| Author | Christian H. Whiting |
|---|---|
| Title | Stabilized Finite Element Methods for Fluid Dynamics Using a Hierarchical Basis |
| Year | 1999 |
| School | School of Engineering |
| Institution | Rensselaer Polytechnic Institute |
| Abstract | Stabilized finite element methods have been shown to yield robust, accurate numerical solutions to both the compressible and incompressible Navier-Stokes equations for laminar and turbulent flows. This work presents an application of mesh entity based, hierarchical basis functions to a new stabilized finite element formulation, which is shown to yield high accuracy and more cost effective simulations when compared with the traditional, linear basis methods. The new formulation is then demonstrated numerically to yield nearly optimal rates of convergence with respect to the interpolation error. A second-order accurate, implicit time integrator with user-controllable numerical dissipation is also presented for advancing the semidiscrete system of equations in time. This time integrator is proven to be stable and second-order accurate for a linear model problem, and demonstrated to have excellent characteristics on more complicated flows. A variety of examples are provided that demonstrate that the most cost-effective simulations (in terms of CPU time, memory, and disk storage) can be obtained using higher-order basis functions when compared with the standard linear basis. The formulation has also been successfully applied to unsteady flows, and several examples will be given. An application to a direct numerical simulation (DNS) of turbulent channel flow at Ret = 180 is then presented to assess the usability of the hierarchical basis for a more complex turbulent flow. Postprocessing techniques are described for the effective visualization of hierarchical solutions, as well as numerical evaluation of turbulent statistics. |
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