A flow past two side-by-side identical circular cylinders was numerically investigated with the unstructured spectral element method. From the computational results at various non-dimensional distances between cylinde...A flow past two side-by-side identical circular cylinders was numerically investigated with the unstructured spectral element method. From the computational results at various non-dimensional distances between cylinder centers T/D and the Reynolds number Re, a total of nine kinds of wake patterns were observed： four steady wake patterns, including single bluff-body steady pattern, separated double-body steady pattern and transition steady pattern for sub-critical Reynolds numbers and biased steady pattern for super-critical Reynolds numbers, and five unsteady wake patterns, including single bluff-body periodic pattern, biased quasi-steady pattern, quasi-periodic （flip-flopping） pattern, in-phase-synchronized pattern and anti-phase-synchronized pattern. Time evolution of lift and drag coefficients corresponding to each unsteady wake pattern was given.展开更多
We construct a new stabilized finite volume method on rectangular grids for the Stokes equations. The lowest equal-order conforming finite element pair （piecewise bilinear veloc- ities and pressures） and piecewise c...We construct a new stabilized finite volume method on rectangular grids for the Stokes equations. The lowest equal-order conforming finite element pair （piecewise bilinear veloc- ities and pressures） and piecewise constant test spaces for both the velocity and pressure are employed in this method. We show the stability of this method and prove first optimal rate of convergence for the velocity in the H1 norm and the pressure in the L2 norm. In addition, a second order optimal error estimate for the velocity in the L2 norm is derived. Numerical experiments illustrating the theoretical results are included.展开更多
基金the National Natural Science Foundation of China (Grant Nos. 10432020 and 10602056)the Fund for Foreign Scholars in University Research and Teaching programs (Grant No. B07033).
文摘A flow past two side-by-side identical circular cylinders was numerically investigated with the unstructured spectral element method. From the computational results at various non-dimensional distances between cylinder centers T/D and the Reynolds number Re, a total of nine kinds of wake patterns were observed： four steady wake patterns, including single bluff-body steady pattern, separated double-body steady pattern and transition steady pattern for sub-critical Reynolds numbers and biased steady pattern for super-critical Reynolds numbers, and five unsteady wake patterns, including single bluff-body periodic pattern, biased quasi-steady pattern, quasi-periodic （flip-flopping） pattern, in-phase-synchronized pattern and anti-phase-synchronized pattern. Time evolution of lift and drag coefficients corresponding to each unsteady wake pattern was given.
文摘We construct a new stabilized finite volume method on rectangular grids for the Stokes equations. The lowest equal-order conforming finite element pair （piecewise bilinear veloc- ities and pressures） and piecewise constant test spaces for both the velocity and pressure are employed in this method. We show the stability of this method and prove first optimal rate of convergence for the velocity in the H1 norm and the pressure in the L2 norm. In addition, a second order optimal error estimate for the velocity in the L2 norm is derived. Numerical experiments illustrating the theoretical results are included.
