3.3 The Bondi Problem3 Characteristic Evolution Codes3.1 One+One Dimensional Codes

3.2 Two-D Codes

One dimensional 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 three dimensional 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 exactly the same as in the one dimensional 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 finite subset of propagation equations. The latter approach has been successfully applied by Butler [48] to the Cauchy evolution of 2-dimensional fluid flow but there seems to have been very little follow-up along these lines.

The formal ideas behind the construction of two or three dimensional characteristic codes are the same, although there are some additional technical complications in three dimensions associated with a nonsingular choice of angular coordinates for the null rays. Historically, most characteristic work graduated first from 1D to 2D because of the available computing power.



3.3 The Bondi Problem3 Characteristic Evolution Codes3.1 One+One Dimensional Codes

image Characteristic Evolution and Matching
Jeffrey Winicour
http://www.livingreviews.org/lrr-1998-5
© Max-Planck-Gesellschaft. ISSN 1433-8351
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