Nakazawa

Pittman, J. F.T. and Nakazawa, S., 1984. Finite element analysis of polymer processing operations. In Pittman, J.F. T., Zienkiewicz, O.C., Wood, R.D. and Alexander, J. M. (eds), Num,erical Analysis of Forming Processes, Wiley, Chichester. 

Pittman, J.F.T. and Nakazawa, S., 1984. Finite element analysis of polymer processing... 

Level of enforcement of the incompressibility condition depends on the magnitude of the penalty parameter. If this parameter is chosen to be excessively large then the working equations of the scheme will be dominated by the incompressibility constraint and may become singular. On the other hand, if the selected penalty parameter is too small then the mass conservation will not be assured. In non-Newtonian flow problems, where shear-dependent viscosity varies locally, to enforce the continuity at the right level it is necessary to maintain a balance between the viscosity and the penalty parameter. To achieve this the penalty parameter should be related to the viscosity as A = Xorj (Nakazawa et al, 1982) where Ao is a large dimensionless parameter and tj is the local viscosity. The recommended value for Ao in typical polymer flow problems is about 10. ... 

This matrix is usually diagonalized using a simple mass lumping technique (Pittman and Nakazawa, 1984) to minimize the computational cost of pressure calculations in this method. 

M. Toda, K. Sato, H. Nakazawa, M. Inoue, and S. Mits dii2ishi,Antimicrob. Agents Chemother. 18, 837 (1980). 

Nakazawa, T., Murayama, S., Miyashita, K., Aoki, S. and Tanaka, M. (1992). Longitudinally different variations of lower tropospheric carbon dioxide concentrations over the North Pacific Ocean, Tellus, Ser. B, 44,161-172. 

Tans, P. P., Conway, T. J. and Nakazawa, T. (1989). Latitudinal distribution of the sources and sinks of atmospheric carbon dioxide derived from surface observations and an atmospheric transport model, /. Geophys. Res. 94, 5151-5172. 

Machida, T., Nakazawa, T., Fujji, Y. et al. (1995). Increase in atmospheric nitrous oxide concentration during the last 250 years. Geophys. Res. Lett. 22, 2921-2924. 

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