MacCormack method

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). 

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 ... 

The reason is that the finite element method is not well suited to problems like this, with convection but no diffusion. Your job is to use enough artificial diffusion to eliminate the oscillations in the solution but without obscuring the essential details. A variety of specialized methods are available to do that, as described by Finlayson (1992). The specialized methods include Random Choice, Euler-Lagrange, MacCormack, and Taylor-Galerkin. 

It appears interesting, as a verification, to determine by a finite difference method (based on the MacCormack scheme ) a computed FF... 

The results obtained by the inverse method have to be compared with those obtained in the same case of a partially open end of the duct by the direct method based upon a MacCormack scheme, which arc shown in Figs, 18-20. 

R. W. MacCormack. A numerical method fra solving the equations of compressible viscous flow. AMA, 81-0110, 1981. 

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