# Numerical Simulation of Acoustics-Acoustics- and Structural Mechanics-Acoustics-Couplings on Nonmatching Grids. Part I.

Project manager: |
Prof. Dr. rer. nat. B. I. Wohlmuth |

Projektbearbeiter: |
Dr. B. Flemisch, Dr. I. Shevchenko |

Projektpartner: |
Lehtstuhl für Sensorik, Universität Erlangen-Nürnberg |

#### Project description

The project is aimed at investigation and implementation of new numerical methods for efficient solution of the acoustic- and mechanical-acoustic coupled models on nonconforming grids.#### Current results

The numerical simulations of acoustic- and mechanical-acoustic coupled models usually confront with spatial-discretization problems due to various space-scales in different regions of the computational domain. It may take place, for instance, when computing a wave propagation generated by a transmitter. The spatial region where the wave is propagated can be discretized with a coarse grid while the computation domain of the transmitter must be performed using a much fine grid. A demonstrative example of such different space-scales regions is the emission of acoustic waves by multiple structures which admits the steering of the waves by exciting the structures in a specified chronological order (figure 1).Figure 1. Cylindrical plates attached to the fluid domain (left),
isosurfaces of the acoustic potential, deformed plates (right) |

Figure 2. Evolution of the acoustic velocity potential and of the deformed structures, synchronous excitation: snapshots after 10, 20, ... ,80 timesteps. |

Figure 3. Evolution of the acoustic velocity potential and of the deformed structures, successive excitation: snapshots after 10, 20, ... ,80 timesteps. |

# Numerical Simulation of Acoustics-Acoustics- and Structural Mechanics-Acoustics-Couplings on Nonmatching Grids. Part II.

Project manager: |
Prof. Dr. rer. nat. B. I. Wohlmuth |

Projektbearbeiter: |
Dr. I. Shevchenko |

Projektpartner: |
Applied Mechatronics, Alps-Adriatic University of Klagenfurt |

#### Project description

The project is aimed at investigation and implementation of new numerical methods for efficient solution of the acoustic- and mechanical-acoustic coupled models on nonconforming grids.#### Current results

**Multi-time stepping integration in multiphysics problems.**The heating of media by high-intensity focused ultrasound waves offers a desirable effect for a variety of applications. For instance, the ultrasonic thermotherapy of cancer in which destruction of soft tissues in the body is effected through high temperatures generated by the local absorption of wave energy. Within the framework of the project, we investigate the Pennes bio-heat transfer equation coupled with the non-linear Kuznetsov wave equation. In this multiphysics problem, an ultrasound transducer, located on the bottom of the computational domain (see Fig.4), generates waves of frequency 1 MHz which are propagated from bottom to top and heat up the tissue. Figure 4 shows snapshots, taken every 1.0 ms, of the evolution of the temperature and acoustic fields in the liquid (lower subdomain) and in the tissue (upper subdomain).

Figure 4. A series of snapshots after 1.0 ms, 2.0 ms, 3.0 ms, 4.0 ms and 5.0 ms of insonation.
The evolution of the temperature and acoustic fields. |

**Self-adapting absorbing boundary conditions for wave equations.**Within the framework of the project we proposed a self-adapting absorbing boundary condition (ABC) for the linear wave equation. The construction of ABC is based on a local computation of the incidence angle of the outgoing wave and on the use of the classical lowest order Engquist--Majda absorbing boundary condition. In order to obtain a good approximation of the incidence angle, we decompose adaptively the absorbing boundary into subsegments and locally apply the Fourier transformation. In Fig.5, a monofrequency transducer is located on the left vertical boundary of the computational domain which emits sinusoidal acoustic waves traveling from the left to the right. The absorbing boundary, inclined at the angle 30 degree to the horizontal axis, is set on the right boundary of the domain. Rows

**a**and

**b**stand for the first and second order Engquist--Majda ABCs while in row

**c**we show the results of the newly designed self-adapting ABC. For this setup, the reference solution is a plane wave.

Figure 5. The evolution of the acoustic potential for the absorbing boundary inclined at 30 degree to the horizontal axis. The time t is in microseconds |