This paper examines the role of continuity of the basis in the computation of turbulent flows. We compare standard finite elements and non-uniform rational B-splines (NURBS) discretizations that are employed in Isogeometric Analysis (Hughes et al. in Comput Methods Appl Mech Eng, 194:4135-4195, 2005). We make use of quadratic discretizations that are C 0 -continuous across element boundaries in standard finite elements, and We also find that the effect of continuity is greater for higher Reynolds number flows.

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SUMMARYThe present contribution is concerned with the design of a family of consistent uid-structure interaction algorithms based on a unique temporal and spatial discretization of the governing equations. The characterization of the moving uid-structure interface is realized by means of the arbitrary Lagrangian Eulerian technique. The spatial discretization is performed with the ÿnite-element method, whereby either a ÿrst-order upwind scheme or the classical second-order upwind Petrov-Galerkin technique are used to discretize the linearized uid equations while the standard Bubnov-Galerkin method is applied to the structural equations. In order to streamline coupling, the structure is discretized in a velocity-based fashion. The temporal discretization of both the uid and the structural equations is embedded in the generalized-framework by making use of classical Newmark approximations in time. To quantify the sources of error of the proposed algorithms, systematic studies in terms of the one-dimensional piston model problem are presented.

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SUMMARYA new algorithm for the computation of the spectral expansion of the eigenvalues and eigenvectors of a random non-symmetric matrix is proposed. The algorithm extends the deterministic inverse power method using a spectral discretization approach. The convergence and accuracy of the algorithm is studied for both symmetric and non-symmetric matrices. The method turns out to be efficient and robust compared to existing methods for the computation of the spectral expansion of random eigenvalues and eigenvectors.