Local time-space mesh refinement for simulation of elastic wave propagation in multi-scale media

This paper presents an original approach to local time-space grid refinement for the numerical simulation of wave propagation in models with localized clusters of micro-heterogeneities. The main features of the algorithm are the application of temporal and spatial refinement on two different surfaces; the use of the embedded-stencil technique for the refinement of grid step with respect to time; the use of the Fast Fourier Transform (FFT)-based interpolation to couple variables for spatial mesh refinement. The latter makes it possible to perform filtration of high spatial frequencies, which provides stability in the proposed finite-difference schemes. In the present work, the technique is implemented for the finite-difference simulation of seismic wave propagation and the interaction of such waves with fluid-filled fractures and cavities of carbonate reservoirs. However, this approach is easy to adapt and/or combine with other numerical techniques, such as finite elements, discontinuous Galerkin method, or finite volumes used for approximation of various types of linear and nonlinear hyperbolic equations. (C) 2014 Elsevier Inc. All rights reserved.