摘要:

AbstractThe alternating‐direction collocation (ADC) method can be formulated for general parabolic partial differential equations. This is done using a piecewise cubic Hermite trial space defined on a rectangular discretization. As in all alternating‐direction methods, the ADC algorithm produces errors that are additional to the standard discretization errors of multi‐dimensional collocation. These errors increase when the coefficients of the governing equation are spatially variable. Analysis of the additional errors leads to several correction schemes. Numerical results indicate that a variant on the Laplace‐modification procedure is an attractive choice as an improved ADC al

ISSN:0749-159X    

DOI:10.1002/num.1690060302

出版商:John Wiley&Sons, Inc.    

年代:1990

数据来源: WILEY

摘要:

AbstractThe alternating‐direction collocation (ADC) method combines the attractive computational features of a collocation spatial approximation and an alternating‐direction time marching algorithm. The result is a very efficient solution procedure for parabolic partial differential equations. To date, the methodology has been formulated and demonstrated for second‐order parabolic equations with insignificant first‐order derivatives. However, when solving transport equations, significant first‐order advection components are likely to be present. Therefore, in this paper, the ADC method is formulated and analyzed for the transport equation. The presence of first‐order spatial derivatives leads to restrictions that are not present when only second‐order derivatives appear in the governing equation. However, the method still appears to be applicable to a wide variety of transport systems. A formulation of the ADC algorithm for the nonlinear system of equations that describes density‐dependent fluid flow and solute transport in porous media demonstrates this point. An example of seawater intrusion into coastal aquifers is solved to illustrate the applicability of the method.An alternating‐direction collocation solution algorithm has been developed for the general transport equation. The procedure is analogous to that for the model parabolic equations considered by Celia and Pinder [2]. However, the presence of first‐order spatial derivatives requires special attention in the ADC formulation and application. With proper implementation, the ADC procedure effectively combines the efficient equation formulation inherent in the collocation method with the efficient equation solving characteristics of alternating‐direction time marching algorithms. To demonstrate the viability of the method for problems with complex velocity fields, the procedure was applied to the problem of density‐dependent flow and contaminant transport in groundwaters. A standard example of seawater intrusion into coastal aquifers was solved to illustrate the applicability of the method and to demonstrate its potential us

ISSN:0749-159X    

DOI:10.1002/num.1690060303

出版商:John Wiley&Sons, Inc.    

年代:1990

数据来源: WILEY

摘要:

AbstractThe alternating‐direction collocation (ADC) method is an efficient numerical approximation technique for the solution of parabolic partial differential equations. However, to date the ADC method has only been developed for rectangular discretizations. With judicious combination of isoparametric coordinate transformations and an extended ADC approach, the ADC method can be formulated on general nonrectangular domains. This extends the applicability of the ADC method by allowing it to be employed on domains of more general geometr

ISSN:0749-159X    

DOI:10.1002/num.1690060304

出版商:John Wiley&Sons, Inc.    

年代:1990

数据来源: WILEY

摘要:

AbstractThis paper implements a numerical solution of the equations of compressible flow, by a transport method. The model is based on a kinetic model, built for the fluid motion. It transforms the equations of motion into integral equations, solved by an analytical‐numerical method. Precomputation of tables for some canonical integrals reduces the amount of work. A boundary value problem (flow into a wedge) is treated and numerical solutions are exhibited. The paper deals with isentropic flow. It is an important special case, among the variety of problems where the assumption of constant entropy causes a negligible erro

ISSN:0749-159X    

DOI:10.1002/num.1690060305

出版商:John Wiley&Sons, Inc.    

年代:1990

数据来源: WILEY

摘要:

AbstractWe consider the effect of numerical integration in finite element methods applied to a class of nonlinear parabolic equations and give some sufficient conditions to ensure that the order of convergence is unaltered in the presence of numerical integration. Optimal error estimates for the solution and its time derivative in the spacesL∞(H1) andL∞(L2) are established. Moreover, maximum norm error estimates are demonstra

ISSN:0749-159X    

DOI:10.1002/num.1690060306

出版商:John Wiley&Sons, Inc.    

年代:1990

数据来源: WILEY

ISSN:0749-159X    

DOI:10.1002/num.1690060301

出版商:John Wiley&Sons, Inc.    

年代:1990

数据来源: WILEY