Simulation of a 2D heterogeneous medium using the frequency-specific mixed domain method

This example shows how to simulate the frequency-domain wave field in heterogeneous media using the frequency-specific mixed domain method.

Defining the 2D heterogeneous media

Details of defining the computational domain and the phased-array transducer are shown in the example Simulation of a 2D homogeneous medium using the frequency-specific mixed domain method. Medium properties are defined in the example Simulation of a 2D heterogeneous medium using the transient mixed domain method.

2D forward simulation

Assuming linear wave propagation, the center/fundamental frequency pressure field can be calculated with the 2D forward simulation function Forward2D_fund. For weakly nonlinear wave propagation, the pressure field at the second-harmonic frequency can be further calculated with the function Forward2D_sec.The first and second-order reflections are included in the fundamental pressure simulation.


% the maximum order of reflection included in the simulation    
reflection_order = 2;

medium.NRL_gamma = 0.5;  % constant for absorption layer 
medium.NRL_alpha = 0.1;  % decay factor for absorption layer 

% forward propagation of the fundamental pressure   
P_fundamental = Forward2D_fund(mgrid, medium, excit_p, omega_c,...
                reflection_order, 'NRL');

% forward propagation of the second-harmonic pressure     
P_second = Forward2D_sec(mgrid, medium, P_fundamental, omega_c, 'NRL');

The figure on the left shows the acoustic pressure field at the center/fundamental frequency and the one on the right shows the pressure field at the second-harmonic frequency. fundamental and the second-harmonic pressure field

fundamental and the second-harmonic pressure field

These results can be directly compared with the ones in the example Simulation of a 2D heterogeneous medium using the transient mixed domain method. Two points should be noted here. First, multiple reflection is not considered in the function Forward2D_sec. Second, the density heterogeneity is not automatically considered in the function Forward2D_sec. To include the density heterogeneity, 'correction' must be enabled, and the scattering due to the density variation will be considered in an empirical manner. To include the density heterogeneity in a more accurate way, Forward2D can be used. It is, however, more time-consuming.

 
% forward propagation of the second-harmonic pressure   
P_second = Forward2D_sec(mgrid, medium, P_fundamental, omega_c, 'NRL', 'correction');

The figure below shows the acoustic pressure field at the second-harmonic frequency when 'correction' is enabled in the function Forward2D_sec. the second-harmonic pressure field with correction

the second-harmonic pressure field with correction

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