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High Resolution Sharp Computational Methods for Elliptic and Parabolic Problems in Complex Geometries
, 2012
"... In honor of Stan Osher’s 70 th birthday We present a review of some of the stateoftheart numerical methods for solving the Stefan problem and the Poisson and the diffusion equations on irregular domains using (i) the levelset method for representing the (possibly moving) irregular domain’s bound ..."
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In honor of Stan Osher’s 70 th birthday We present a review of some of the stateoftheart numerical methods for solving the Stefan problem and the Poisson and the diffusion equations on irregular domains using (i) the levelset method for representing the (possibly moving) irregular domain’s boundary, (ii) the ghostfluid method for imposing the Dirichlet boundary condition at the irregular domain’s boundary and (iii) a quadtree/octree nodebased adaptive mesh refinement for capturing small length scales while significantly reducing the memory and CPU footprint. In addition, we highlight common misconceptions and describe how to properly implement these methods. Numerical experiments illustrate quantitative and qualitative results. 1
A FLUIDSTRUCTURE INTERACTION STRATEGY WITH APPLICATION TO LOW Reynolds Number Flapping Flight
, 2010
"... In this work a structured adaptive mesh refinement (SAMR) strategy for fluidstructure interaction (FSI) problems in laminar and turbulent incompressible flows is developed. The Eulerian computational grid consists of nested grid blocks at different refinement levels. The grid topology and datastr ..."
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In this work a structured adaptive mesh refinement (SAMR) strategy for fluidstructure interaction (FSI) problems in laminar and turbulent incompressible flows is developed. The Eulerian computational grid consists of nested grid blocks at different refinement levels. The grid topology and datastructure is managed by using the Paramesh toolkit. The filtered NavierStokes equations are evolved in time by means of an explicit secondorder projection scheme, where spatial derivatives are approximated with second order central differences on a staggered grid. The level of accuracy of the required variable interpolation operators is studied, and a novel divergencepreserving prolongation scheme for velocities is evolved. A novel directforcing embeddedboundary method is developed to enforce boundary conditions on a complex moving body not aligned with the grid lines. In this method, the imposition of noslip conditions on immersed bodies is done on the Lagrangian markers that represent their wet surfaces, and the resulting force is transferred to the surrounding Eulerian grid points by a moving least squares formulation. Report Documentation Page Form ApprovedOMB No. 07040188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information,
Numerical Simulation of Two Dimensional Complex Flows around Bluff Bodies Using the Immersed Boundary Method
"... This paper presents a twodimensional numerical simulation of flows around different bluff bodies, at Re = 100 and 200, using the Immersed Boundary (IB) method, as a sequence of a previous work. The force density term required by the IB method is obtained with the Virtual Physical Model (VPM). Simul ..."
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This paper presents a twodimensional numerical simulation of flows around different bluff bodies, at Re = 100 and 200, using the Immersed Boundary (IB) method, as a sequence of a previous work. The force density term required by the IB method is obtained with the Virtual Physical Model (VPM). Simulations were carried out for two circular cylinders of different diameter in tandem, two cylinders of the same diameter in tandem and two cylinders placed in side by side arrangement. The configurations of seven cylinders in a ‘V ’ arrangement, for angles of 40o ≤ α ≤ 180o, were also simulated. A configuration of 23 different bluff bodies, representing a transverse cut in a central tower of an offshore structure, has been also simulated and the results were compared with a single compact square, of equivalent size. The Strouhal number, the drag and the lift coefficients were also calculated. The Strouhal number is calculated using the Fast Fourier Transform (FFT) of the lift coefficient temporal distribution. Visualization of the vorticity and pressure fields and the streamlines are presented for each simulation showing the flow dynamics and patterns. It was possible to verify that the IB method with VPM is a powerful methodology to simulate flows in the presence of complex geometries.
Simulating cardiovascular fluid dynamics by the immersed boundary method
 in 47th AIAA Aerospace Sciences Meeting
, 2009
"... The immersed boundary method is both a general mathematical framework and a particular numerical approach to problems of fluidstructure interaction. In this paper, we describe the application of the immersed boundary method to the simulation of cardiovascular fluid dynamics, focusing on the fluid ..."
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The immersed boundary method is both a general mathematical framework and a particular numerical approach to problems of fluidstructure interaction. In this paper, we describe the application of the immersed boundary method to the simulation of cardiovascular fluid dynamics, focusing on the fluid dynamics of the aortic heart valve (the valve which prevents the backflow of blood from the aorta into the left ventricle of the heart) and aortic root (the initial portion of the aorta, which attaches to the heart). The aortic valve and root are modeled as a system of elastic fibers, and the blood is modeled as a viscous incompressible fluid. Threedimensional simulation results obtained using a parallel and adaptive version of the immersed boundary method are presented. These results demonstrate that it is feasible to perform threedimensional immersed boundary simulations of cardiovascular fluid dynamics in which realistic cardiac output is obtained at realistic pressures. Nomenclature U physical domain x = (x, y, z) ∈ U Cartesian (physical) coordinates u(x, t) fluid velocity p(x, t) fluid pressure f(x, t) Eulerian force density applied by the structure to the fluid δ(x) = δ(x) δ(y) δ(z) threedimensional Dirac delta function δh(x) = δh(x) δh(y) δh(z) threedimensional regularized Dirac delta function Ω Lagrangian coordinate domain (q, r, s) ∈ Ω Lagrangian (material) coordinates X(q, r, s, t) physical position of Lagrangian (material) point (q, r, s) at time t F(q, r, s, t) Lagrangian force density applied by the structure to the fluid I.
Unconditionally Energy Stable Immersed Boundary Method with Application to Vesicle Dynamics
"... Abstract. We develop an unconditionally energy stable immersed boundary method, and apply it to simulate 2D vesicle dynamics. We adopt a semiimplicit boundary forcing approach, where the stretching factor used in the forcing term can be computed from the derived evolutional equation. By using the p ..."
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Abstract. We develop an unconditionally energy stable immersed boundary method, and apply it to simulate 2D vesicle dynamics. We adopt a semiimplicit boundary forcing approach, where the stretching factor used in the forcing term can be computed from the derived evolutional equation. By using the projection method to solve the fluid equations, the pressure is decoupled and we have a symmetric positive definite system that can be solved efficiently. The method can be shown to be unconditionally stable, in the sense that the total energy is decreasing. A resulting modification benefits from this improved numerical stability, as the time step size can be significantly increased (the severe time step restriction in an explicit boundary forcing scheme is avoided). As an application, we use our scheme to simulate vesicle dynamics in NavierStokes flow.
ADAPTIVE NUMERICAL SIMULATIONS OF A TURBULENT JET
"... Abstract. This work is concerned with assessing the performance of a numerical method, which combines an adaptive mesh refinement technique, an implicitexplicit time stepping strategy, and a linear multilevelmultigrid methodology, when applied to a challenging reallife problem: a threedimensiona ..."
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Abstract. This work is concerned with assessing the performance of a numerical method, which combines an adaptive mesh refinement technique, an implicitexplicit time stepping strategy, and a linear multilevelmultigrid methodology, when applied to a challenging reallife problem: a threedimensional turbulent jet flow. Typically, whenever a moving fluid emerges from a narrow opening into an otherwise quiescent fluid, shear is created between the entering and the ambient fluids, causing fluid instabilities, turbulence, and mixing at downstream. Turbulent jets represent an important class of fluid flow phenomena which occurs in many instances both in environmental and in industrial applications such as waste water discharges into rivers, plumes from smokestacks, and flames on combustion nozzles. Mathematically, the fluid dynamics is modeled by the nonsteady NavierStokes equations for a threedimensional incompressible flow whose material properties vary. The turbulence modeling is given by the large eddy simulation approach for which a careful selection of the Smagorinsky constant is performed. To resolve accurately and efficiently sharp gradients, vorticity shedding, and localized small length scale flow features (e.g. the ones present in high turbulence regions), dynamic adaptive mesh refinements are employed which form a
unknown title
, 2014
"... doi:10.1093/imamat/hxu029 Dynamic finitestrain modelling of the human left ventricle in health and disease using an immersed boundaryfinite element method ..."
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doi:10.1093/imamat/hxu029 Dynamic finitestrain modelling of the human left ventricle in health and disease using an immersed boundaryfinite element method
Numerical Study of Stability and Accuracy of the Immersed Boundary Method Coupled to the Lattice Boltzmann BGKModel
, 2014
"... Abstract. This paper aims to study the numerical features of a coupling scheme between the immersed boundary (IB) method and the lattice Boltzmann BGK (LBGK) model by four typical test problems: the relaxation of a circular membrane, the shearing flow induced by a moving fiber in the middle of a c ..."
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Abstract. This paper aims to study the numerical features of a coupling scheme between the immersed boundary (IB) method and the lattice Boltzmann BGK (LBGK) model by four typical test problems: the relaxation of a circular membrane, the shearing flow induced by a moving fiber in the middle of a channel, the shearing flow near a nonslip rigid wall, and the circular Couette flow between two inversely rotating cylinders. The accuracy and robustness of the IBLBGK coupling scheme, the performances of different discrete Dirac delta functions, the effect of iteration on the coupling scheme, the importance of the external forcing term treatment, the sensitivity of the coupling scheme to flow and boundary parameters, the velocity slip near nonslip rigid wall, and the origination of numerical instabilities are investigated in detail via the four test cases. It is found that the iteration in the coupling cycle can effectively improve stability, the introduction of a secondorder forcing term in LBGK model is crucial, the discrete fiber segment length and the orientation of the fiber boundary obviously affect accuracy and stability, and the emergence of both temporal and spatial fluctuations of boundary parameters seems to be the indication of numerical instabil