Numerical Solution of the Navier-Stokes Equations by the Finite Element Method

Occurrences of viscous fluid flows in arbitrary internal passages are numerous, an analytical solution of the governing Navier-Stokes equations cannot be obtained. Even a numerical approach faces difficulties arising from the nonlinearity and complexity of the geometry involved. To remedy these difficulties, the time-dependent Navier-Stokes equations are solved by the finite element method wherein a steady-state solution is assumed when the time-dependent solution becomes convergent. A family of locally constricted channels was considered in the computations, and in each case, the shear stress at the wall was found to be sharply increased at and near the region of constriction. Computations were carried out to Reynolds numbers when a separation eddy was established. The numerical scheme used seems to be fairly stable.