Space–time computations in practical engineering applications: a summary of the 25-year history

Tezduyar, Tayfun E.; Takizawa, Kenji

doi:10.1007/s00466-018-1620-7

Cited by 57 publications

(29 citation statements)

References 118 publications

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“…The ST-SUPS and ST-VMS have also been applied to many classes of FSI, MBI and fluid mechanics problems (see [82] for a comprehensive summary). The classes of problems include spacecraft parachute analysis for the landing-stage parachutes [26,[83][84][85][86], cover-separation parachutes [87] and the drogue parachutes [88][89][90], wind-turbine aerodynamics for horizontal-axis wind-turbine rotors [26,37,91,92], full horizontal-axis wind-turbines [43,[93][94][95] and vertical-axis wind-turbines [6,46,47], flapping-wing aerodynamics for an actual locust [10,26,96,97], bioinspired MAVs [94,95,98,99] and wing-clapping [8,100], blood flow analysis of cerebral aneurysms [94,101], stent-blocked aneurysms [101][102][103], aortas [104][105][106][107][108], heart valves [1,8,9,95,…”

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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View full text Add to dashboard Cite

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“…The ST-SUPS and ST-VMS have also been applied to many classes of FSI, MBI and fluid mechanics problems (see Ref. 84 for a comprehensive summary). The classes of problems include spacecraft parachute analysis for the landing-stage parachutes, 85,28,[86][87][88] cover-separation parachutes 89 and the drogue parachutes, [90][91][92] wind-turbine aerodynamics for horizontal-axis windturbine rotors, 39,93,94,28 full horizontal-axis wind-turbines [95][96][97]45 and vertical-axis wind-turbines, 98,48,49 flapping-wing aerodynamics for an actual locust, 99,100,28,101 Math.…”

Section: Stabilized and Vms Space-time Computational Methodsmentioning

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 ST-SUPS and ST-VMS have also been applied to many classes of FSI, MBI and fluid mechanics problems (see Ref. 76 for a comprehensive summary). The classes of problems include spacecraft parachute analysis for the landing-stage parachutes, 22,[77][78][79][80] cover-separation parachutes 81 and the drogue parachutes, [82][83][84] wind-turbine aerodynamics for horizontal-axis windturbine rotors, 22,32,85,86 full horizontal-axis wind-turbines 38,[87][88][89] and verticalaxis wind-turbines, 9,41,42 flapping-wing aerodynamics for an actual locust, 7,22,90,91 bioinspired MAVs 88,89,92,93 and wing-clapping, 94,95 blood flow analysis of cerebral aneurysms, 88,96 stent-blocked aneurysms, 96-98 aortas [99][100][101][102] and heart valves, 89,94,101,[103][104][105][106] spacecraft aerodynamics, 81,107 thermo-fluid analysis of ground vehicles and their tires, 6,…”

Section: St-vmsmentioning

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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Space–time computations in practical engineering applications: a summary of the 25-year history

Cited by 57 publications

References 118 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 node-numbering-invariant directional length scale for simplex elements

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

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