A hierarchy of low-dimensional Galerkin models is proposed for the viscous, incompressible flow around a circular cylinder building on the pioneering works of Stuart (1958), Deane et al. (1991), and Ma & Karniadakis (2002). The empirical Galerkin model is based on an eight-dimensional Karhunen–Loeve decomposition of a numerical simulation and incorporates a new ‘shift-mode’ representing the mean-field correction. The inclusion of the shift-mode significantly improves the resolution of the transient dynamics from the onset of vortex shedding to the periodic von Karman vortex street. In addition, the Reynolds-number dependence of the flow can be described with good accuracy. The inclusion of stability eigenmodes further enhances the accuracy of fluctuation dynamics. Mathematical and physical system reduction approaches lead to invariant-manifold and to mean-field models, respectively. The corresponding two-dimensional dynamical systems are further reduced to the Landau amplitude equation.

/pdf/a-hierarchy-of-low-dimensional-models-for-the-transient-and-mndofad8te.pdf

A hierarchy of low-dimensional models for the transient and post-transient cylinder wake

An efficient ghost-cell immersed boundary method (GCIBM) for simulating turbulent flows in complex geometries is presented. A boundary condition is enforced through a ghost cell method. The reconstruction procedure allows systematic development of numerical schemes for treating the immersed boundary while preserving the overall second-order accuracy of the base solver. Both Dirichlet and Neumann boundary conditions can be treated. The current ghost cell treatment is both suitable for staggered and non-staggered Cartesian grids. The accuracy of the current method is validated using flow past a circular cylinder and large eddy simulation of turbulent flow over a wavy surface. Numerical results are compared with experimental data and boundary-fitted grid results. The method is further extended to an existing ocean model (MITGCM) to simulate geophysical flow over a three-dimensional bump. The method is easily implemented as evidenced by our use of several existing codes.

A Ghost-Cell Immersed Boundary Method for Flow in Complex Geometry

The interactions between incompressible fluid flows and immersed struc- tures are nonlinear multi-physics phenomena that have applications to a wide range of scientific and engineering disciplines In this article, we review representative numeri- cal methods based onconforming and non-conforming meshes that arecurrentlyavail- able for computing fluid-structure interaction problems, with an emphasis on some of the recent developments in the field A goal is to categorize the selected methods and assess their accuracy and efficiency We discuss challenges faced by researchers in this field, and we emphasize the importance of interdisciplinary effort for advancing the study in fluid-structure interactions

/pdf/numerical-methods-for-fluid-structure-interaction-a-review-2raeajc0ja.pdf

Numerical Methods for Fluid-Structure Interaction — A Review

http://croccolab.umd.edu/publications/journal-docs/06-MartinTaylorWuWeirs_JCP06_vol220_no1.pdf

A bandwidth-optimized WENO scheme for the effective direct numerical simulation of compressible turbulence

Curvilinear immersed boundary method for simulating fluid structure interaction with complex 3D rigid bodies

http://faculty.smu.edu/sxu/publications/2006_JCP_Xu_Wang.pdf

An immersed interface method for simulating the interaction of a fluid with moving boundaries

A description of different inflow methodologies for turbulent boundary layers, including validity and limitations, is presented. We show that the use of genuine periodic boundary conditions, in which no alteration of the governing equations is made, results in growing mean flow and decaying turbulence. Premises under which the usage is valid are presented and explained, and comparisons with the extended temporal approach [T. Maeder, N. A. Adams, and L. Kleiser, “Direct simulation of turbulent supersonic boundary layers by an extended temporal approach,” J. Fluid Mech. 429, 187 (2001)] are used to assess the validity. Extending the work by Lund et al. [J. Comput. Phys. 140, 233 (1998)], we propose an inflow generation method for spatial simulations of compressible turbulent boundary layers. The method generates inflow by reintroducing a rescaled downstream flow field to the inlet of a computational domain. The rescaling is based on Morkovin’s hypothesis [P. Bradshaw, “Compressible turbulent shear layers,” Annu. Rev. Fluid Mech. 9, 33 (1977)] and generalized temperature–velocity relationships. This method is different from other existing rescaling techniques [S. Stolz and N. A. Adams, “Large-eddy simulation of high-Reynolds-number supersonic boundary layers using the approximate deconvolution model and a rescaling and recycling technique,” Phys. Fluids 15, 2398 (2003); G. Urbin and D. Knight, “Large-eddy simulation of a supersonic boundary layer using an unstructured grid,” AIAA J. 39, 1288 (2001)], in that a more consistent rescaling is employed for the mean and fluctuating thermodynamic variables. The results are compared against the well established van Driest II theory and indicate that the method is efficient and accurate.

http://faculty.smu.edu/sxu/publications/2004_POF_Xu_Martin.pdf

Assessment of inflow boundary conditions for compressible turbulent boundary layers

Wing pitch reversal, the rapid change of angle of attack near stroke transition, represents a difference between hovering with flapping wings and with a continuously rotating blade (e.g. helicopter flight). Although insects have the musculature to control the wing pitch during flight, we show here that aerodynamic and wing inertia forces are sufficient to pitch the wing without the aid of the muscles. We study the passive nature of wing pitching in several observed wing kinematics, including the wing motion of a tethered dragonfly, Libellula pulchella, hovering fruitfly, hovering hawkmoth and simplified dragonfly hovering kinematics. To determine whether the pitching is passive, we calculate rotational power about the torsion axis owing to aerodynamic and wing inertial forces. This is done using both direct numerical simulations and quasi-steady fluid force models. We find that, in all the cases studied here, the net rotational power is negative, signifying that the fluid force assists rather than resists the wing pitching. To further understand the generality of these results, we use the quasi-steady force model to analyse the effect of the components of the fluid forces at pitch reversal, and predict the conditions under which the wing pitch reversal is passive. These results suggest the pitching motion of the wings can be passive in insect flight.

Passive wing pitch reversal in insect flight

In this paper, we systematically derive jump conditions for the immersed interface method [SIAM J. Numer. Anal., 31 (1994), pp. 1019-1044; SIAM J. Sci. Comput., 18 (1997), pp. 709-735] to simulate three-dimensional incompressible viscous flows subject to moving surfaces. The surfaces are represented as singular forces in the Navier--Stokes equations, which give rise to discontinuities of flow quantities. The principal jump conditions across a closed surface of the velocity, the pressure, and their normal derivatives have been derived by Lai and Li [Appl. Math. Lett., 14 (2001), pp. 149-154]. In this paper, we first extend their derivation to generalized surface parametrization. Starting from the principal jump conditions, we then derive the jump conditions of all first-, second-, and third-order spatial derivatives of the velocity and the pressure. We also derive the jump conditions of first- and second-order temporal derivatives of the velocity. Using these jump conditions, the immersed interface method is applicable to the simulation of three-dimensional incompressible viscous flows subject to moving surfaces, where near the surfaces the first- and second-order spatial derivatives of the velocity and the pressure can be discretized with, respectively, third- and second-order accuracy, and the first-order temporal derivatives of the velocity can be discretized with second-order accuracy.

/pdf/systematic-derivation-of-jump-conditions-for-the-immersed-1dxpjnhgne.pdf

Systematic Derivation of Jump Conditions for the Immersed Interface Method in Three-Dimensional Flow Simulation

In this paper we present results from a numerical investigation of turbulent channel flow in the presence of a compliant wall. The compliant wall is modelled as a homogeneous spring-supported plate. The simulation code is validated both by comparison with an alternative code and by reproducing results of linear stability theory. Our results demonstrate that with the wall compliance we used in the simulation there is little change in the very long-time behaviour of the turbulent skin friction drag and little modification to the near-wall turbulent coherent structures. The values of pertinent statistical quantities of the turbulence near the compliant walls converge to those near a rigid wall and the statistical effect of the wall compliance on the turbulent channel flow is small.

http://faculty.smu.edu/sxu/publications/2003_JFM_Xu_Rempfer_Lumley.pdf

Sheng Xu

Papers

An immersed interface method for simulating the interaction of a fluid with moving boundaries

Assessment of inflow boundary conditions for compressible turbulent boundary layers

Passive wing pitch reversal in insect flight

Systematic Derivation of Jump Conditions for the Immersed Interface Method in Three-Dimensional Flow Simulation

Turbulence over a compliant surface: numerical simulation and analysis