Simulation Of Nonlinear Wave Propagation Research Articles

High performance calculation of nonlinear wave propagation on GPU for focused ultrasound treatment planning

High intensity focused ultrasound (HIFU) is very promising new technology that has many therapeutic application, and among them are the treatment of cancer in different organs without major side effects. Some of the limitations of HIFU are the long treatment time and incomplete ablation. High performance computing can help in this regard. Simulation of nonlinear wave propagation in three dimensional geometry is very time consuming process especially when shocks are presented. In the current work, we are going to present three dimensional parallel solver on GPU. Some examples for the simulation in a patient specific geometry will be also presented. The presented results can be used for the optimization of the treatment. For the validation of the results, ex-vivo and in-vivo experiments have been performed. It has been shown that large volume can be ablated within a short period of time.

Numerical Simulation of Nonlinear Wave Propagation from Deep to Shallow Water

Herein, a numerical model is proposed to simulate the nonlinear wave propagation from deep to shallow water and wave breaking phenomena. In the numerical model, the governing equations selected, in which the momentum equations were added to the eddy-viscous breaking and bottom friction terms to simulate the wave breaking phenomenon, are suitable for the wave propagation from deep to shallow water. The spatial derivations of the governing equations are discretized with the hybrid scheme, combining the finite-difference and finite-volume methods. To numerically simulate the nonlinear wave propagation in waters with various depths accurately, the non-conservative governing equations are reorganized as conservative to facilitate a total variation diminishing (TVD) type scheme using a Riemann solver. Extensive numerical tests of nonlinear wave propagation have been realized in waters with large relative water depths and varying water depths. The comparisons between numerical and analytical or experimental results indicated that the numerical results are reasonable and reliable, and the present numerical model can effectively simulate the wave-breaking phenomenon.

Evidence of the formation of the shock scattering induced violent cavitation cluster during boiling histotripsy insonation: A numerical case study

Boiling histotripsy is a promising noninvasive ultrasonic technique that can be used to mechanically destroy solid tumours. In boiling histotripsy, the formations and dynamics of a boiling vapour bubble and cavitation clouds contribute towards mechanical tissue fractionation. Whilst a number of numerical and experimental studies have been performed to examine and understand the evolution of a boiling bubble at the HIFU focus in a viscoelastic medium, little is known about the subsequent generation of cavitation clouds that form in between the boiling bubble and the HIFU transducer during boiling histotripsy insonation. Previous experimental observations suggest that the shock scattering by a boiling bubble may play a significant role in producing cavitation clouds. The main objective of the present study is, therefore, to investigate the relationship between the shock scattering phenomenon and the occurrence of cavitation clouds through (a) performing a numerical simulation of nonlinear wave propagation with the presence of a bubble at the HIFU focus and (b) comparing with the previous high speed camera observations of a cavitation cluster formation. The size of a bubble (i.e., 95.7, 128.1 and 258 μm in diameter) as well as the HIFU exposure conditions (i.e., a driving frequency of 1.1 MHz, peak positive and negative pressures of 68.4 MPa and −13.9 MPa) used in the simulations were obtained from the previous boiling histotripsy experiments conducted with a tissue gel phantom. The numerical results presented in this study clearly demonstrate that the shock scattering is the main cause of the creation of a cavitation cluster in boiling histotripsy.

Inversions of synthetic umbral flashes: a selection of wavelength sampling

Context. Imaging spectrographs are popular instruments used to obtain solar data. They record quasi-monochromatic images at selected wavelength positions. By scanning the spectral range of the line, it is possible to obtain bidimensional maps of the field-of-view with a moderate spectral resolution. Aims. In this work, we evaluate the quality of spectropolarimetric inversions obtained from various wavelength samplings during umbral flashes. Methods. We computed numerical simulations of nonlinear wave propagation in a sunspot and constructed synthetic Stokes profiles in the Ca II 8542 Å line during an umbral flash using the NLTE code NICOLE. The spectral resolution of the Stokes profiles was downgraded to various cases with differences in the wavelength coverage. A large set of wavelength samplings was analyzed and the performance of the inversions was evaluated by comparing the inferred chromospheric temperature, velocity, and magnetic field with the actual values at the chromosphere of the numerical simulation. Results. The errors in the inverted results depend to a large extent on the location of the wavelength points across the profile of the line. The inferred magnetic field improves with the increase of the spectral resolution. In the case of velocity and temperature, low spectral resolution data produce a match of the inverted atmospheres with the actual values comparable to wavelength samplings with finer resolution, while providing a higher temporal cadence in the data acquisition. Conclusions. We validated the NLTE inversions of spectropolarimetric data from the Ca II 8542 Å during umbral flashes, during which the atmosphere undergoes sudden dramatic changes due to the propagation of a shock wave. Our results favor the use of fine spectral resolution for analyses that focus on the inference of the magnetic field, whereas the estimation of temperature and velocity fluctuations can be performed with lower spectral resolution.

Inversions of synthetic umbral flashes: Effects of scanning time on the inferred atmospheres

Context. The use of instruments that record narrowband images at selected wavelengths is a common approach in solar observations. They allow scanning of a spectral line by sampling the Stokes profiles with two-dimensional images at each line position, but require a compromise between spectral resolution and temporal cadence. The interpretation and inversion of spectropolarimetric data generally neglect changes in the solar atmosphere during the scanning of line profiles. Aims. We evaluate the impact of the time-dependent acquisition of various wavelengths on the inversion of spectropolarimetric profiles from chromospheric lines during umbral flashes. Methods. Numerical simulations of nonlinear wave propagation in a sunspot model were performed with the code MANCHA. Synthetic Stokes parameters in the Ca II 8542 Å line in NLTE were computed for an umbral flash event using the code NICOLE. Artificial profiles with the same wavelength coverage and temporal cadence from reported observations were constructed and inverted. The inferred atmospheric stratifications were compared with the original simulated models. Results. The inferred atmospheres provide a reasonable characterization of the thermodynamic properties of the atmosphere during most of the phases of the umbral flash. The Stokes profiles present apparent wavelength shifts and other spurious deformations at the early stages of the flash, when the shock wave reaches the formation height of the Ca II 8542 Å line. These features are misinterpreted by the inversion code, which can return unrealistic atmospheric models from a good fit of the Stokes profiles. The misguided results include flashed atmospheres with strong downflows, even though the simulation exhibits upflows during the umbral flash, and large variations in the magnetic field strength. Conclusions. Our analyses validate the inversion of Stokes profiles acquired by sequentially scanning certain selected wavelengths of a line profile, even in the case of rapidly changing chromospheric events such as umbral flashes. However, the inversion results are unreliable during a short period at the development phase of the flash.

A constitutive model for the analysis of second harmonic Lamb waves in unidirectional composites

In recent research on Structural Health Monitoring (SHM) guided waves, especially nonlinear Lamb waves, turned out to be a suitable means for monitoring material deterioration in thin-walled structures. In the corresponding numerical simulations on wave propagation the nonlinear elastic theory by Murnaghan is often implemented, which requires 14 material parameters for transversely isotropic materials. Enhancing an existing linear strain energy potential, a new nonlinear hyperelastic transversely isotropic material model is introduced which reduces the number of independent material parameters to six. In order to verify the applicability of the presented material model with respect to the simulation of nonlinear wave propagation in composite structures, and the generation of higher harmonic wave modes, the existence of a power flux from the fundamental to the higher harmonic mode is investigated analytically and numerically. Analytical considerations show that this power flux exists like in Murnaghan’s theory. For the numerical validation the S0–S0 mode pair in the low frequency range is used. Therefore, the amplitude of the second harmonic wave mode is oscillating with increasing propagation distance. This behavior is in excellent agreement with the theoretical prediction. It is shown further, that even for an oscillating behavior the amplitude of the second harmonic mode can be approximated by a linear curve fit over a considerably propagation distance and hence shows a quasi cumulative behavior. Therefore, the introduced material model is an advantageous alternative to Murnaghan’s theory to simulate the second harmonic Lamb wave generation due to in composite structures.

Computational simulation of the mechanical response of brain tissue under blast loading.

In the present study, numerical simulations of nonlinear wave propagation and shock formation in brain tissue have been presented and a new mechanism of injury for blast-induced neurotrauma (BINT) is proposed. A quasilinear viscoelastic (QLV) constitutive material model was used that encompasses the nonlinearity as well as the rate dependence of the tissue relevant to BINT modeling. A one-dimensional model was implemented using the discontinuous Galerkin finite element method and studied with displacement- and pressure-input boundary conditions. The model was validated against LS-DYNA finite element code and theoretical results for specific conditions that resulted in shock wave formation. It was shown that a continuous wave can become a shock wave as it propagates in the QLV brain tissue when the initial changes in acceleration are beyond a certain limit. The high spatial gradient of stress and strain at the shock front cause large relative motions at the cellular scale at high temporal rates even when the maximum stresses and strains are relatively low. This gradient-induced local deformation may occur away from the boundary and is proposed as a contributing factor to the diffuse nature of BINT.

Feasibility of Second Harmonic Imaging in Active Sonar: Measurements and Simulations

Nonlinear acoustics allows for applications like tissue harmonic imaging in medicine and parametric arrays in underwater acoustics. Mainstream sonars transmit and receive signals at the same frequency and up to now energy transferred to higher harmonic frequencies has been mainly seen as a disturbance for target strength estimation, e.g., in fishery research. This paper investigates the feasibility of utilizing the part of the signal generated around the second harmonic frequency band by nonlinear propagation of sound in water. It presents the potential enhancements the second harmonic signal may provide for target imaging as well as multifrequency target recognition. It compares measurements of the pressure field radiated by commercial transducers in water at 121 and 200 kHz up to a range of 12 m with numerical simulations. The detected levels of higher harmonic signals agree with simulations of nonlinear wave propagation. This verifies the implementation of the simulator and allows a comparison of the beam characteristics at longer ranges when filtered around the fundamental or second harmonic frequencies. An example of pulse-echo imaging with spherical targets is also shown using signals at the fundamental and second harmonic frequencies where the second harmonic signal can detect one of the targets that the fundamental signal cannot. Using the active sonar equation to estimate the maximum range, simulations based on a simple model including ambient noise and volume reverberation confirm that with a source level of 228 dB and a detection threshold of 12 dB the fundamental signal at 200 kHz can detect a fish of target strength -36 dB to approximately 343 m while the detection range of the second harmonic signal is approximately 243 m. The combined use of the signal components in the second harmonic and fundamental frequency bands provides a high-resolution image at short range and a long-range imaging capability at a lower resolution as well as a multifrequency characterization of targets.

Chebyshev Finite-Spectral Method for 1D Boussinesq-Type Equations

In this paper, an accurate Chebyshev finite-spectral method for one-dimensional (1D) Boussinesq-type equations is proposed. The method combines the advantages of both the finite-difference and spectral methods. The spatial derivatives in the governing equations can be calculated accurately in an efficient way, while some flexibility is allowed for treating irregular grids. The efficiency and accuracy of the proposed method are verified by successfully solving the problem of solitary wave propagation over a flat bottom where analytical solutions are available for comparison. A simple formula to calculate the wave celerity of the solitary wave propagation has also been derived. Finally, the applicability of the numerical method to periodic and random waves was validated by the simulation of nonlinear wave propagation over a bar where laboratory data are available for comparison. The method can be easily extended to treat 2D problems.

Waves in magnetic flux concentrations: The critical role of mode mixing and interference

Time-dependent numerical simulations of nonlinear wave propagation in a two-dimensional (slab) magnetic field geometry show wave mixing and interference to be important aspects of oscillatory phenomena in starspots and sunspots. Discrete sources located within the umbra generate both fast and slow MHD waves. The latter are compressive acoustic waves which are guided along the magnetic field lines and steepen into N-waves with increasing height in the spot atmosphere. The former are less compressive, and accelerate rapidly upward through the overlying lowportion of the umbral photosphere and chromosphere ( ). As the fast wave fronts impinge upon the penumbral “magnetic canopy” from above, they interfere with the outward-propagating field-guided slow waves, and they also mode convert to (non-magnetic) acoustic-gravity waves as they penetrate into the weak magnetic field region which lies between the penumbral canopy and the base of the surrounding photosphere. In a three-dimensional situation, one expects additional generation, mixing and interference with the remaining torsional Alfven waves.

Finite element simulation of nonlinear wave propagation in thermoviscous fluids including dissipation.

A recently developed finite element method (FEM) for the numerical simulation of nonlinear sound wave propagation in thermoviscous fluids is presented. Based on the nonlinear wave equation as derived by Kuznetsov, typical effects associated with nonlinear acoustics, such as generation of higher harmonics and dissipation resulting from the propagation of a finite amplitude wave through a thermoviscous medium, are covered. An efficient time-stepping algorithm based on a modification of the standard Newmark method is used for solving the non-linear semidiscrete equation system. The method is verified by comparison with the well-known Fubini and Fay solutions for plane wave problems, where good agreement is found. As a practical application, a high intensity focused ultrasound (HIFU) source is considered. Impedance simulations of the piezoelectric transducer and the complete HIFU source loaded with air and water are performed and compared with measured data. Measurements of radiated low and high amplitude pressure pulses are compared with corresponding simulation results. The obtained good agreement demonstrates validity and applicability of the nonlinear FEM.

Simulation of Hamiltonian light-beam propagation in nonlinear media

The simulation of nonlinear wave propagation in the ray regime, i.e., in the limit of geometrical optics, is discussed. The medium involved is nonlinear, which means that the field amplitudes affect the constitutive parameters (e.g., dielectric constant) involved in the propagation formalism. Conventionally, linear ray propagation is computed by the use of Hamilton’s ray equations whose terms are derived from the appropriate dispersion equation. The formalism used to solve such a set of equations is the Runge–Kutta algorithm in one of its variants. In the present case of nonlinear propagation, a proper dispersion equation must first be established from which the rays can be computed. Linear ray tracing with Hamilton’s ray theory allows for the computation of ray trajectories and wave fronts. The convergence or divergence of rays suggests heuristic methods for computing the variation of amplitudes. Here, terms appearing in the Hamiltonian ray equations involve field amplitudes, which themselves are determined by the convergence (or divergence) of the rays. This dictates the simultaneous computation of a beam comprising many rays, so it is necessary to modify the original Runge–Kutta scheme by building into it some iteration mechanism such that the process converges to the values that take into account the amplitude effect. This research attempts to modify the existing propagation formalism and apply the new algorithm to simple problems of nonlinear ray propagation. The results display self-focusing effects characteristic of nonlinear optics problems. The influence of weak losses on the beam propagation and its self focusing is also discussed. Some displayed results obtained by simulating the modified formalism seem to be physically plausible and are in excellent agreement with experimental results reported in the literature.

The generalized TLM-based FDTD-summary of recent progress

The transmission-line-matrix (TLM)-based finite-difference time-domain (FDTD) method has been generalized recently to incorporate graded mesh and anisotropic media. The method is equivalent to the three-dimensional TLM symmetrical condensed node, but is formulated and computed in a FDTD fashion. Therefore, it retains certain features of both the TLM and FDTD methods. The authors report recent progress in modeling with the TLM-based FDTD method, namely, successful implementation of the perfectly matched layer (PML) and simulation of nonlinear wave propagation.

Numerical simulation of nonlinear wave propagation over a bar

Numerical computations based on a one-dimensional time domain Boussinesq model with improved dispersion characteristics are carried out to model relatively long, unidirectional waves propagating over a submerged obstacle. Comparisons for non-breaking waves show good agreement between the numerical results and measurements obtained from experiments in a wave flume with a submerged trapezoidal bar. The observed phenomena of bound harmonics generation in the shoaling region (upslope) and their release, or wave decomposition, in the deepening part of the flume (downslope) are well predicted by the numerical model both for regular and random waves. The inclusion of the effects of wave breaking is briefly discussed.