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66
A fast variational framework for accurate solid-fluid coupling
- ACM Trans. Graph
, 2007
"... Figure 1: Left: A solid stirring smoke runs at interactive rates, two orders of magnitude faster than previously. Middle: Fully coupled rigid bodies of widely varying density, with flow visualized by marker particles. Right: Interactive manipulation of immersed rigid bodies. Physical simulation has ..."
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Cited by 75 (4 self)
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Figure 1: Left: A solid stirring smoke runs at interactive rates, two orders of magnitude faster than previously. Middle: Fully coupled rigid bodies of widely varying density, with flow visualized by marker particles. Right: Interactive manipulation of immersed rigid bodies. Physical simulation has emerged as a compelling animation tech-nique, yet current approaches to coupling simulations of fluids and solids with irregular boundary geometry are inefficient or cannot handle some relevant scenarios robustly. We propose a new varia-tional approach which allows robust and accurate solution on rela-tively coarse Cartesian grids, allowing possibly orders of magnitude faster simulation. By rephrasing the classical pressure projection step as a kinetic energy minimization, broadly similar to modern approaches to rigid body contact, we permit a robust coupling be-tween fluid and arbitrary solid simulations that always gives a well-posed symmetric positive semi-definite linear system. We provide several examples of efficient fluid-solid interaction and rigid body coupling with sub-grid cell flow. In addition, we extend the frame-work with a new boundary condition for free-surface flow, allowing fluid to separate naturally from solids.
An immersed interface method for viscous incompressible flows involving rigid and flexible boundaries
- J. Comp. Phys
, 2006
"... We present an immersed interface method for the incompressible Navier-Stokes equations capable of handling rigid immersed boundaries. The immersed boundary is represented by a set of Lagrangian control points. In order to guarantee that the no-slip condition on the boundary is satisfied, singular fo ..."
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Cited by 37 (3 self)
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We present an immersed interface method for the incompressible Navier-Stokes equations capable of handling rigid immersed boundaries. The immersed boundary is represented by a set of Lagrangian control points. In order to guarantee that the no-slip condition on the boundary is satisfied, singular forces are applied on the fluid. The forces are related to the jumps in pressure and the jumps in the derivatives of both pressure and velocity, and are interpolated using cubic splines. The strength of the singular forces is determined by solving a small system of equations iteratively at each time step. The Navier-Stokes equations are discretized on a staggered Cartesian grid by a second order accurate projection method for pressure and velocity. Keywords: Immersed interface method, Navier-Stokes equations, Cartesian grid method, finite difference, fast Poisson solvers, irregular domains.
Wake topology and hydrodynamic performance of low-aspect-ratio flapping foils
- J. Fluid Mech
, 2006
"... Numerical simulations are used to investigate the effect of aspect ratio on the wake topology and hydrodynamic performance of thin ellipsoidal flapping foils. The study is motivated by the quest to understand the hydrodynamics of fish pectoral fins. The simulations employ an immersed boundary method ..."
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Cited by 21 (2 self)
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Numerical simulations are used to investigate the effect of aspect ratio on the wake topology and hydrodynamic performance of thin ellipsoidal flapping foils. The study is motivated by the quest to understand the hydrodynamics of fish pectoral fins. The simulations employ an immersed boundary method that allows us to simulate flows with complex moving boundaries on fixed Cartesian grids. A detailed analysis of the vortex topology shows that the wake of low-aspect-ratio flapping foils is dominated by two sets of interconnected vortex loops that evolve into distinct vortex rings as they convect downstream. The flow downstream of these flapping foils is characterized by two oblique jets and the implications of this characteristic on the hydrodynamic performance are examined. Simulations are also used to examine the thrust and propulsive efficiency of these foils over a range of Strouhal and Reynolds numbers as well as pitch-bias angles. 1.
Numerical Methods for Fluid-Structure Interaction -- A Review
, 2012
"... 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 numerical methods based on conforming and non-conforming me ..."
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Cited by 21 (0 self)
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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 numerical methods based on conforming and non-conforming meshes that are currently avail-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.
Formation criterion for synthetic jets
- AIAA journal
"... A formation criterion for synthetic jets is proposed and validated. A synthetic jet actuator is a zero-net mass-flux device that imparts momentum to its surroundings. Jet formation is defined as the appearance of a time-averaged outward velocity along the jet axis and corresponds to the generation a ..."
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Cited by 20 (2 self)
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A formation criterion for synthetic jets is proposed and validated. A synthetic jet actuator is a zero-net mass-flux device that imparts momentum to its surroundings. Jet formation is defined as the appearance of a time-averaged outward velocity along the jet axis and corresponds to the generation and subsequent convection or escape of a vortex ring. It is shown that over a wide range of operating conditions synthetic jet formation is governed by the jet Strouhal number Sr (or Reynolds number Re and Stokes number S). Both numerical simulations and experiments are performed to supplement available two-dimensional and axisymmetric synthetic jet formation data in the literature. The data support the jet formation criterion 1/Sr = Re/S2> K, where the constant K is approximately 1 and 0.16 for two-dimensional and axisymmetric synthetic jets, respectively. In addition, the dependence of the constant K on the normalized radius of curvature of a rounded orifice or slot is addressed. The criterion is expected to serve as a useful design guide for synthetic jet formation in flow control, heat transfer, and acoustic liner applications, in which a stronger jet is synonymous with increased momentum transfer, vorticity generation, and acoustic nonlinearities. I.
A representation of curved boundaries for the solution of the Navier–Stokes equations on a staggered three-dimensional Cartesian grid
, 2003
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A new high-order immersed interface method for solving elliptic equations with imbedded interface of discontinuity
- J. Comput. Phys
, 2007
"... Abstract This paper presents a new high-order immersed interface method for elliptic equations with imbedded interface of discontinuity. Compared with the original second-order immersed interface method of [R.J. LeVeque, Z. Li. The immersed interface method for elliptic equations with discontinuous ..."
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Cited by 13 (1 self)
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Abstract This paper presents a new high-order immersed interface method for elliptic equations with imbedded interface of discontinuity. Compared with the original second-order immersed interface method of [R.J. LeVeque, Z. Li. The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J. Numer. Anal. 31 (1994) 1001-25], the new method achieves arbitrarily high-order accuracy for derivatives at an irregular grid point by imposing only two physical jump conditions together with a wider set of grid stencils. The new interface difference formulas are expressed in a general explicit form so that they can be applied to different multi-dimensional problems without any modification. The new interface algorithms of up to O(h 4 ) accuracy have been derived and tested on several one and twodimensional elliptic equations with imbedded interface. Compared to the standard second-order immersed interface method, the test results show that the new fourth-order immersed interface method leads to a significant improvement in accuracy of the numerical solutions. The proposed method has potential advantages in the application to two-phase flow because of its high-order accuracy and simplicity in applications.
Systematic derivation of jump conditions for the immersed interface method in three-dimensional flow simulation
- SIAM J. Sci. Comput
"... Abstract. In this paper, we systematically derive jump conditions for the immersed interface ..."
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Cited by 12 (3 self)
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Abstract. In this paper, we systematically derive jump conditions for the immersed interface
An embedded boundary method for the Navier-Stokes equations on a time-dependent domain
- Comm. App. Math. Comp. Sci
"... mathematical sciences publishersCOMM. APP. MATH. AND COMP. SCI. ..."
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Cited by 4 (0 self)
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mathematical sciences publishersCOMM. APP. MATH. AND COMP. SCI.
