A Pseudospectral Chebychev Method for the 2D Wave Equation with Domain Stretching and Absorbing Boundary Conditions

therefore the damping layer has to be large enough to prevent reentrant waves at the physical boundary. Hence In this paper we develop a method for the simulation of wave propagation on artificially bounded domains. The acoustic wave the approach is not only costly in terms of memory requireequation is solved at all points away from the boundaries by a ments but also it is not very flexible. In particular, the pseudospectral Chebychev method. Absorption at the boundaries appropriate damping layer must be determined for each is obtained by applying one-way wave equations at the boundaries, problem solved, dependent on location of the initial signal without the use of damping layers. The theoretical reflection coeffiand the time interval over which a solution is required. cient for the method is compared to theoretical estimates of reflection coefficients for a Fourier model of the problem. These estimates The method proposed here, in which a one-way wave equaare confirmed by numerical results. Modification of the method by tion is applied at the boundary, avoids these problems by a transformation of the grid to allow for better resolution at the removing both periodicity and damping layers. Moreover, center of the grid reduces the maximum eigenvalues of the differenthe high-accuracy advantage of the pseudospectral spatial tial operator. Consequently, for stability the maximum timestep is approximation is maintained by the use of a Chebychev O(1/N) as compared to O(1/N 2) for the standard Chebychev method. Therefore, the Chebychev method can be implemented with effipseudospectral formulation. We note that the new techciency comparable to that of the Fourier method. Moreover, numerinique is similar to a method proposed by Kopriva [3], for cal results presented demonstrate the superior performance of the the linearized gas dynamics equations, and by Carcione new method. Q 1996 Academic Press, Inc. [3] for the solution of the 2D wave equation recast as a first-order linear hyperbolic system. In Section 2 of the paper the absorbing boundary formu