Acoustic tomography of two dimensional velocity field by using meshless radial basis function and modified Tikhonov regularization method

A meshless radial basis function (RBF) method combined with the modified Tikhonov regularization is proposed to reconstruct the two-dimensional velocity field. Time-of-flight data is obtained to capture the flow information of the region of interest. Three kinds of RBFs are employed to acquire the coefficient matrix of the AT. It also adds the prior information of continuity into the flow field reconstruction. Modified Tikhonov regularization is introduced to reconstruct the velocity field which alleviates the severe ill-posedness of the acoustic tomography (AT) problem. The influence of shape parameters, types of RBF, and the collocation of central points on reconstruction are investigated. Proof-of-concept simulations and corresponding Tomographic PIV data based simulation verification are conducted to prove the feasibility and effectiveness of the proposed method in velocity field reconstruction. All these results confirm that it is appropriate to solve severely ill-posed and underdetermined AT problems and in recovering the velocity field distribution.