摘要:

AbstractIn this article, we report two fourth‐order difference methods for the numerical integration of the system of general 3‐D nonlinear elliptic equations subject to Dirichlet boundary conditions on a uniform cubic grid. When the coefficients ofuxy,uyz, anduzxare not equal to zero and the coefficients ofuxx,uyy, anduzzare equal, we require 27 grid points; when the coefficients ofuxy,uyz, anduzxare equal to zero, we require only 19 grid points. The utility of the new methods is shown by testing the methods on various examples, including 3‐D steady state viscous incompressible Navier–Stokes' model equations and Poisson's equation in polar coordinates, which confirm the accurate and oscillation‐free solutions for large Reynolds numbers even in the vicinity of singularity. © 1995 John Wiley

ISSN:0749-159X    

DOI:10.1002/num.1690110303

出版商:John Wiley&Sons, Inc.    

年代:1995

数据来源: WILEY

摘要:

AbstractIn this article, we present several numerical multilevel schemes for the solution of nonlinear eigenvalue problems. Using the Incremental Unknowns, we construct some generalization of the Marder and Weitzner method, which is well suited for the calculation of unstable solutions. The new methods that we present are based on a different treatment of the several structures appearing with the utilization of the hierarchical preconditioner. We illustrate the efficiency of the new methods with the calculation of unstable solutions of a reaction diffusion problem. © 1995 John Wiley&Sons, Inc

ISSN:0749-159X    

DOI:10.1002/num.1690110304

出版商:John Wiley&Sons, Inc.    

年代:1995

数据来源: WILEY

摘要:

AbstractThe microbial degradation of organic contaminants in the subsurface holds significant potential as a mechanism forin‐situremediation strategies. The mathematical models that describe contaminant transport with biodegradation involve a set of advective–diffusive–reactive transport equations. These equations are coupled through the nonlinear reaction terms, which may involve reactions with all of the species and are themselves coupled to growth equations for the subsurface bacterial populations. In this article, we develop Eulerian–Lagrangian localized adjoint methods (ELLAM) to solve these transport equations. ELLAM are formulated to systematically adapt to the changing features of governing partial differential equations. The relative importance of retardation, advection, diffusion, and reaction is directly incorporated into the numerical method by judicious choice of the test functions that appear in the weak form of the governing equation. Different ELLAM schemes for linear variable–coefficient advective–diffusive–reactive transport equations are developed based on different operator splittings. Specific linearization techniques are discussed and are combined with the ELLAM schemes to solve the nonlinear, multispecies transport equations. © 1995 John W

ISSN:0749-159X    

DOI:10.1002/num.1690110305

出版商:John Wiley&Sons, Inc.    

年代:1995

数据来源: WILEY

摘要:

AbstractA hybrid finite‐element method, combining ideas from a modified method of characteristics and the streamline diffusion method, delivers accurate solutions to the advection–diffusion equation. An error analysis for the case of tensorial diffusion shows that the lowest‐order version of the scheme, which allows one to use a symmetric linear solvers at each time step, possesses first‐order accuracy in time and space. Numerical experiments demonstrate the scheme's ability to model advection‐dominated transport of solute plumes without distorting sharp fronts. © 1995 John Wiley

ISSN:0749-159X    

DOI:10.1002/num.1690110306

出版商:John Wiley&Sons, Inc.    

年代:1995

数据来源: WILEY

摘要:

AbstractSeparate theoretical and numerical analyses have been conducted for the prediction of the mean bulk‐and wall‐temperatures of hot fluids flowing inside horizontal tubes. Heat transmission between the internal forced flow and the external free flow of the surrounding fluid occurs through the solid wall of the tube. The mathematical formulation of this problem is expressed in terms of a parabolic, partial differential equation with a temperature‐dependent, nonlinear boundary condition of third kind. The aim of the article is to critically examine the thermal response of this kind of in‐tube flows utilizing two different mathematical models: (a) a complete 2‐D differential model and (b) a largely simplified 1‐D lumped model. For the 1‐D lumped model, streamwise‐mean values for the internal Nusselt numbers and the circumferential‐mean values for the external Nusselt numbers have been taken from standard correlations that appear in basic textbooks. The combination of both mean Nusselt numbers leads to the calculation of a mean, equivalent Nusselt number, which serves to regulate the thermal interaction between the perpendicular fluid streams. For the two models tested, the computed results consistently demonstrate that the simplistic 1‐D lumped model provides accurate estimates of the mean bulk‐ and wall‐temperatures, when compared with those computed with the rigorous 2‐D differential model. The former is associated with hand calculations, whereas the latter inevitably necessitated a finite‐difference methodology and a personal computer.

ISSN:0749-159X    

DOI:10.1002/num.1690110307

出版商:John Wiley&Sons, Inc.    

年代:1995

数据来源: WILEY

摘要:

AbstractNumerical analysis of some finite element methods for the quasi‐static thermoelastic consolidation problem of fluid‐filled porous materials is presented for the case of smooth exact solutions. Taking advantage of the exponential decay of the error in the initial data with time, error estimates describing the long‐time behavior of the semidiscrete approximation are presented and postprocessing techniques are proposed to improve the accuracy of the pore pressure, heat flux, and effective stress approximations. © 1995 John Wiley&Son

ISSN:0749-159X    

DOI:10.1002/num.1690110308

出版商:John Wiley&Sons, Inc.    

年代:1995

数据来源: WILEY

ISSN:0749-159X    

DOI:10.1002/num.1690110302

出版商:John Wiley&Sons, Inc.    

年代:1995

数据来源: WILEY