Onedimensional characteristic codes enjoy a very special
simplicity due to the two preferred sets (ingoing and outgoing)
of characteristic null hypersurfaces. This eliminates a source of
gauge freedom that otherwise exists in either two or
threedimensional characteristic codes. However, the manner in
which characteristics of a hyperbolic system determine domains of
dependence and lead to propagation equations for shock waves is
the same as in the onedimensional case. This makes it desirable
for the purpose of numerical evolution to enforce propagation
along characteristics as extensively as possible. In basing a
Cauchy algorithm upon shooting along characteristics, the
infinity of characteristic rays (technically,
bicharacteristics) at each point leads to an arbitrariness which, for a practical
numerical scheme, makes it necessary either to average the
propagation equations over the sphere of characteristic
directions or to select out some preferred subset of propagation
equations. The latter approach was successfully applied by
Butler [37] to the Cauchy evolution of twodimensional fluid flow but there
seems to have been very little followup along these lines.
The formal ideas behind the construction of two or
threedimensional characteristic codes are the same, although
there are different technical choices of angular coordinates for
the null rays. Historically, most characteristic work graduated
first from 1D to 2D because of the available computing power.

Characteristic Evolution and Matching
Jeffrey Winicour
http://www.livingreviews.org/lrr20013
© MaxPlanckGesellschaft. ISSN 14338351
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livrev@aeipotsdam.mpg.de
