An explicit numerical time domain formulation to simulate pulsedpressure waves in viscous fluids exhibiting arbitrary frequency powerlaw attenuation

摘要

An explicit time domain algorithm is developed which is capable ofnnumerically simulating pulsed pressure waves propagating through medianwhose attenuation increases with frequency according to a power lawndependency. Because of possible noninteger exponents in the power lawnformulation, standard temporal differential operators cannot be definednand traditional finite difference approximations are thereforeninappropriate. We derive a method that is consistent with the fact thatnthe complex wavenumber often must include a nonlinear phase if systemncausality is to be ensured. This phase is derived from the power lawnattenuation and, due to their interdependency, the two terms in the wavenequation corresponding to attenuation and phase can be combined into ansingle factor. This so-called dispersion wave equation is mapped intoncomplex discrete-time frequency. In this domain, noninteger exponentsncan be eliminated via a power series expansion, and the resultingnequations transform naturally to discrete time operators. The algorithmnis tested by comparing numerically evaluated attenuation with the exactnpower law form, and the issues of stability in relation to thenconvergence of the power series and the accuracy of the mapping areninvestigated