SUMMARYA time-accurate least-squares finite element method is used to simulate three-dimensional flows in a cubic cavity with a uniform moving top. The time-accurate solutions are obtained by the Crank-Nicolson method for time integration and Newton linearization for the convective terms with extensive linearization steps. A matrix-free algorithm of the Jacobi conjugate gradient method is used to solve the symmetric, positive definite linear system of equations. To show that the least-squares finite element method with the Jacobi conjugate gradient technique has promising potential to provide implicit, fully coupled and time-accurate solutions to large-scale three-dimensional fluid flows, we present results for three-dimensional lid-driven flows in a cubic cavity for Reynolds numbers up to 3200.
A two‐dimensional thermoviscoelastic problem is analyzed by the finite element method based on free volume theory and thermoviscoelasticity. The stresses are computed according to a shift factor; the shift factor is in turn calculated from the free volume ratio, defined as the free volume divided by the total volume. The free volume ratio depends on normal stress as well as hydrostatic pressure, in addition to temperature. The effect of hydrostatic pressure on the free volume ratio can be approached by an equivalent temperature effect. A finite element analysis is developed, in which the constitutive equations are formulated in recursive form. As a nonlinear analysis, the procedure finds the solution iteratively, using a shift factor as the convergence parameter. For poly(vinyl acetate) stress‐strain curves under several loading conditions are discussed with respect to temperature and pressure.
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