Acoustic tomography of temperature and velocity fields by using the radial basis function and alternating direction method of multipliers

Considering the acoustic refraction effect, an investigation of simultaneously visualizing the temperature and velocity fields is carried out by using the combined meshfree radial basis function and alternating direction method of multipliers (RBF-ADMM). The radial basis function is introduced to recover the null-space component. It assumes that the reconstructed fields are continuous functions according to their nature, which, therefore, adds the prior information of the continuity in the fields’ reconstruction. Meanwhile, the alternating direction method of multipliers with improving anti-noise capacity is employed to iteratively resolve the inverse acoustic tomographic problem in low Mach number, which makes the parallel implementation and distributed optimization possible. Different from the traditional methods for solving boundary value problems, a fast two-point ray-tracing algorithm is introduced to trace the curved sound waves more efficiently. Proof-of-concept demonstrations including the representative temperature and aerodynamic fields are performed. For the two scenarios of two-peak and two-vortex inhomogeneous fields with 10% measurement errors, the averaged absolute errors of the reconstructed temperature fields are 120.7 K, and 39.9 K, respectively, and that of the reconstructed velocity fields are 0.24 m/s and 1.23 m/s, respectively. In addition, a data-based verification, which depicts the Karman vortex street phenomenon, is carried out to prove the ability of this method. All the results confirm the feasibility and effectiveness of the proposed RBF-ADMM in simultaneously reconstructing the temperature and velocity fields under different complicated environment. The proposed method for visualizing the arbitrary temperature and velocity fields will provide crucial input for control system such as the engines and boilers to optimize the thermal fluid and combustion process.