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
The present study develops implicit physical domain-based discontinuous Galerkin(DG)methods for efficient scale-resolving simulations on mixed-curved meshes.Implicit methods are essential to handle stiff systems in ma...The present study develops implicit physical domain-based discontinuous Galerkin(DG)methods for efficient scale-resolving simulations on mixed-curved meshes.Implicit methods are essential to handle stiff systems in many scale-resolving simulations of interests in computational science and engineering.The physical domain-based DGmethod can achieve high-order accuracy using the optimal bases set and preserve the required accuracy on non-affinemeshes.When using the quadraturebased DG method,these advantages are overshadowed by severe computational costs on mixed-curved meshes,making implicit scale-resolving simulations unaffordable.To address this issue,the quadrature-free direct reconstruction method(DRM)is extended to the implicit DG method.In this approach,the generalized reconstruction approximates non-linear flux functions directly in the physical domain,making the computing-intensive numerical integrations precomputable at a preprocessing step.The DRM operator is applied to the residual computation in the matrix-free method.The DRM operator can be further extended to the system matrix computation for the matrix-explicit Krylov subspace method and preconditioning.Finally,the A-stable Rosenbrock-type Runge–Kutta methods are adopted to achieve high-order accuracy in time.Extensive verification and validation from the manufactured solution to implicit large eddy simulations are conducted.The computed results confirm that the proposed method significantly improves computational efficiency compared to the quadrature-based method while accurately resolving detailed unsteady flow features that are hardly captured by scale-modeled simulations.展开更多
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
A discontinuous Galerkin method based on an artificial viscosity model is investigated in the context of the simulation of compressible turbulence. The effects of artificial viscosity on shock capturing ability, broad...A discontinuous Galerkin method based on an artificial viscosity model is investigated in the context of the simulation of compressible turbulence. The effects of artificial viscosity on shock capturing ability, broadband accuracy and under-resolved instability are examined combined with various orders and mesh resolutions. For shock-dominated flows, the superior accuracy of high order methods in terms of discontinuity resolution are well retained compared with lower ones. For under-resolved simulations, the artificial viscosity model is able to enhance stability of the eighth order discontinuous Galerkin method despite of detrimental influence for accuracy. For multi-scale flows, the artificial viscosity model demonstrates biased numerical dissipation towards higher wavenumbers. Capability in terms of boundary layer flows and hybrid meshes is also demonstrated.It is concluded that the fourth order artificial viscosity discontinuous Galerkin method is comparable to typical high order finite difference methods in the literature in terms of accuracy for identical number of degrees of freedom, while the eighth order is significantly better unless the under-resolved instability issue is raised. Furthermore, the artificial viscosity discontinuous Galerkin method is shown to provide appropriate numerical dissipation as compensation for turbulent kinetic energy decaying on moderately coarse meshes, indicating good potentiality for implicit large eddy simulation.展开更多
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.
基金the financial support provided by the Defense Acquisition Program Administration(DAPA)under Grant UD200046CD(Data-driven Flow Modeling Research Laboratory)the Korea Research Institute for defense Technology planning and advancement(KRIT)under Grant KRIT-CT-22-030(Reusable Unmanned Space Vehicle Research Center,2023)supported by the program of the National Research Foundation of Korea(NRF-2021R1A2C2008348).
文摘The present study develops implicit physical domain-based discontinuous Galerkin(DG)methods for efficient scale-resolving simulations on mixed-curved meshes.Implicit methods are essential to handle stiff systems in many scale-resolving simulations of interests in computational science and engineering.The physical domain-based DGmethod can achieve high-order accuracy using the optimal bases set and preserve the required accuracy on non-affinemeshes.When using the quadraturebased DG method,these advantages are overshadowed by severe computational costs on mixed-curved meshes,making implicit scale-resolving simulations unaffordable.To address this issue,the quadrature-free direct reconstruction method(DRM)is extended to the implicit DG method.In this approach,the generalized reconstruction approximates non-linear flux functions directly in the physical domain,making the computing-intensive numerical integrations precomputable at a preprocessing step.The DRM operator is applied to the residual computation in the matrix-free method.The DRM operator can be further extended to the system matrix computation for the matrix-explicit Krylov subspace method and preconditioning.Finally,the A-stable Rosenbrock-type Runge–Kutta methods are adopted to achieve high-order accuracy in time.Extensive verification and validation from the manufactured solution to implicit large eddy simulations are conducted.The computed results confirm that the proposed method significantly improves computational efficiency compared to the quadrature-based method while accurately resolving detailed unsteady flow features that are hardly captured by scale-modeled simulations.
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supported by the National Natural Science Foundation of China(Grant No.11402016)the Fundamental Research Funds for the Central Universities(Grant Nos.50100002014105020&50100002015105033)
文摘A discontinuous Galerkin method based on an artificial viscosity model is investigated in the context of the simulation of compressible turbulence. The effects of artificial viscosity on shock capturing ability, broadband accuracy and under-resolved instability are examined combined with various orders and mesh resolutions. For shock-dominated flows, the superior accuracy of high order methods in terms of discontinuity resolution are well retained compared with lower ones. For under-resolved simulations, the artificial viscosity model is able to enhance stability of the eighth order discontinuous Galerkin method despite of detrimental influence for accuracy. For multi-scale flows, the artificial viscosity model demonstrates biased numerical dissipation towards higher wavenumbers. Capability in terms of boundary layer flows and hybrid meshes is also demonstrated.It is concluded that the fourth order artificial viscosity discontinuous Galerkin method is comparable to typical high order finite difference methods in the literature in terms of accuracy for identical number of degrees of freedom, while the eighth order is significantly better unless the under-resolved instability issue is raised. Furthermore, the artificial viscosity discontinuous Galerkin method is shown to provide appropriate numerical dissipation as compensation for turbulent kinetic energy decaying on moderately coarse meshes, indicating good potentiality for implicit large eddy simulation.
