摘要:

AbstractThis article addresses the questions of existence, uniqueness, and finite element approximation (including some computational aspects) of solutions to the equations of steady‐state magnetohy‐drodynamic (MHD) when buoyancy effects due to temperature differences in the flow cannot be neglected. We couple the MHD equations to the heat equation and employ the well‐known Boussinesq approximation. We consider the equations posed on a bounded three‐dimensional domain. The boundary conditions for the velocity are of Dirichlet type; the boundary conditions for the temperature are mixed (of Dirichlet type and of Neumann type); we also specify the normal component of the magnetic field and tangential component of the electric field on the boundary. We point out that these problems are relevant to many physical phenomena such as the cooling of nuclear reactors by electrically conducting fluids, continuous metal casting, crystal growth, and semi‐conductor manufacture. © 1995 John Wiley

ISSN:0749-159X    

DOI:10.1002/num.1690110403

出版商:John Wiley&Sons, Inc.    

年代:1995

数据来源: WILEY

摘要:

AbstractExplicit time differencing methods for solving differential equations are advantageous in that they are easy to implement on a computer and are intrinsically very parallel. The disadvantage of explicit methods is the severe restrictions that are placed on stable time‐step intervals. Stability bounds for explicit time differencing methods on advective–diffusive problems are generally determined by the diffusive part of the problem. These bounds are very small and implicit methods are used instead. The linear systems arising from these implicit methods are generally solved by iterative methods. In this article we develop a methodology for increasing the stability bounds of standard explicit finite differencing methods by combining explicit methods, implicit methods, and iterative methods in a novel way to generate new time‐difference schemes, called preconditioned time‐difference methods. A Jacobi preconditioned time differencing method is defined and analyzed for both diffusion and advection–diffusion equations. Several computational examples of both linear and nonlinear advective‐diffusive problems are solved to demonstrate the accuracy and improved stability limits. © 1995 John Wil

ISSN:0749-159X    

DOI:10.1002/num.1690110404

出版商:John Wiley&Sons, Inc.    

年代:1995

数据来源: WILEY

摘要:

AbstractThis article is concerned with numerical solutions of finite difference systems of reaction diffusion equations with nonlinear internal and boundary reaction functions. The nonlinear reaction functions are of general form and the finite difference systems are for both time‐dependent and steady‐state problems. For each problem a unified system of nonlinear equations is treated by the method of upper and lower solutions and its associated monotone iterations. This method leads to a monotone iterative scheme for the computation of numerical solutions as well as an existence‐comparison theorem for the corresponding finite difference system. Special attention is given to the dynamical property of the time‐dependent solution in relation to the steady‐state solutions. Application is given to a heat‐conduction problem where a nonlinear radiation boundary condition obeying the Boltzmann law of cooling is considered. This application demonstrates a bifurcation property of two steady‐state solutions, and determines the dynamic behavior of the time‐dependent solution. Numerical results for the heat‐conduction problem, including a test problem with known analytical solution, are presented to illustrate the various theoretical conclusions. © 1995 Jo

ISSN:0749-159X    

DOI:10.1002/num.1690110405

出版商:John Wiley&Sons, Inc.    

年代:1995

数据来源: WILEY

摘要:

AbstractThe authors compare the behavior of hybrid Trefftz p‐elements with two different types of shape functions identically fulfilling governing differential equations. Numerical examples include several boundary problems for Laplace, Poisson, and plane elasticity equations. Accuracy of the solutions, convergence properties, numerical stability and sensitivity for mesh distortion are investigated. It is shown that both systems of the functions can be efficiently applied, although they have different properties. © 1995 John Wiley&Sons, I

ISSN:0749-159X    

DOI:10.1002/num.1690110406

出版商:John Wiley&Sons, Inc.    

年代:1995

数据来源: WILEY

摘要:

AbstractThe earlier fractional step algorithm for solving the diffusion–migration equation in electrochemistry is extended to a multi‐dimensional multi‐species system with second‐order spatial accuracy. For each time‐step increment, the algorithm consists of three stages: (i) diffusion, (ii) satisfaction of the electroneutrality constraint, and (iii) migration. Each stage accounts for one individual physical process. Exact analytical solutions are derived for a two‐species system and comparisons between exact and numerical results are made. Numerical results are also obtained for a two‐dimensional three‐species electrochemical model. © 1995 John

ISSN:0749-159X    

DOI:10.1002/num.1690110407

出版商:John Wiley&Sons, Inc.    

年代:1995

数据来源: WILEY

摘要:

AbstractA fully Sinc–Galerkin method for solving advection–diffusion equations subject to arbitrary radiation boundary conditions is presented. This procedure gives rise to a discretization, which has its most natural representation in the form of a Sylvester system where the coefficient matrix for the temporal discretization is full. The word “full” often implies a computationally more complex method compared to, for example, temporal marching. In a comparison of time‐marching versus this sinc‐temporal procedure, the Sylvester formulation defines a common framework within which these procedures can be evaluated. This framework has been included in the introduction to illustrate an efficiency measure for either method. Similar remarks with regard to fullness versus sparseness in the Sylvester formulation apply when the spatial discretization is spectral or, for example, differencing. Although it is indicated how this sinc‐temporal method can be combined with alternative spatial discretizations, the natural affinity between sinc methods for space and time discretizations motivate carrying out the numerical illustrations using the sinc basis in each. © 1995 John W

ISSN:0749-159X    

DOI:10.1002/num.1690110408

出版商:John Wiley&Sons, Inc.    

年代:1995

数据来源: WILEY

摘要:

AbstractThis article presents a numerical study of a spectral problem that models the vibrations of a solid–fluid structure. It is a quadratic eigenvalue problem involving incompressible Stokes equations. In its numerical approximation we use Lagrange finite elements. To approximate the velocity, degree 2 polynomials on triangles are used, and for the pressure, degree 1 polynomials. The numerical results obtained confirm the theory, as they show in particular that the known theoretical bound for the maximum number of nonreal eigenvalues admitted by such a system is optimal. The results also take account of the dependence of vibration frequencies with respect to determined physical parameters, which have a bearing on the model. © 1995 John Wiley&Sons, I

ISSN:0749-159X    

DOI:10.1002/num.1690110409

出版商:John Wiley&Sons, Inc.    

年代:1995

数据来源: WILEY

ISSN:0749-159X    

DOI:10.1002/num.1690110402

出版商:John Wiley&Sons, Inc.    

年代:1995

数据来源: WILEY