A Numerical Scheme for Transport Equations with Spatially Distributed Coefficients Based on Locally Exact Difference Method

✍ Scribed by Katsuhiro Sakai; Gen Sheng Zhang

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 420 KB
• Volume: 134
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1997.5711

✦ Synopsis

second order) [13] were proposed. Versions of LECUSSO have been proposed, which are formulated in conservation A numerical difference scheme to solve stationary transport equations with spatially distributed coefficients is presented. The spatial form for uniform mesh size grids [14] and for nonuniform distribution of the coefficients in the transport equations is taken into mesh sizes [15]. consideration based on a four-region model among three adjacent Those locally exact schemes are characterized by decontrol volumes, in which continuous conditions for solutions are termining difference coefficients so that the resulting difimposed on the boundary between two adjacent regions. The coefference equation will satisfy locally the exact solution of the ficients in the difference scheme are determined so that it will be satisfied exactly by any local solution of the continuous equations convection-diffusion equation with constant coefficients. with piecewise constant coefficients in each region. The present The difference coefficients depend on local velocities. The scheme is examined through numerical experiments for one-dimenlocally exact schemes have been extended to transport sional convection-diffusion equations with spatially distributed coequations with absorption [16, 17] and source terms [18, efficients and source term and a two-dimensional cavity flow prob-19]. In most cases numerical experiments with these locally lem. The present scheme shows good solutions. ᮊ 1997 Academic Press exact schemes have shown stable and good solutions [15, 17].