| Summary: | 博士 === 國立臺灣大學 === 機械工程學研究所 === 88 === A class of implicit weighted ENO schemes for solving the two- and three-dimensional compressible Euler/Navier-Stokes equations with one equation turbulence model is presented. Weighted essentially non-oscillatory spatial operator is employed for inviscid fluxes and central differencing for viscous fluxes. A form with flux limiter of WENO scheme is adopted, which consists of first-order and high-order fluxes and allows for a more flexible choice of first order dissipative methods. For turbulent flow calculations, a point-wise version of Baldwin-Barth one equation turbulence model modified by Goldberg and Ramakrishnan is adopted. In order to improve the efficiency and convergence to the steady state, the lower-upper symmetric Gauss-Seidel (LU-SGS) implicit algorithm is used. For the complex configurations treatment, a parallel multiblock implementation is adopted. The data communication is accomplished by using the Message Passing Interface (MPI), which is a set of library interface standards for message passing.
We apply the resulting schemes to compute two- and three-dimensional inviscid/viscous flows, which include inviscid/viscous flows over airfoils, wings, delta wing and supersonic flow over F-16 fighter aircraft. The results show that the weighted ENO spatial operator for the inviscid fluxes not only enhances the accuracy but also improves the convergence rate for steady-state computation as compared with those using the ENO counterpart. It is found that for all cases computed, the solutions of the present algorithms are in good agreement with the experimental data. The parallel efficiencies are very good, especially for the case of ONERA M6 wing, the results demonstrate the linear speedup for a large number of processors
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