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Grid anisotropy

The grid spacing and time step were chosen to reliably create spiral waves with appropriately smooth profiles and propagation speeds. A criterion of numerical accuracy was that small changes in the grid or time step should not give rise to large differences in the solution. With numerical parameters chosen as in Sect.2.4 neither reducing the steps tex2html_wrap_inline892 or tex2html_wrap_inline1034 by tex2html_wrap_inline1036 nor reducing the time step by tex2html_wrap_inline1038 changed the wave period by more than tex2html_wrap_inline1040 . Nevertheless, even in the absence of any forcing, a radial drift of spiral waves away from the centre was observed. The radial drift velocity tex2html_wrap_inline1042 su/tu was less than 0.2% of the plane wave velocity. Numerical experiments evidenced that the mentioned radial drift velocity decreased as the tex2html_wrap_inline892 became smaller, tex2html_wrap_inline1046 su/tu for tex2html_wrap_inline1048 ; tex2html_wrap_inline1042 su/tu for tex2html_wrap_inline1052 ; tex2html_wrap_inline1054 su/tu for tex2html_wrap_inline918 ; and tex2html_wrap_inline1058 su/tu for tex2html_wrap_inline1060 . In these test computations the time step tex2html_wrap_inline1062 was used to satisfy the stability criterion for the case of the smallest tex2html_wrap_inline1060 . The very slow radial drift should probably be attributed to the grid anisotropy produced by the summation of local errors of approximation in integrating the discrete analog of equations (1)-(5) in polar coordinates. In numerical experiments described below, this numerical artefact was always much smaller than the resonant drift.



Vadim Biktashev
Fri Apr 4 17:38:59 GMT 1997