Modeling and analysis of nonlinear acoustic Mach stem generation

This work presents a numerical investigation of Mach stem formation in nonlinear acoustic wave interactions using the open-source k-Wave toolbox. Mach stems, characterized by the coalescence of shock fronts in strong wave interactions, are a hallmark of nonlinear wave behavior with critical implications for high-intensity focused ultrasound (HIFU), lithotripsy, and blast wave physics. Leveraging the pseudospectral time-domain (PSTD) capabilities of k-Wave, we modeled the interaction of angled acoustic shocks at the air-ground and water-sediment boundary. Simulations captured the transition from regular reflection to Mach reflection regimes, validating critical angle thresholds and exhibiting the nonlinear amplification and geometric focusing intrinsic to Mach stem growth. The model incorporated realistic acoustic parameters, including frequency-dependent absorption and nonlinear coefficients, to accurately replicate physical scenarios. This study establishes a k-Wave as a baseline computational platform for exploring nonlinear wave interactions and offers a foundation for experimental validation and future parametric studies in high-amplitude acoustics.