A new method to overcome some limitations in the simulation of the propagation of waves originating from a point source through a very long path in a turbulent medium is presented. Existing propagation simulation algorithms suffer from eitherwindowing or lack of resolution when applied to long paths. If Cartesian coordinates are used, the limited size of the numerical mesh eventually leads to windowing errors. Casting the classical split-step Fourier algorithm in a spherically divergingcoordinate system allows one to get around this problem. In this way an angular mesh matching the source and the propagation algorithm to the problem geometry is used. But for long-path propagation, this spherical divergent mesh causes a loss ofresolution that can become a serious problem in the evaluation of the field statistical moments. The method discussed in this paper overcomes both the windowing effect associated with Cartesian coordinates and the loss of resolution accompanying spherical coordinates by using a spherical-coordinate algorithm and performing repeated interpolations of the numerically propagated field before the mesh grows too large to sample the field accurately. Each time an interpolation is done, the angular window isdecreased to maintain the matrix size.
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