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A generalized-$$\alpha$$ method for integrating the filtered Navier-Stokes equations with a stabilized finite element method. (English) Zbl 0973.76048
Summary: A generalized-$$\alpha$$ method is developed and analyzed for linear, first-order systems. The method is then extended to the filtered Navier-Stokes equations within the context of a stabilized finite element method. The formulation is studied through the application to laminar flow past a circular cylinder and turbulent flow past a long, transverse groove. The method is formulated to obtain a second-order accurate family of time integrators whose high-frequency amplification factor is the sole free parameter. Such an approach allows the replication of midpoint rule (zero damping), Gear’s method (maximal damping), or anything in between.

##### MSC:
 76M10 Finite element methods applied to problems in fluid mechanics 76N15 Gas dynamics (general theory)
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##### References:
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