TRANSIENT SOLUTIONS FOR 3-DIMENSIONAL LID-DRIVEN CAVITY FLOWS BY A LEAST-SQUARES FINITE-ELEMENT METHOD

A time-accurate least-squares finite element method is used to simulat e three-dimensional flows in a cubic cavity with a uniform moving top. The time- accurate solutions are obtained by the Crank-Nicolson metho d for time integration and Newton linearization for the convective ter ms with extensive linearization steps. A matrix-free algorithm of the Jacobi conjugate gradient method is used to solve the symmetric, posit ive definite linear system of equations. To show that the least-square s finite element method with the Jacobi conjugate gradient technique h as promising potential to provide implicit, fully coupled and time-acc urate solutions to large-scale three-dimensional fluid flows, we prese nt results for three-dimensional lid-driven flows in a cubic cavity fo r Reynolds numbers up to 3200.