valley
capturing, and adaptive local grid refinement. A second-order tracking was implemented to accurately and efficiently track
all fictitious particles. Shanks’ method was introduced to deal with slowly converging case. The accuracy and efficiency of
the algorithm were verified with the Burger equation for a variety of cases. The robustness of the algorithm to achieve convergent
solutions was demonstrated by highly nonlinear reactive contaminant transport and multiphase flow problems. 相似文献
14.
We present the theory of space–time elasticity and demonstrate that it is the extended reversible thermodynamics and gives the coupled model of thermoelasticity and heat conductivity and involves traditional thermoelasticity. We formulate the generally covariant variational model’s dynamic thermoelasticity and heat conductivity in which the basic kinematic and static variables are unified tensor objects (subject, matter). Variation statement defines the whole set of the initial-boundary problems for the 4D vector governing equation (Euler equation), the spatial projections of which define motion equations and the time projection gives the heat conductivity equation. We show that space–time elasticity directly implies the Fourier and the Maxwell–Cattaneo laws of heat conduction. However, space–time elasticity is richer than classical thermoelasticity, and it advocates its own equations of motion for coupled thermoelasticity. Moreover, we establish that the Maxwell–Cattaneo law and Fourier law can be defined for the reversible processes as compatibility equations without introducing dissipation. We argue that the present framework of space–time elasticity should prove adequate to describe the thermoelastic phenomena at low temperatures for interpreting the results of molecular simulations of heat conduction in solids and for the optimal heat and stress management in the microelectronic components and the thermoelectric devices. 相似文献
15.
A model is proposed to investigate heat and moisture transfer in porous media during freezing process based on Luikov’s model
by considering the effect of variation of phase transformation number, ε. This parameter has been mostly used as a constant by researchers. Three-dimensional Luikov’s equations are considered and
solved numerically. The model is compared with obtained experimental data. It is shown that the effect of variable phase transformation
number is noticeable in heat and moisture transfer process. 相似文献
16.
A semi-analytical solution for linearized multicomponent cation exchange reactive transport in groundwater 总被引:1,自引:0,他引:1
Cation exchange in groundwater is one of the dominant surface reactions. Mass transfer of cation exchanging pollutants in
groundwater is highly nonlinear due to the complex nonlinearities of exchange isotherms. This makes difficult to derive analytical
solutions for transport equations. Available analytical solutions are valid only for binary cation exchange transport in 1-D
and often disregard dispersion. Here we present a semi-analytical solution for linearized multication exchange reactive transport
in steady 1-, 2- or 3-D groundwater flow. Nonlinear cation exchange mass–action–law equations are first linearized by means
of a first-order Taylor expansion of log-concentrations around some selected reference concentrations and then substituted
into transport equations. The resulting set of coupled partial differential equations (PDEs) are decoupled by means of a matrix
similarity transformation which is applied also to boundary and initial concentrations. Uncoupled PDE’s are solved by standard
analytical solutions. Concentrations of the original problem are obtained by back-transforming the solution of uncoupled PDEs.
The semi-analytical solution compares well with nonlinear numerical solutions computed with a reactive transport code (CORE2D) for several 1-D test cases involving two and three cations having moderate retardation factors. Deviations of the semi-analytical
solution from numerical solutions increase with increasing cation exchange capacity (CEC), but do not depend on Peclet number.
The semi-analytical solution captures the fronts of ternary systems in an approximate manner and tends to oversmooth sharp
fronts for large retardation factors. The semi-analytical solution performs better with reference concentrations equal to
the arithmetic average of boundary and initial concentrations than it does with reference concentrations derived from the
arithmetic average of log-concentrations of boundary and initial waters. 相似文献
17.
Gianfranco Capriz 《Meccanica》2005,40(4-6):505-509
I have found in previous works that most special models proposed to represent bodies with some type of microstructure can
be classified easily under the general umbrella of a theory where each element of the continuum is thought of as a Lagrangian
system. To study phenomena in ‘kinetic’ continua I proposed an apparently different approach; the outcome is again a set of
evolution equations. They mimic equations familiar in continua with affine microstructure: a Cauchy’s equation and an equation
of balance of tensor moment of momentum, with the addition, however, of an equation of balance for a ‘Reynolds’ tensor’, an
equation which, in a sense, shifts the boundary between kinetic and thermal properties of matter. I will show that there is
no contrast between the two approaches. The latter one is based on an adequate and appropriately justified expression of the
kinetic energy of the continuum, comprising the trace of the quoted Reynolds’ tensor and thus importing into the mechanical
energy a term usually accounted by additional heat. 相似文献
18.
The prime objective of the present study is to examine the effect of temperature dependent viscosity μ(T) on the revolving axi-symmetric laminar boundary layer flow of an incompressible, electrically non-conducting ferrofluid in the presence of a stationary plate subjected to a magnetic field and maintained at a uniform temperature. To serve this purpose, the non-linear coupled partial differential equations are firstly converted into the ordinary differential equations using well-known similarity transformations. The popular finite difference method is employed to discretize the non-linear coupled differential equations. These discretized equations are then solved using the Newton method in MATLAB, for which an initial guess is made with the help of the Flex PDE Solver. Along with the velocity profiles, the effects of temperature dependent viscosity are also examined on the skin friction, the heat transfer, and the boundary layer displacement thickness. The obtained results are presented numerically as well as graphically. 相似文献
19.
B. D. Annin V. V. Alekhin S. N. Korobeinikov 《Journal of Applied Mechanics and Technical Physics》2000,41(5):937-944
The equations of quasistatic deformation of elastoplastic bodies are considered in a geometrical linear formulation. After
discretization of the equations with respect to spatial variables by the finite-element method, the problem of determining
equilibrium onfigurations reduces to integration of a system of nonlinear ordinary differential equations. In the ultimate
state of a body of an ideal elastoplastic material, the matrix of the system degenerates and the problem becomes singular.
A regularization algorithm for determining solutions of the problems for the ultimate states of bodies is proposed. Numerical
solutions of test problems of determining the ultimate loads and equilibrium configurations for ideal elastoplastic bodies
confirm the reliability of the regularization algorithm proposed.
Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 5, pp. 196–204, September–October, 2000. 相似文献
20.
Ebrahim Momoniat 《Acta Mechanica Sinica》2012,28(2):444-449
A formulation of the fin efficiency based on Newton’s law of cooling is compared with a formulation based on a ratio of heat transferred from the fin surface to the surrounding fluid to the heat conducted through the base.The first formulation requires that the solution of the nonlinear fin equations for constant heat transfer coefficient and constant thermal conductivity is known,whilst the second formulation of the fin efficiency requires only that a first integral of the model equation is known.This paper shows the first formulation of the fin efficiency contains approximation errors as only power series and approximate solutions to the nonlinear fin equations have been determined.The second formulation of the fin efficiency is exact when the first integrals can be determined. 相似文献