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

Takizawa, Kenji; Ueda, Yuki; Tezduyar, Tayfun E.

doi:10.1142/s0218202519500581

Cited by 33 publications

(25 citation statements)

References 163 publications

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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 [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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“…We require the element lengths, including the directional element lengths, to have node-numbering invariance for all element types, including simplex elements. The directional element length expression introduced in [173] meets that requirement. This is accomplished by using in the element length calculations for simplex elements a preferred parametric space instead of the standard integration parametric space.…”

Section: Preferred Parametric Space and Directional Element Lengths Fmentioning

confidence: 99%

Element length calculation in B-spline meshes for complex geometries

2020

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Variational multiscale methods, and their precursors, stabilized methods, have been playing a core-method role in semi-discrete and space-time (ST) flow computations for decades. These methods are sometimes supplemented with discontinuity-capturing (DC) methods. The stabilization and DC parameters embedded in most of these methods play a significant role. Various wellperforming stabilization and DC parameters have been introduced in both the semi-discrete and ST contexts. The parameters almost always involve some element length expressions, most of the time in specific directions, such as the direction of the flow or solution gradient. Until recently, stabilization and DC parameters originally intended for finite element discretization were being used also for isogeometric discretization. Recently, element lengths and stabilization and DC parameters targeting isogeometric discretization were introduced for ST and semi-discrete computations, and these expressions are also applicable to finite element discretization. The key stages of deriving the direction-dependent element length expression were mapping the direction vector from the physical (ST or space-only) element to the parent element in the parametric space, accounting for the discretization spacing along each of the parametric coordinates, and mapping what has been obtained back to the physical element. Targeting B-spline meshes for complex geometries, we introduce here new element length expressions, which are outcome of a clear and convincing derivation and more suitable for element-level evaluation. The new expressions are based on a preferred parametric space and a transformation tensor that represents the relationship between the integration and preferred parametric spaces. The test computations we present for advection-dominated cases, including 2D computations with complex meshes, show that the proposed element length expressions result in good solution profiles.

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

Cited by 33 publications

References 163 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

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

Element length calculation in B-spline meshes for complex geometries

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