Journal of Aeronautics, Astronautics and Aviation, Series A
We extend our previous study of the least-squares finite-element methods (LSFEMs) for Stokes equations to Navier-Stokes equation. Both unweighted and weighted LSFEM based on the first-order velocity-vorticity-pressure (VVP) formulation are developed. Several issues related to LSFEMs, such as the choice of interpolation functions (types of elements) and property of mass conservation, are studied. We use flow past a circular cylinder as the model problem to examine the effect of these issues on the approximations. Computed results show that high-resolution and high-order element, and appropriate weights of the weighted LSFEM can improve the accuracy as well as local and global mass conservation. It is found that weighted LSFEM is effective for coarse and low-order elements, and approximations are sensitive to the weights of weighted LSFEM. Among the various equal-order triangular and quadrilateral elements considered, such as 3-node and 6-node triangular elements, as well as 4-node, 8-node and 9-node quadrilateral elements, the piecewise 4-node and 9-node iso-parametric quadratic element outperforms other elements in terms of accuracy, satisfaction of mass conservation, and its robustness to the value of weights of the weighted LSFEM.