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The paper compares one-point quadrature and analytic integration as efficient alternatives to the standard two-points Gaussian quadrature for CFD finite element codes that use 4-node, bi-linear, quadrilateral elements. The differentially-heated square cavity problem, for which benchmark solutions exist, is used to compare the accuracy and computation time of the three integration methods. The results obtained show that one-point quadrature requires less computational time than analytic integration. Unlike the analytic integration, one-point quadrature also required minor modifications to existing finite-element codes that use two-points quadrature. Moreover, the code that applies Gauss quadrature is easily vecorizable, which is beneficial on supercomputers. In general, one-point quadrature requires an "hour-glass" correction to be made, but for the cavity-flow considered here this was not necessary thanks to the Dirichlet boundary condition applied over a large part of the solution domain.

Computational Fluid Dynamics (CFD) is used to simulate the flow filed in a rotor-casing assembly for different elliptic rotor aspect ratios and inlet flow velocities. The flow was simulated with the rotor fixed at its extreme positions, i.e. vertical and horizontal arrangement. The flow field results were used to ascertain the changes in the efficiency of a rotor-casing assembly. This included: inlet pressure, maximum velocity, and maximum turbulence values. A more fundamental quantity, integrated entropy generation was also calculated. Entropy generation is based on the second law of thermodynamic and accounts for all types of irreversibilties within the assembly. Of the different traditional quantities calculated, only the inlet pressure results were inline with the entropy generation results.