Research On A Modified Radial Point Interpolation Meshfree Method For Two-dimensional Underwater Acoustic Problems

With the proposing of marine development strategies,the underwater acoustics problems gain more attention.Using high-performance numerical methods to solve the Helmholtz equation in ideal fluid medium is the key to those problems.It is common knowledge that the conventional finite element method(FEM)is unreliable to solve acoustic problems at high wavenumbers because of its over ‘rigid' stiffness matrix as well as the pollution error.Relative researches showed that the radial point interpolation method can obtain more accurate numerical solutions than the finite element by the same calculation model in acoustic scattering problems,but there were still large errors at high frequencies.This paper proposes an improved scheme for node selection when constructing radial point interpolation shape function,namely improved radial point interpolation method.This scheme makes the shape function of each interpolation point in the same background integration unit continuous,so it can more effectively reduce the error in numerical integration.This paper first introduces the finite element method and radial point interpolation method suitable for acoustic calculation,and elaborates the basic theory of improved radial point interpolation method,and at the same time lists the error evaluation criteria adopted in this paper.Afterwards,the application of the improved method in the infield acoustics problem,the outfield acoustic radiation problem,and the sound scattering problem was explored through several calculation examples.The calculation model of each problem included a simple structure with a theoretical solution and a structure with a complex geometric shape.By comparing the calculation results of the finite element method,the radial point interpolation method and the improved method and the related error analysis,the effectiveness and efficiency of the improved method are proved.In the case of using the same node distribution,the results of each calculation example show that compared with the original radial point interpolation method,the improved method has higher calculation accuracy and can improve calculation efficiency.In addition,compared with the traditional finite element method,this method can significantly suppress the effect of pollution error,and is more reliable when dealing with irregular node distribution.