摘要:

AbstractThe simulation of multiphase and multicomponent fluid flows often requires the solution of large, coupled systems of nonlinear partial differential equations of convection‐advection type. The equations are usually advection dominated with small but important local diffusive effects. An operator‐splitting technique is used to address these different phenomena. A modified method of characteristics is used to try to eliminate the nonsymmetry in the operators due to advection. Although this method does not completely symmetrize the problem with nonlinear, nonconvex flux functions, the remaining operator is almost symmetric and can be stabilized via Petrov‐Galerkin techniques with optimal or near optimal test functions. Effective localized test functions are descrbed. A coarse grid is defined to treat the slow variation of the fluid velocity away from fronts. A substructuring of this grid gives a proper frontal resolution via local patch grid refinement. Preconditioning techniques are presented to efficiently solve the resulting composite‐grid problem. Error estimates for the total approximation procedure are presented. Finally, certain two‐dimensional computations are

ISSN:0749-159X    

DOI:10.1002/num.1690060402

出版商:John Wiley&Sons, Inc.    

年代:1990

数据来源: WILEY

摘要:

AbstractA two‐level implicit difference scheme using three spatial grid points of Crandall form ofO(k2+kh2+h4) is obtained for solving the one‐dimensional quasilinear parabolic partial differential equation,uxx=f(x,t,u,ut,ux) with Dirichlet boundary conditions. The method, when applied to a linear convection‐diffusion problem, is shown to be unconditionally stable. The numerical results show that the proposed method produces accurate and oscillation‐free so

ISSN:0749-159X    

DOI:10.1002/num.1690060403

出版商:John Wiley&Sons, Inc.    

年代:1990

数据来源: WILEY

摘要:

AbstractA new method for solving the first biharmonic equation via a double splitting into coupled systems of ordinary differential equations is presented. The first splitting reduces this fourth order partial differential equation into the coupled systemuxx+uyy=vandvxx+vyy=f, whereucarries both Dirichlet and Neumann boundary data andvcarries no boundary data. The pair is then iteratively solved using coupled alternating direction collocation on the resulting systems of ordinary differential equations. This can also be viewed as an alternating direction method of lines for a system of partial differential equations. Although there is no separation of variables underlying the splitting, the method yields a convergent sequence of iterates for a variety of examples under a restricted range of acceleration parameters, and possessesO(h4) accuracy. Desirable features of the algorithm are discussed together with the reduction of bandwidth of the associated collocation matrices under intersticing ofuandvvariables. Interesting open questions are also discussed.

ISSN:0749-159X    

DOI:10.1002/num.1690060404

出版商:John Wiley&Sons, Inc.    

年代:1990

数据来源: WILEY

摘要:

AbstractBased on the Feynman‐Kac formula an algorithm for solving the scalar reaction‐diffusion equation is given. The method reduces the approximation to a simple nonrandom averaging which does not require a simulation of Brownian motion. The rate of convergence is also establis

ISSN:0749-159X    

DOI:10.1002/num.1690060405

出版商:John Wiley&Sons, Inc.    

年代:1990

数据来源: WILEY

摘要:

AbstractThe paper is the second in the series addressing theh‐pversion of the finite element method for parabolic equations. The present paper addresses the case when in both variables, the spatial and time, theh‐pversion is used. Error estimation is given and numerical computations are presen

ISSN:0749-159X    

DOI:10.1002/num.1690060406

出版商:John Wiley&Sons, Inc.    

年代:1990

数据来源: WILEY

摘要:

AbstractA special approach to deal with elliptic problems with singularities is introduced. It is shown that this approach, to be calledan auxiliary mapping technique, in the framework of thep‐version of the finite element method yields an exponential rate of convergence. It is also shown that this technique can deal with elliptic problems on unbounded domains inR2as well. (AMS(MOS) subject classifications: Primary, 65N30, 65N15

ISSN:0749-159X    

DOI:10.1002/num.1690060407

出版商:John Wiley&Sons, Inc.    

年代:1990

数据来源: WILEY

ISSN:0749-159X    

DOI:10.1002/num.1690060401

出版商:John Wiley&Sons, Inc.    

年代:1990

数据来源: WILEY