Accurate Non-Reflecting Boundary Conditions for Time-Dependent
Acoustic Scattering
Lonny L. Thompson and Runnong Huan
Advanced Computational Mechanics Research Laboratory
Department of Mechanical Engineering
Clemson University
Clemson, South Carolina 29634-0921
Proceedings of the Seventh International
Congress on Sound and Vibration, 4-7 July 2000,
Garmisch-Partenkirchen, Germany. pp. 2211-2218
Abstract
Accurate radiation boundary conditions for the
time-dependent wave equation are formulated in the finite
element method as an auxiliary problem for each radial harmonic
on a spherical boundary. The method is based on residuals
of an asymptotic expansion for the time-dependent radial harmonics.
A decomposition into orthogonal transverse modes on the spherical
boundary is used so that the residual
functions may be computed efficiently and
concurrently without altering the local/sparse character of
the finite element equations. The method has the ability
to vary separately, and up to any desired order,
the radial and transverse modal orders of the radiation boundary condition.
With the number of equations in the auxiliary Cauchy problem equal to the
transverse mode number, the conditions are exact.
If fewer equations are used, then the boundary conditions
form high-order accurate asymptotic approximations to the exact condition,
with corresponding reduction in work and memory.
Numerical studies are performed to assess the accuracy and convergence
properties of the radiation boundary conditions.
The results demonstrate dramatically improved accuracy for time domain simulations compared to standard boundary treatments
and improved efficiency over the exact condition.
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