Modeling Arteriolar Flow and Mass Transport Using the Immersed Boundary Method

Arthurs, Kayne M.; Moore, Leon C.; Peskin, Charles S.; Pitman, E. Bruce; Layton, Harold E.

doi:10.1006/jcph.1998.6097

Cited by 84 publications

(71 citation statements)

References 30 publications

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“…The distribution of shear stress in the beam has a parabolic shape along the transverse direction, having a maximum shear stress at the center and zero values on the upper and lower surfaces [41]. The maximum shear stress per unit width is calculated as (24) The maximum shear stress at the center is 32 g·cm −1 ·s −2 in the simulated result, which agrees with the analytical solution of 34 g·cm −1 ·s −2 calculated by Eq. (24).…”

Section: Flow-induced Vibration Of An Elastic Platesupporting

confidence: 73%

“…It has widespread applications in diverse fields such as deformation of artificial lung [6], analyses of industrial applications [19], aeroelastic analysis [16,20], wind response of buildings and structures [21], blood flow in veins and arteries [22][23][24], heart valves dynamics [25], and airflow in collapsible airways [26]. However, an accurate and efficient computational model for this problem still poses a great challenge, which is often aggravated by large deformations and complex geometries of the closely coupled fluid-structure system.…”

Section: Introductionmentioning

confidence: 99%

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An unstructured finite volume approach for structural dynamics in response to fluid motions

Xia

Lin

2008

Computers & Structures

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A new cell-vortex unstructured finite volume method for structural dynamics is assessed for simulations of structural dynamics in response to fluid motions. A robust implicit dual-time stepping method is employed to obtain time accurate solutions. The resulting system of algebraic equations is matrix-free and allows solid elements to include structure thickness, inertia, and structural stresses for accurate predictions of structural responses and stress distributions. The method is coupled with a fluid dynamics solver for fluid-structure interaction, providing a viable alternative to the finite element method for structural dynamics calculations. A mesh sensitivity test indicates that the finite volume method is at least of second-order accuracy. The method is validated by the problem of vortex-induced vibration of an elastic plate with different initial conditions and material properties. The results are in good agreement with existing numerical data and analytical solutions. The method is then applied to simulate a channel flow with an elastic wall. The effects of wall inertia and structural stresses on the fluid flow are investigated.

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Section: Flow-induced Vibration Of An Elastic Platesupporting

confidence: 73%

Section: Introductionmentioning

confidence: 99%

An unstructured finite volume approach for structural dynamics in response to fluid motions

Xia

Lin

2008

Computers & Structures

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“…The interaction between the fluid and immersed boundary can be modeled by a well chosen discretized approximation to the Dirac delta function, which is called a discrete delta function. This approach has been applied successfully to problems of blood flow pattern in the heart [20][21][22][23][24], wave propagation in the cochlea [3,12], flow in collapsible tubes [27], aquatic animal locomotion [7][8][9], platelet aggregation during blood clotting [8,11], the flow of suspensions [10,30], flow and transport in a renal arteriole [1], and the cell and tissue deformation under shear flow [4,6,29].…”

Section: Introductionmentioning

confidence: 99%

An Immersed Boundary Method with Formal Second-Order Accuracy and Reduced Numerical Viscosity

Lai

Peskin

2000

Journal of Computational Physics

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780

508

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A formally second-order accurate immersed boundary method is presented and tested in this paper. We apply this new scheme to simulate the flow past a circular cylinder and study the effect of numerical viscosity on the accuracy of the computation by comparing the numerical results with those of a first-order method. The numerical evidence shows that the new scheme has less numerical viscosity and is therefore a better choice for the simulation of high Reynolds number flows with immersed boundaries.

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“…The central idea of the IB method is that the Navier-Stokes solver does not need to know anything about the complicated time-dependent geometry of the elastic boundary, and that therefore we can escape from the difficulties caused by the interaction between the elastic boundary and the fluid flow. This whole approach has been applied successfully to problems of blood flow in the heart [18,[20][21][22][23]25], wave propagation in the cochlea [3,6], platelet aggregation during blood clotting [5], and several other problems [2,8,9,11,13].…”

Section: Introductionmentioning

confidence: 99%

Penalty immersed boundary method for an elastic boundary with mass

2007

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The immersed boundary (IB) method has been widely applied to problems involving a moving elastic boundary that is immersed in fluid and interacting with it. But most of the previous applications of the IB method have involved a massless elastic boundary and used efficient Fourier transform methods for the numerical solutions.Extending the method to cover the case of a massive boundary has required spreading the boundary mass out onto the fluid grid and then solving the Navier-Stokes equations with a variable mass density. The variable mass density of this previous approach makes Fourier transform methods inapplicable, and requires a multigrid solver. Here we propose a new and simple way to give mass to the elastic boundary and show that the new method can be applied to many problems for which the boundary mass is important. The new method does not spread mass to the fluid grid, retains the use of Fourier transform methodology, and is easy to implement in the context of an existing IB method code for the massless case.

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Modeling Arteriolar Flow and Mass Transport Using the Immersed Boundary Method

Cited by 84 publications

References 30 publications

An unstructured finite volume approach for structural dynamics in response to fluid motions

An unstructured finite volume approach for structural dynamics in response to fluid motions

An Immersed Boundary Method with Formal Second-Order Accuracy and Reduced Numerical Viscosity

Penalty immersed boundary method for an elastic boundary with mass

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