Estimation of Element-Based Zero-Stress State in Arterial FSI Computations with Isogeometric Wall Discretization

Takizawa, Kenji; Tezduyar, Tayfun E.; Sasaki, Takafumi

doi:10.1007/978-3-319-59548-1_7

Cited by 36 publications

(26 citation statements)

References 58 publications

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“…115,116 The imagebased arterial geometries used in patient-specific arterial FSI computations do not come from the zero-stress state (ZSS) of the artery. A number of methods 20,22,[121][122][123][124][125][126][127][128][129][130] have been proposed for estimating the ZSS required in the computations. Using IGA basis functions in space is now a key part of some of the newest ZSS estimation methods [128][129][130] and related shell analysis.…”

Section: St-igamentioning

confidence: 99%

Space–time Isogeometric flow analysis with built-in Reynolds-equation limit

Kuraishi

Takizawa

Tezduyar

2019

Math. Models Methods Appl. Sci.

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We present a space–time (ST) computational flow analysis method with built-in Reynolds-equation limit. The method enables solution of lubrication fluid dynamics problems with a computational cost comparable to that of the Reynolds-equation model for the comparable solution quality, but with the computational flexibility to go beyond the limitations of the Reynolds-equation model. The key components of the method are the ST Variational Multiscale (ST-VMS) method, ST Isogeometric Analysis (ST-IGA), and the ST Slip Interface (ST-SI) method. The VMS feature of the ST-VMS serves as a numerical stabilization method with a good track record, the moving-mesh feature of the ST framework enables high-resolution flow computation near the moving fluid–solid interfaces, and the higher-order accuracy of the ST framework strengthens both features. The ST-IGA enables more accurate representation of the solid-surface geometries and increased accuracy in the flow solution in general. With the ST-IGA, even with just one quadratic NURBS element across the gap of the lubrication fluid dynamics problem, we reach a solution quality comparable to that of the Reynolds-equation model. The ST-SI enables moving-mesh computation when the spinning solid surface is noncircular. The mesh covering the solid surface spins with it, retaining the high-resolution representation of the flow near the surface, and the SI between the spinning mesh and the rest of the mesh accurately connects the two sides of the solution. We present detailed 2D test computations to show how the method performs compared to the Reynolds-equation model, compared to finite element discretization, at different circumferential and normal mesh refinement levels, when there is an SI in the mesh, and when the no-slip boundary conditions are weakly-enforced.

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Section: St-igamentioning

confidence: 99%

Space–time Isogeometric flow analysis with built-in Reynolds-equation limit

Kuraishi

Takizawa

Tezduyar

2019

Math. Models Methods Appl. Sci.

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“…It has been used in ST computational flow analysis of turbocharger turbines, [123][124][125][126] flow-driven string dynamics in turbomachinery, 121,122 ram-air parachutes, 132 spacecraft parachutes, 134 aortas, [111][112][113] heart valves, 116,117,111,113 tires with road contact and deformation, [128][129][130] and fluid films. 131,130 Using IGA basis functions in space is now a key part of some of the newest arterial zero-stress-state estimation methods [138][139][140][141]113 and related shell analysis. 142…”

Section: St Isogeometric Analysismentioning

confidence: 99%

A node-numbering-invariant directional length scale for simplex elements

Takizawa

Ueda

Tezduyar

2019

Math. Models Methods Appl. Sci.

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Variational multiscale methods, and their precursors, stabilized methods, have been very popular in flow computations in the past several decades. Stabilization parameters embedded in most of these methods play a significant role. The parameters almost always involve element length scales, most of the time in specific directions, such as the direction of the flow or solution gradient. We require the length scales, including the directional length scales, to have node-numbering invariance for all element types, including simplex elements. We propose a length scale expression meeting that requirement. We analytically evaluate the expression in the context of simplex elements and compared to one of the most widely used length scale expressions and show the levels of noninvariance avoided.

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“…The version of the EBZSS estimation method with isogeometric wall discretization, using NURBS basis functions, was introduced in [68]. With isogeometric discretization, we can obtain the element-based mapping directly, instead of extracting it from the mapping between the artery and straight-tube segments.…”

mentioning

confidence: 99%

“…With NURBS basis functions, we may be able to achieve a similar level of accuracy as with the linear basis functions, but using larger-size and fewer elements, and the NURBS basis functions enable representation of more complex shapes within an element. The 2D test computations with straight-tube configurations presented in [68] showed how the EBZSS estimation method with NURBS discretization works. In [69], which is an expanded, journal version of [68], how the method can be used in a 3D computation where the target geometry is coming from medical image of a human aorta was also shown.…”

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Medical-image-based aorta modeling with zero-stress-state estimation

2019

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Because the medical-image-based geometries used in patient-specific arterial fluid-structure interaction computations do not come from the zero-stress state (ZSS) of the artery, we need to estimate the ZSS required in the computations. The task becomes even more challenging for arteries with complex geometries, such as the aorta. In a method we introduced earlier the estimate is based on T-spline discretization of the arterial wall and is in the form of integration-point-based ZSS (IPBZSS). The T-spline discretization enables dealing with complex arterial geometries, such as an aorta model with branches, while retaining the desirable features of isogeometric discretization. With higher-order basis functions of the isogeometric discretization, we may be able to achieve a similar level of accuracy as with the linear basis functions, but using larger-size and fewer elements. In addition, the higher-order basis functions allow representation of more complex shapes within an element. The IPBZSS is a convenient representation of the ZSS because with isogeometric discretization, especially with T-spline discretization, specifying conditions at integration points is more straightforward than imposing conditions on control points. The method has two main components. 1. An iteration technique, which starts with a calculated ZSS initial guess, is used for computing the IPBZSS such that when a given pressure load is applied, the medical-image-based target shape is matched. 2. A design procedure, which is based on the Kirchhoff-Love shell model of the artery, is used for calculating the ZSS initial guess. Here we increase the scope and robustness of the method by introducing a new design procedure for the ZSS initial guess. The new design procedure has two features. (a) An IPB shell-like coordinate system, which increases the scope of the design to general parametrization in the computational space. (b) Analytical solution of the force equilibrium in the normal direction, based on the Kirchhoff-Love shell model, which places proper constraints on the design parameters. This increases the estimation accuracy, which in turn increases the robustness of the iterations and the convergence speed. To show how the new design procedure for the ZSS initial guess performs, we first present 3D test computations with a straight tube and a Y-shaped tube. Then we present a 3D computation where the target geometry is coming from medical image of a human aorta, and we include the branches in the model.

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Estimation of Element-Based Zero-Stress State in Arterial FSI Computations with Isogeometric Wall Discretization

Cited by 36 publications

References 58 publications

Space–time Isogeometric flow analysis with built-in Reynolds-equation limit

Space–time Isogeometric flow analysis with built-in Reynolds-equation limit

A node-numbering-invariant directional length scale for simplex elements

Medical-image-based aorta modeling with zero-stress-state estimation

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