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Extra resources for Hyperbolic Partial Differential Equations: Modern Applied Mathematics and Computer Science
C. 2) where h"+V2 = h(u], u"+l), and X = At/Ax. 3) h(uj9 Uj) = f(Uj). Consider a numerical scheme with a numerical flux function of the following form: fy + i/2 = 2^j + ^ +1 ~~ W fl y + i / 2 ) ^ + i/2«]» (2-4a) where /, = f(uj), A; + 1 / 2 w = uJ + ] - w, and 7 [«(",) A, + 1/2w = 0. Here i|i is a function of aj+m and X. The function i|> is sometimes referred to as the coefficient of numerical viscosity. 1/2)](/; - /;_,). 5) can be written as < + 1 = ui ~ \w+> - fj-i - \a]+m\Aj+l/2u" + \a]-l/2\bj-mu"].
Hamiltonian structure and higher equations. Funct. Anal. Appl. 12(1), 20-29 (1978). 18. B. A. Kupershmidt, A review of superintegrable systems. In Lect. Appl. Math. 23 Part 1, 83-120 (1985). 19. I. M. Gel'Fand and I. Ya. Dorfman, Hamiltonian operators and infinite-dimensional Lie algebras. Funct. Anal. Appl. 15, 23-40 (1981) (Russian); 173-187 (English). Camp. & Maths, with Appls. Vol. 12A, Nos. 4/5, pp. 413-432, 1986 Printed in Great Britain. 00 © 1986 Pergamon Press Ltd. LINEARIZED FORM OF IMPLICIT TVD SCHEMES FOR THE MULTIDIMENSIONAL EULER AND NAVIER-STOKES EQUATIONS H.
The value Cp in all of the pressure coefficient figures indicates the critical pressure coefficient. One can see in all cases that shocks can be captured within 1-2 grid points. When the same cases are run with the FL052R code of Jameson and the improved ARC2D code (version 150) of Pulliam and Steger, 3-4 points in the shock transition are generally observed. Away from the shocks, the three methods produce almost identical results. As a side remark, the accuracy and efficiency of FL052R and the improved version of ARC2D are comparable; see Ref.