Time-domain acoustic wave propagations in multi-fluids using a weak-form meshfree method

Abstract

In this work, we focus on the derivation of the weak-form for meshfree methods in analyzing the time-domain acoustic wave propagation in multi-fluids. Due to the employment of meshfree shape functions not restricted to a local background cell, the continuity condition for acoustic particle velocity cannot be spontaneously satisfied, leading to inaccurate simulations of acoustic wave upon the interface. Thus, the penalty function method is utilized here in the weak-form for meshfree methods in order to cure this discontinuity issue without introducing any addition degrees of freedom. By conducting a number of numerical analyses, the numerical results obtained from a radial point interpolation meshfree method are in accord with the analytical solutions and the numerical results of bilinear and quadratic finite elements, validating the effectiveness of the weak-form derived for meshfree methods. Moreover, the numerical accuracy of the used meshfree method can surpass those of bilinear and quadratic finite elements when the same sets of nodes are employed, especially for relatively high frequencies.