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

2020 ◽  
Vol 65 (4) ◽  
pp. 1167-1187 ◽  
Author(s):  
Takuya Terahara ◽  
Kenji Takizawa ◽  
Tayfun E. Tezduyar ◽  
Yuri Bazilevs ◽  
Ming-Chen Hsu
Keyword(s):  
Fluid Mechanics ◽  
Heart Valve ◽  
Complex Geometry ◽  
Space Time ◽  
Multiscale Methods ◽  
Topology Change ◽  
Mesh Resolution ◽  
Flow Through ◽  
Isogeometric Discretization ◽  
Variational Multiscale Methods

AbstractHeart 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.

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

2020 ◽  
Vol 65 (5) ◽  
pp. 1343-1363 ◽  
Author(s):  
Takuya Terahara ◽  
Kenji Takizawa ◽  
Tayfun E. Tezduyar ◽  
Atsushi Tsushima ◽  
Kensuke Shiozaki
Keyword(s):  
Flow Analysis ◽  
Space Time ◽  
Topology Change ◽  
And Topology ◽  
Isogeometric Discretization

scholarly journals Wind Turbine and Turbomachinery Computational Analysis with the ALE and Space-Time Variational Multiscale Methods and Isogeometric Discretization

2020 ◽  
Vol 4 (1) ◽  
pp. 1 ◽  
Author(s):  
Yuri Bazilevs ◽  
Kenji Takizawa ◽  
Tayfun E. Tezduyar ◽  
Ming-Chen Hsu ◽  
Yuto Otoguro ◽  
...  
Keyword(s):  
Wind Turbine ◽  
Wind Turbines ◽  
Computational Analysis ◽  
Vertical Axis ◽  
Space Time ◽  
Multiscale Methods ◽  
Arbitrary Lagrangian Eulerian ◽  
Variational Multiscale ◽  
Creative Commons ◽  
Isogeometric Discretization

The challenges encountered in computational analysis of wind turbines and turbomachinery include turbulent rotational flows, complex geometries, moving boundaries and interfaces, such as the rotor motion, and the fluid-structure interaction (FSI), such as the FSI between the wind turbine blade and the air. The Arbitrary Lagrangian-Eulerian (ALE) and Space-Time (ST) Variational Multiscale (VMS) methods and isogeometric discretization have been effective in addressing these challenges. The ALE-VMS and ST-VMS serve as core computational methods. They are supplemented with special methods like the Slip Interface (SI) method and ST Isogeometric Analysis with NURBS basis functions in time. We describe the core and special methods and present, as examples of challenging computations performed, computational analysis of horizontal and vertical-axis wind turbines and flow-driven This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.

Space–time fluid mechanics computation of heart valve models

2014 ◽  
Vol 54 (4) ◽  
pp. 973-986 ◽  
Author(s):  
Kenji Takizawa ◽  
Tayfun E. Tezduyar ◽  
Austin Buscher ◽  
Shohei Asada
Keyword(s):  
Fluid Mechanics ◽  
Heart Valve ◽  
Space Time

scholarly journals Element length calculation in B-spline meshes for complex geometries

2020 ◽  
Vol 65 (4) ◽  
pp. 1085-1103 ◽  
Author(s):  
Yuto Otoguro ◽  
Kenji Takizawa ◽  
Tayfun E. Tezduyar
Keyword(s):  
Finite Element ◽  
Multiscale Methods ◽  
Complex Geometries ◽  
Finite Element Discretization ◽  
Element Discretization ◽  
B Spline ◽  
Parametric Space ◽  
Stabilized Methods ◽  
Isogeometric Discretization ◽  
Variational Multiscale Methods

AbstractVariational 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 well-performing 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.

scholarly journals Stress Energy Tensor Study in Fluid Mechanics

2019 ◽  
Author(s):  
Roman Baudrimont
Keyword(s):  
General Relativity ◽  
Fluid Mechanics ◽  
Space Time ◽  
Newtonian Fluids ◽  
Third Party ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Perfect Fluids ◽  
Stress Energy

This paper is to summarize the involvement of the stress energy tensor in the study of fluid mechanics. In the first part we will see the implication that carries the stress energy tensor in the framework of general relativity. In the second part, we will study the stress energy tensor under the mechanics of perfect fluids, allowing us to lead third party in the case of Newtonian fluids, and in the last part we will see that it is possible to define space-time as a no-Newtonian fluids.

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