Dispersion analysis and numerical simulation of wave motion in finite element algorithm with triangular meshes

The finite element discretization of wave motion can cause numerical error. The numerical dispersion is in essence the non-physical solution caused by the propagation of numerical error. Not only has the numerical dispersion no practical meaning, but also it can affect the understanding of real fluctuations. In order to clarify the influence factors of numerical dispersion in finite element algorithm with triangular meshes, the dispersion functions of lumped mass matrix and consistent mass matrix are derived respectively, and the dispersion function of combined mass matrix is also given. And then the numerical dispersion of different mass matrices are compared. The results of theoretical analysis and numerical simulation indicate: ① The numerical dispersion in finite element algorithm with triangular meshes depend on the mesh layout, direction of wave propagation, the ratio of vertical length to horizontal length and the mass matrix; ② The numerical dispersion of consistent mass marix is more easily affected by wave propagation direction than that of lumped mass matrix; ③ The irrational triangular meshes have a bad effect on numerical phase velocity (numerical dispersion); ④ Equilateral triangular meshes can provide superior results regardless of the propagation direction; ⑤ The linear combination of lumped mass matrix and consistent mass matrix can effectively suppress numerical dispersion.