A meshfree method based on moving Kriging interpolation for the analysis of acoustic wave propagation problems

Abstract Accurate simulation of acoustic-wave propagation is important in many engineering and biomedical applications, such as nondestructive testing, noise control, and focused ultrasound therapies. Although the finite-element method (FEM) is commonly used for these analyses, it often suffers from numerical dispersion—especially when the wavelength is small—which can reduce the reliability of the results. Meshfree methods offer an alternative by using scattered nodes instead of fixed element meshes; this flexibility helps reduce dispersion and eliminates the need for complex mesh generation. This study introduces the Moving Kriging Interpolation Method (MKIM), which is based on the Moving Least-Squares (MLS) approach. The combination yields a continuously differentiable and more stable solution space. The problem is formulated for a two-dimensional chamber with Dirichlet boundary conditions and for a two-dimensional submarine-like shape with Neumann boundary conditions. The method is implemented in MATLAB, employing Gauss points for domain integration to solve the weak form of the Helmholtz wave equation. To evaluate its performance, the numerical results are validated against both closed-form analytical solutions and the other numerical schemes discussed above. The outcomes demonstrate higher accuracy and better control of numerical dispersion than traditional methods. These findings highlight the potential of meshfree techniques for tackling increasingly complex acoustic problems in the future.