High order finite point method for the solution to the sound propagation problems

•The accuracy of the meshfree Finite point method (FPM) was improved.•The Godunov Riemann solver was used with the polynomial reconstruction.•Modified FPM was used to solve the acoustic propagation problems.•The propagation of sound was simulated using the linearized Euler equations.•High order of the FPM was confirmed by the convergence study.

In this paper we present an accuracy improvement of the meshfree Finite point method. This high-order method has been used to solve the sound propagation problems, which can be modelled by linearized Euler equations. High accuracy has been obtained using polynomial reconstruction of variables involved in the Riemann solver. The order of the meshfree method will be verified on 2D acoustic pulse problem which serves as a benchmark problem with known analytical solution.