CAUCHY-CHARACTERISTIC EVOLUTION AND WAVE-FORMS

We investigate a new methodology for the computation of waves generate d by isolated sources. This approach consists of a global spacetime ev olution algorithm based on a Cauchy initial-value formulation in a bou nded interior region and based on characteristic hypersurfaces in the exterior; we match the two schemes at their common interface. The char acteristic formulation allows accurate description of radiative infini ty in a compactified finite coordinate interval, so that our numerical solution extends to infinity and accurately models the free-space pro blem. The matching interface need not be situated far from the sources , the wavefronts may have arbitrary nonspherical geometry, and strong nonlinearity may be present in both the interior and the exterior regi ons. Stability and second-order convergence of the algorithms (to the exact solution of the infinite-domain problem) are established numeric ally in three space dimensions. The matching algorithm is compared wit h examples of both local and nonlocal radiation boundary conditions pr oposed in the literature. For linear problems, matching outperformed t he local radiation conditions chosen for testing, and was about as acc urate (for the same grid resolution) as the exact nonlocal conditions. However, since the computational cost of the nonlocal conditions is m any times that of matching, this algorithm may be used with higher gri d resolutions, yielding a significantly higher final accuracy. For str ongly nonlinear problems, matching was significantly more accurate tha n all other methods tested. This seems to be due to the fact that curr ently available local and nonlocal conditions are based on linearizing the governing equations in the far field, while matching consistently takes nonlinearity into account in both interior and exterior regions . (C) 1997 Academic Press.