摘要:

AbstractA recent article by Leonard and Mokhtari (1990) discusses the order of accuracy of discrete equations used for numerical simulation. They maintain that discrete operators derived for the finite‐volume method should be Taylor‐series‐analysed using the various points that appear in a finite‐volume discrete equation. The current paper argues that any discrete scheme must be analysed from a single point. It is shown that while Leonard's finite‐difference QUICK scheme is O(h3)‐accurate, his implementation of QUICK for the finite‐volume method is only O(h2). An alternative finite‐volume formulation is shown to yield a locally third‐order‐accurate operator in the final discrete equation. Also, third‐order‐accurate formulae are discussed for various numerical implementations. Numerical examples are included to demonstrate actual rates of convergenc

ISSN:0748-8025    

DOI:10.1002/cnm.1630081202

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA technique is described for using Newton's identities to compute the coefficients of multi‐step recurrence formulae for simulating ordinary linear differential equations of high order. This approach gives the exact root‐matched recurrence formula without having to determine the complex roots of the characteristic polynomi

ISSN:0748-8025    

DOI:10.1002/cnm.1630081203

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractHeat and mass transfer during crystallization in a square cavity, involving natural laminary convection of liquid metal with temperature‐dependent viscosity, are investigated numerically on a grid with 51 × 51 nodes. A brief survey of existing techniques for convection/diffusion phase change problems is given. A fixed grid numerical methodology, based on the fictitious regions method, is used for solving the 2‐D Stefan problem coupled with the Navier–Stokes equations in the Boussinesq approximation. The viscosity variation is modelled by an exponential form, ν/ν0= exp ( – α(T– 1)). The influence of the Grashof number and of the parameter α on heat and mass transfer ar

ISSN:0748-8025    

DOI:10.1002/cnm.1630081204

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractWe formulate a higher‐order (superconvergent) Petrov–Galerkin method by determining, using a finite‐difference approximation, the optimal selection of quadratic and cubic modifications to the standard linear test function for bilinear elements. Application of this method to linear elliptic problems results in improved accuracy and higher rates of convergence for problems with constant coefficients and improved accuracy for problems with variable coefficients. Supporting numerical examples are

ISSN:0748-8025    

DOI:10.1002/cnm.1630081205

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

ISSN:0748-8025    

DOI:10.1002/cnm.1630081206

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

ISSN:0748-8025    

DOI:10.1002/cnm.1630081201

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY