Efficient implementation of high order methods for the advection–diffusion equation

✍ Scribed by A. Kolesnikov; A.J. Baker

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 591 KB
• Volume: 189
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/s0045-7825(99)00307-2

✦ Synopsis

A new approach to designing high order ± de®ned here to exceed third ± accurate methods has been developed and tested for a linear advection±diusion equation in one and two dimensions. The systematic construction of progressively higher order spatial approximations is achieved via a modi®ed equation analysis, which allows one to determine the computational stencil coecients appropriate for a desired accuracy order. A distinguishing desirable property of the developed method is solution matrix bandwidth containment, i.e. bandwidth always remains equal to that of the second-order discretization. Numerical simulations compare performance of the developed fourth-and sixth-order methods to that of the linear and bilinear basis Galerkin weak statement formulations in one and two dimensions, respectively. Uniform mesh re®nement convergence results con®rm the order of truncation error for each method. High order approximations are shown to require signi®cantly fewer nodes to accurately resolve solution gradients for convection dominated problems.