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**A transient solution method for the finite element incompressible Navier- Stokes equations.**
*(English)*
Zbl 0619.76027

The authors present a numerical method for solving the unsteady incompressible Navier-Stokes equations for plane flows. The procedure is based on the spatial discretization of the Navier-Stokes equations and the continuity equation via the conventional Galerkin finite element method, employing the primitive variable formulation. The ordinary triangular element of linear interpolation is used for the velocity field and the pressure is assumed to be constant on each element. A direct time integration method, developed by the authors elsewhere, is applied to the integration of the finite element equations. The integration method has unique features in its formulation as well as in its evaluation of the contribution of extended functions. Particular processes concerning the continuity condition and the boundary conditions lead to a set of nonlinear recurrence equations representing the evolution of the velocities and pressures under the constraint of incompressibility. As for the nonlinear terms, an iterative process is performed until convergence is achieved in each integration step.

Numerical results are presented for flow past a rectangular cylinder of various width to height ratio at different Reynolds numbers, and the calculated flow fields are compared with experimentally observed ones reported in the literature. Agreement with the experimentally visualized flow fields turns out to be fairly well.

Numerical results are presented for flow past a rectangular cylinder of various width to height ratio at different Reynolds numbers, and the calculated flow fields are compared with experimentally observed ones reported in the literature. Agreement with the experimentally visualized flow fields turns out to be fairly well.

Reviewer: J.Siekmann

### MSC:

76D05 | Navier-Stokes equations for incompressible viscous fluids |

### Keywords:

unsteady incompressible Navier-Stokes equations; plane flows; spatial discretization; continuity equation; Galerkin finite element method; primitive variable formulation; triangular element of linear interpolation; direct time integration method; finite element equations; boundary conditions; nonlinear recurrence equations; convergence; rectangular cylinder
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\textit{Y. Yoshida} and \textit{T. Nomura}, Int. J. Numer. Methods Fluids 5, 873--890 (1985; Zbl 0619.76027)

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