AbstractWe develop high-order, non-reflecting boundary equations for a semi discrete approximation of the simple (hyperbolic) advection equation U+ CU = 0
These boundary equations are based on a discrete interpretation of *Summerfield's radiation condition for a second order wave equation which is associated with the semi-discrete equations. The performance of these schemes is expressed by an exact measure of the energy reflected at the boundary. For low order cases, the discrete Summerfield boundary equations are identical with the standard finite difference equations, but for high orders of approximation (starting with 4 points),the discrete Summerfield schemes differ from standard finite differences. It -is shown, and verified experimentally, that the discrete Summerfield schemes are optimal, in the sense that they produce the least amount of reflected energy. Moreover, it is known theoretically, and we verify experimentally, that the reflected energy remains invariant when the semi-discrete equations are time-discredited with the trapezoidal (Crank- Nicolson] method. The corresponding fully discrete boundary equations are thus also optimal in the sense that they minimize the reflected energy.
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