http://arc.aiaa.org/doi/pdf/10.2514/3.60901

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http://adsabs.harvard.edu/abs/1982cofd.vkif.....B

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Richard M. Beam, R. F. Warming

ABSTRACT

A systematic development and analysis of noniterative implicit schemes

for systems of conservation laws are presented. The inviscid gasdynamic

equations are a special case. If transport phenomena in addition to

convection (e.g., diffusion, viscosity, and thermal conductivity) are

included, then the system of conservation laws has the more general

form. The compressible Navier-Stokes equations have the form. The

conservation or divergence form was chosen for two reasons. First, weak

solutions (e.g., shock waves, shear layers, etc.) were anticipated, and

conservative difference approximations are essential if a

"shock-capturing' method is used. (Shock capturing is defined as

ignoring the presence of embedded discontinuities in the sense that they

are not treated as internal boundaries in the difference algorithm.)

Second, it is easier to derive a noniterative, second order, implicit

algorithm if the nonlinear equations are in conservation form.

Prof. R. Zomorrodian