Simulating nonlinear acoustic using Lattice-Boltzmann equation in a lossy fluid

There are numerous applications for acoustics in medical diagnosis and treatment. An important fact to consider is accurate simulation of the acoustic waves and their interaction with body tissues. In medical applications, the nonlinearity of the ultrasound wave propagation plays a significant role in its interactions with body tissues. Currently, there are three approaches to modeling and simulation of nonlinear ultrasound waves in fluid mediums: macroscopic, mesoscopic and microscopic methods. In this study, a Lattice Boltzmann based mesoscopic method (LBM) is investigated. The Boltzmann equation is employed to simulate the flow of a Newtonian fluid in place of the conventional system of Navier- Stokes’, continuity and state equations. Through the application of the proposed model distorted nonlinear waves and the shock wave have been calculated for the ultrasound waves in a lossy medium. Moreover, the results are compared to the published results of the macroscopic methods. Resolution of the results signifies the accuracy and effectiveness of the LBM for modeling and simulation of nonlinearity of ultrasound waves for Mach numbers up to 0.01, which stands in the range of ultrasound waves availed for treatment cases (eg HIFU).