Linear stability of incompressible flow using a mixed finite element method
By means of the fractional step finite element method, the two-dimensional base flows are numerically computed over a range of Reynolds numbers, and then they are perturbed with three-dimensional disturbances. By using linear stability and normal mode analysis, we obtain the equations governing the evolution of perturbation from linearized Navier-Stokes equations with slight compressibility. In terms of the mixed finite element discretization (in which six-node quadratic Lagrange triangular elements with quadratic interpolation for velocities \((P_2)\) and three-node linear Lagrange triangular elements for pressure \((P_1)\) are used), a nonsingular generalized eigenproblem is formulated whose solution gives the dispersion relationship between the complex growth rate and the wave number. As an example, we examine the stability of lid-driven cavity flow.
six-node quadratic Lagrange triangular elements
three-node linear Lagrange triangular elements
scientific article; zbMATH DE number 1160724
scientific article