The spectral/hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomia...The spectral/hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials,modified to accommodate a C~0-continuous expansion. Computationally and theoretically, by increasing the polynomial order p,high-precision solutions and fast convergence can be obtained and, in particular, under certain regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/hp element method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use of the spectral/hp element method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/hp element method in more complex science and engineering applications are discussed.展开更多
The present paper focuses on the erosive cavitation behavior around a plane convex hydrofoil. The Zwart-Gerber-Belamri cavitation model is implemented in a library form to be used with the OpenFOAM. The implicit large...The present paper focuses on the erosive cavitation behavior around a plane convex hydrofoil. The Zwart-Gerber-Belamri cavitation model is implemented in a library form to be used with the OpenFOAM. The implicit large eddy simulation （ILES） is app- lied to analyze the three-dimensional unsteady cavitating flow around a plane convex hydrofoil. The numerical results in the cases under the hydrodynamic conditions, which were experimentally tested at the high speed cavitation tunnel of the l^cole Polytechnique F6d＆ale de Lausanne （EPFL）, clearly show the sheet cavitation development, the shedding and the collapse of vapor clouds. It is noted that the cavitation evolutions including the maximum vapor length, the detachment and the oscillation frequency, are captured fairly well. Furthermore, the pressure pulses due to the cavitation development as well as the complex vortex structures are reasona- bly well predicted. Consequently, it may be concluded that the present numerical method can be used to investigate the unsteady cavitation around hydrofoils with a satisfactory accuracy.展开更多
文摘The spectral/hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials,modified to accommodate a C~0-continuous expansion. Computationally and theoretically, by increasing the polynomial order p,high-precision solutions and fast convergence can be obtained and, in particular, under certain regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/hp element method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use of the spectral/hp element method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/hp element method in more complex science and engineering applications are discussed.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.51306018,51536008 and 51179091)
文摘The present paper focuses on the erosive cavitation behavior around a plane convex hydrofoil. The Zwart-Gerber-Belamri cavitation model is implemented in a library form to be used with the OpenFOAM. The implicit large eddy simulation （ILES） is app- lied to analyze the three-dimensional unsteady cavitating flow around a plane convex hydrofoil. The numerical results in the cases under the hydrodynamic conditions, which were experimentally tested at the high speed cavitation tunnel of the l^cole Polytechnique F6d＆ale de Lausanne （EPFL）, clearly show the sheet cavitation development, the shedding and the collapse of vapor clouds. It is noted that the cavitation evolutions including the maximum vapor length, the detachment and the oscillation frequency, are captured fairly well. Furthermore, the pressure pulses due to the cavitation development as well as the complex vortex structures are reasona- bly well predicted. Consequently, it may be concluded that the present numerical method can be used to investigate the unsteady cavitation around hydrofoils with a satisfactory accuracy.
