Finite Volume Method For Solving The Helmholtz Equation With Interface Problem

Helmholtz equations are often used to characterize the acoustic, electromagnetic scattering, radiation and vibration phenomena building, which is focused on how to solve by many scholars, there are many efficient numerical methods, such as finite volume method, finite difference method and finite element method as so on. It will be more difficult to solve Helmholtz equations with discontinuous wave number or singular source term.In this paper, the finite volume method will be used to solve the problem, it can not only keep the local conservation of physical quantity, but also get the desired order. The main work is organized as following. Firstly, using the high-order method developed in reference to solve the one-dimensional Helmholtz equation without source term, expanding the method to solve the one-dimensional Helmholtz equation with source term by improving the discretion process of the flux, developing the new high-order compact scheme for the case of continuous wave number and discontinuous wave number. Secondly, developing high-order compact difference scheme for two-dimensional Helmholtz equation with source term, solving it in the case of continuous wave number and discontinuous wave number. Finally, obtaining the coefficient matrix and solving it by Jacobi iterative method and SOR iterative method, demonstrating the effectiveness and feasibility of the scheme developed in the paper by numerical examples, and also verifying the developed scheme suitability for large wave number. And the next step is prospected.