Finite line method for acoustic problems in time domain

A new numerical method called the finite line method (FLM), is used to solve time-domain acoustic problems in this paper. The FLM is a strong-form numerical method. In the method, the computational domain is discretized into a series of collocation points, and a set of lines or curves passing through each collocation point is formed, which is called line-set. The shape function of each line is constructed using a Lagrange interpolation polynomial, and the first-order partial derivative of any physical quantity with respect to the global coordinates is created by calculating the directional derivative along the arc length of each line. The second-order partial derivative is then calculated using a recursive technique. The derived partial derivatives can be directly substituted into the governing differential equations and the corresponding boundary conditions of the acoustic problem, so as to establish the discrete system equations. As a strong-form numerical method, the FLM does not need to use the variational principle or energy principle to establish the calculation scheme, and the whole solution process does not require integration. In addition, the coefficient matrix generated by the FLM is highly sparse, making it computationally efficient. This paper introduces the Newmark difference technique to discretize the time domain and solve the system of equations containing time terms. For a point sound source represented by Dirac function, a source density function is proposed to approximate the effect of the point sound source, so that it can be applied to the FLM. Four numerical examples are given to verify the correctness and application potential of the proposed method.