Far Field Boundary Conditions for Time-Dependent Hyperbolic Systems,
STANFORD UNIV CA CENTER FOR LARGE SCALE SCIENTIFIC COMPUTATION
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For problems defined on infinite domains, the most common computational methods use an artificial boundary gamma in order to make the computation finite. Since data are usually not available at this boundary, conditions must be used that somehow are related to the behavior of the solution outside the computational domain omega. This means that some apriori knowledge of the solution is necessary. In particular, if the system of differential equations has variable coefficients or is non-linear, then we shall make the coefficients constant outside omega. In this way there is a possibility to compute the solution exactly, or to compute it approximately in a simple way outside omega, such that boundary conditions can be derived on gamma. A previous work in the basic principles concerning artificial boundaries for hyperbolic systems were discussed. The one-dimensional case was analyzed thoroughly, and it was shown under what conditions it is possible to derive accurate conditions at the artificial boundary. A two-dimensional example was also treated, and a method leading to exact conditions for steady state solutions was presented. This paper at treats hyperbolic systems in two space-dimensions with non-zero initial data also outside omega.
- Numerical Mathematics