Element length calculation in B-spline meshes for complex geometries

Otoguro, Yuto; Takizawa, Kenji; Tezduyar, Tayfun E.

doi:10.1007/s00466-019-01809-w

Cited by 39 publications

(27 citation statements)

References 169 publications

(298 reference statements)

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“…There are many ways of defining the stabilization parameters. Some of the newer options for the stabilization parameters used with the SUPS and VMS can be found in [2,5,6,10,92,93,[127][128][129][130]. Some of the earlier stabilization parameters used with the SUPS and VMS were also used in computations with other SUPG-like methods, such as the computations reported in [70,[131][132][133][134][135][136][137][138][139][140][141][142].…”

Section: St-vms and St-supsmentioning

confidence: 99%

Ventricle-valve-aorta flow analysis with the Space–Time Isogeometric Discretization and Topology Change

et al. 2020

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We address the computational challenges of and presents results from ventricle-valve-aorta flow analysis. Including the left ventricle (LV) in the model makes the flow into the valve, and consequently the flow into the aorta, anatomically more realistic. The challenges include accurate representation of the boundary layers near moving solid surfaces even when the valve leaflets come into contact, computation with high geometric complexity, anatomically realistic representation of the LV motion, and flow stability at the inflow boundary, which has a traction condition. The challenges are mainly addressed with a Space-Time (ST) method that integrates three special ST methods around the core, ST Variational Multiscale (ST-VMS) method. The three special methods are the ST Slip Interface (ST-SI) and ST Topology Change (ST-TC) methods and ST Isogeometric Analysis (ST-IGA). The ST-discretization feature of the integrated method, ST-SI-TC-IGA, provides higher-order accuracy compared to standard discretization methods. The VMS feature addresses the computational challenges associated with the multiscale nature of the unsteady flow in the LV, valve and aorta. The moving-mesh feature of the ST framework enables high-resolution computation near the leaflets. The ST-TC enables moving-mesh computation even with the TC created by the contact between the leaflets, dealing with the contact while maintaining high-resolution representation near the leaflets. The ST-IGA provides smoother representation of the LV, valve and aorta surfaces and increased accuracy in the flow solution. The ST-SI connects the separately generated LV, valve and aorta NURBS meshes, enabling easier mesh generation, connects the mesh zones containing the leaflets, enabling a more effective mesh moving, helps the ST-TC deal with leaflet-leaflet contact location change and contact sliding, and helps the ST-TC and ST-IGA keep the element density in the narrow spaces near the contact areas at a reasonable level. The ST-SI-TC-IGA is supplemented with two other special methods in this article. A structural mechanics computation method generates the LV motion from the CT scans of the LV and anatomically realistic values for the LV volume ratio. The Constrained-Flow-Profile (CFP) Traction provides flow stability at the inflow boundary. Test computation with the CFP Traction shows its effectiveness as an inflow stabilization method, and computation with the LV-valve-aorta model shows the effectiveness of the ST-SI-TC-IGA and the two supplemental methods.

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Section: St-vms and St-supsmentioning

confidence: 99%

Ventricle-valve-aorta flow analysis with the Space–Time Isogeometric Discretization and Topology Change

et al. 2020

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“…There are many ways of defining the stabilization parameters. Some of the newer options for the stabilization parameters used with the SUPS and VMS can be found in [7,14,16,30,105,130,[136][137][138][139]. Some of the earlier stabilization parameters used with the SUPS and VMS were also used in computations with other SUPG-like methods, such as the computations reported in [86,[140][141][142][143][144][145][146][147][148][149][150][151].…”

Section: St-vms and St-supsmentioning

confidence: 99%

Heart valve isogeometric sequentially-coupled FSI analysis with the space–time topology change method

et al. 2020

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Heart valve fluid-structure interaction (FSI) analysis is one of the computationally challenging cases in cardiovascular fluid mechanics. The challenges include unsteady flow through a complex geometry, solid surfaces with large motion, and contact between the valve leaflets. We introduce here an isogeometric sequentially-coupled FSI (SCFSI) method that can address the challenges with an outcome of high-fidelity flow solutions. The SCFSI analysis enables dealing with the fluid and structure parts individually at different steps of the solutions sequence, and also enables using different methods or different mesh resolution levels at different steps. In the isogeometric SCFSI analysis here, the first step is a previously computed (fully) coupled Immersogeometric Analysis FSI of the heart valve with a reasonable flow solution. With the valve leaflet and arterial surface motion coming from that, we perform a new, higher-fidelity fluid mechanics computation with the space-time topology change method and isogeometric discretization. Both the immersogeometric and space-time methods are variational multiscale methods. The computation presented for a bioprosthetic heart valve demonstrates the power of the method introduced. Keywords Bioprosthetic heart valve FSI analysis • Contact • Sequentially-coupled FSI • Immersogeometric analysis • Space-time topology change method • Space-time VMS method • Isogeometric discretization B Kenji Takizawa

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“…There are many ways of defining the stabilization parameters. Some of the newer options for the stabilization parameters used with the SUPS and VMS can be found in [10,82,83,86,87,121,[146][147][148][149]. Some of the earlier stabilization parameters used with the SUPS and VMS were also used in computations with other SUPG-like methods, such as the computations reported in [61,[150][151][152][153][154][155][156][157][158][159][160][161].…”

Section: Stabilization Parameters and Their Mesh Sensitivitymentioning

confidence: 99%

A low-distortion mesh moving method based on fiber-reinforced hyperelasticity and optimized zero-stress state

2020

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In computation of flow problems with moving boundaries and interfaces, including fluid-structure interaction, moving-mesh methods enable mesh-resolution control near the interface and consequently high-resolution representation of the boundary layers. Good moving-mesh methods require good mesh moving methods. We introduce a low-distortion mesh moving method based on fiber-reinforced hyperelasticity and optimized zero-stress state (ZSS). The method has been developed targeting isogeometric discretization but is also applicable to finite element discretization. With the large-deformation mechanics equations, we can expect to have a unique mesh associated with each step of the boundary or interface motion. With the fibers placed in multiple directions, we stiffen the element in those directions for the purpose of reducing the distortion during the mesh deformation. We optimize the ZSS by seeking orthogonality of the parametric directions, by mesh relaxation, and by making the ZSS time-dependent as needed. We present 2D and 3D test computations with isogeometric discretization. The computations show that the mesh moving method introduced performs well.

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Element length calculation in B-spline meshes for complex geometries

Cited by 39 publications

References 169 publications

Ventricle-valve-aorta flow analysis with the Space–Time Isogeometric Discretization and Topology Change

Ventricle-valve-aorta flow analysis with the Space–Time Isogeometric Discretization and Topology Change

Heart valve isogeometric sequentially-coupled FSI analysis with the space–time topology change method

A low-distortion mesh moving method based on fiber-reinforced hyperelasticity and optimized zero-stress state

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