MacCormack

The concentration profile is steeper for the MacCormack method than for the upstream derivatives, but oscillations can still be present. The flux-corrected transport method can be added to the MacCormack method. A solution is obtained both with the upstream algorithm and the MacCormack method and then they are combinea to add just enough diffusion to ehminate the oscillations without smoothing the solution too much. The algorithm is comphcated and lengthy but well worth the effort (Refs. 37, 107, and 270). 

Ruberto L, SC Vazquez, WP MacCormack (2003) Effectiveness of the natural flora, biostimulation and bioaugmentation on the bioremediation of a hydrocarbon contaminated Antarctic soil. Int Biodet Biodeg 52 115-125. 

David ARJ, MacCormack T, Morris AW, Worsfold PJ (1998) Anal Chim Acta 31 63... 

Important features of the reaction mechanism were clarified by Orzechow-ski and MacCormack (70). These authors simplified the problem by considering the initial reaction rates for (218) and (219), obtained by extrapolation (i.e., the rates in the absence of reaction products). They arrived at a conclusion that the reaction is basically composed of irreversible adsorption of oxygen and the removal of adsorbed oxygen by ethylene with the formation either ethylene oxide or an intermediate substance, most likely acetaldehyde, that is rapidly oxidized to C02 and H20. 

Equations (249) and (250) coincide in their form with equations proposed by Orzechowski and MacCormack for the initial rates. 

MacCormack AC, McDonnell CM, O Donoghue AC, More O Ferrall RA. Modern problems in organic chemistry, vol. 14. St. Petersburg St. Petersburg Press 2003 88 111. 

The MacCormack explicit scheme is second-order accurate with the stability criterion of... 

Use the linear Burgers equation for heat convection in a channel where the water is flowing with uniform velocity of 0.1 m/s across the cross section of the channel (boundary layers are neglected). The water is initially at 25°C throughout. At time t = 0 sec, waste heat is continuously rejected at x = 0 m, and the channel is long such that dT/dx = 0 for x > 1 m. The amount of heat rejected is 6.23 W/m2 for t > 0. Using the MacCormack explicit scheme, calculate the first 9 time steps to show the transient temperature distributions. 

The conventional route to 3-phosphelium salts 207 is via the MacCormack reaction in which the five-membered ring is formed via a cycloaddition reaction between a 1,3-diene and a dihalogenophosphine <1996CHEC-II(2)757>. A variant of... 

B. Brown, A. R. Khokhar, M. P. Hacker, J. J. MacCormack, and R. A. Newman, Synthesis and Biological Studies of a New Class of Antitumor Platinum Complexes, in S. J. Lippard, ed.. Platinum, Gold, and Other Metal Chemotherapeutic Agents, American Chemical Society, Washington, DC, 1983, pp. 265-277. 

This paper deals with thermal wave behavior during frmisient heat conduction in a film (solid plate) subjected to a laser heat source with various time characteristics from botii side surfaces. Emphasis is placed on the effect of the time characteristics of the laser heat source (constant, pulsed and periodic) on tiiermal wave propagation. Analytical solutions are obtained by memis of a numerical technique based on MacCormack s predictor-corrector scheme to solve the non-Fourier, hyperbolic heat conduction equation. 

Glass et al. [7] reported that MacCormack s method [22], which is a second-order accurate explicit scheme, can handle these moving discontinuities quite well and is valid for the HHC problems. Since the hyperbolic problems considered here have step discontinuities at the thermal wave front, MacCormack s prediction-correction scheme is used in the present study. When MacCormack s method is applied to Eqs. (2.7) and (2.8), the following finite difference formulation results ... 

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