A time‐accurate finite element algorithm for incompressible flow problems

A finite element solution procedure is presented for the simulation of transient incompressible fluid flows using triangular meshes. The algorithm is based on the artificial compressibility technique in connection with a dual time‐stepping approach. A second‐order discretization is employed to achieve the required accuracy in real‐time while an explicit multistage Runge‐Kutta scheme is used to march in the pseudo‐time domain. A standard Galerkin finite element method, stabilized by using an artificial dissipation technique, is used for the spatial discretization. The performance of the proposed algorithm is demonstrated by solving a set of internal and external problems including flows with purely transient and periodic behavior.