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Numerical simulation of atmospheric turbulence is one of the biggest bottlenecks in developing computational techniques for solving the inverse problem in long-range imaging. The classical split-step method is based upon numerical wave propagation which splits the propagation path into many segments and propagates every pixel in each segment individually via the Fresnel integral. This repeated evaluation becomes increasingly time-consuming for larger images. As a result, the split-step simulation is often done only on a sparse grid of points followed by an interpolation to the other pixels. Even so, the computation is expensive for real-time applications. In this paper, we present a new simulation method that enables \emph{real-time} processing over a \emph{dense} grid of points. Building upon the recently developed multi-aperture model and the phase-to-space transform, we overcome the memory bottleneck in drawing random samples from the Zernike correlation tensor. We show that the cross-correlation of the Zernike modes has an insignificant contribution to the statistics of the random samples. By approximating these cross-correlation blocks in the Zernike tensor, we restore the homogeneity of the tensor which then enables Fourier-based random sampling. On a $512\times512$ image, the new simulator achieves 0.025 seconds per frame over a dense field. On a $3840 \times 2160$ image which would have taken 13 hours to simulate using the split-step method, the new simulator can run at approximately 60 seconds per frame.