Abstract
AbstractIn this paper, we discuss the performance of a least-squares-based spectral element solver for Oseen equations on two-dimensional curvilinear domains and three-dimensional Navier-Stokes equations. Both equations are solved in primitive form without any first-order reformulation. The spectral approximation is nonconforming, and the same order spectral element functions are used for both velocity and pressure variables. A suitable preconditioner has been proposed using ADN theory in order to control the condition number of the system. Numerical results are obtained using the preconditioned conjugate gradient method. Numerical results show that the method is exponentially accurate in both velocity and pressure variables. Mass conservation property of the used solver has been displayed.
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