Comments on Analysis of A FourthOrder Compact Scheme for ConvectionDiffusion.pdfVIP

Comments on Analysis of A FourthOrder Compact Scheme for ConvectionDiusion Jules Kouatchou Scho ol of Engineering Morgan State University Perring Parkway Baltimore MD Jun Zhang Department of Computer Science University of Kentucky Anderson Hall Lexington KY April Key words Convectiondiusion equation fourthorder compact discretization scheme iterative metho ds Classication N E D Intro duction In Yavneh analyzed a fourthorder compact nite dierence scheme for the convectiondiusion equation of the form u xy u xy pxyu xy qxyu xy fxy xy 2 xx y y x y uxy gxy xy 2 where is a smo oth convex domain in R2 and is assumed to consist of union of continuous rect angles Here uxy is the solution with sucient regularity pxy and qxy are the convection co ecients and fxy is the forcing function Traditionally the strength of the convection is measured by the socalled Reynolds numb er denoted by Re Typically the magnitudes of pxy and qxy are of the order Re Yavneh showed that the fourthorder compact scheme do es not suer from a crossstream articial viscosity as do es the rstorder upwind scheme when the characteristic direction is not aligned with the grid but do es include a streamwise articial viscosity that is inversely prop ortional to the natural viscosity It has b een known to the second author b efore was published that the fourthorder compact scheme is similar to some streamwise nite element discretization scheme He claimed that thi