Title: a Mesh-free Method with Arbitrary-order Accuracy for Acoustic Wave Propagation Authors: Hitoshi Mikada 1 Naoto Imamura 1 Junichi Takekawa

1 In the present study, we applied a novel mesh-free method to solve acoustic wave equation. 2 Although the conventional finite difference methods determine the coefficients of its operator 3 based on the regular grid alignment, the mesh-free method is not restricted to regular 4 arrangements of calculation points. We derive the mesh-free approach using the 5 multivariable Taylor expansion. The methodology can use arbitrary-order accuracy scheme 6 in space by expanding the influence domain which controls the number of neighboring 7 calculation points. The unique point of the method is that the approach calculates the 8 approximation of derivatives using the differences of spatial variables without parameters as 9 e.g. the weighting functions, basis functions. Dispersion analysis using a plane wave reveals 10 that the choice of the higher-order scheme improves the dispersion property of the method 11 although the scheme for the irregular distribution of the calculation points is more dispersive 12 than that of the regular alignment. In numerical experiments, a model of irregular 13 distribution of the calculation points reproduces acoustic wave propagation in a homogeneous 14 medium same as that of a regular lattice. In an inhomogeneous model which includes low 15 velocity anomalies, partially fine arrangement improves the effectiveness of computational 16 cost without suffering from accuracy reduction. Our result indicates that the method would 17 provide accurate and efficient solutions for acoustic wave propagation using adaptive 18