Heart Valve Flow Computation with the Space–Time Slip Interface Topology Change (ST-SI-TC) Method and Isogeometric Analysis (IGA)

2017 ◽  
pp. 77-99 ◽  
Author(s):  
Kenji Takizawa ◽  
Tayfun E. Tezduyar ◽  
Takuya Terahara ◽  
Takafumi Sasaki
Keyword(s):  
Heart Valve ◽  
Isogeometric Analysis ◽  
Space Time ◽  
Topology Change ◽  
Flow Computation

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.

Space‐Time Isogeometric Analysis of Parabolic Diffusion Problems in Moving Spatial Domains

PAMM ◽  
2019 ◽  
Vol 19 (1) ◽  
Author(s):  
Svetlana Kyas ◽  
Ulrich Langer ◽  
Sergey Repin
Keyword(s):  
Isogeometric Analysis ◽  
Space Time ◽  
Spatial Domains ◽  
Diffusion Problems

TOPOLOGY CHANGE AND SIGNATURE CHANGE IN NON-LINEAR FIRST-ORDER GRAVITY

2007 ◽  
Vol 04 (04) ◽  
pp. 647-667 ◽  
Author(s):  
ANDRZEJ BOROWIEC ◽  
MAURO FRANCAVIGLIA ◽  
IGOR VOLOVICH
Keyword(s):  
Space Time ◽  
Relativistic Cosmology ◽  
Lagrangian Formalism ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Topology Change ◽  
First Order ◽  
Signature Change ◽  
Nonlinear Lagrangians ◽  
Momentum Complex

We show that different topologies of a space-time manifold and different signatures of its metric can be encompassed into a single Lagrangian formalism, provided one adopts the first-order (Palatini) formulation and relies on nonlinear Lagrangians, that were earlier shown to produce, in the generic case, universality of Einstein field equations and of Komar's energy-momentum complex as well. An example in Relativistic Cosmology is provided.

scholarly journals Low-Rank Space-Time Decoupled Isogeometric Analysis for Parabolic Problems with Varying Coefficients

2019 ◽  
Vol 19 (1) ◽  
pp. 123-136 ◽  
Author(s):  
Angelos Mantzaflaris ◽  
Felix Scholz ◽  
Ioannis Toulopoulos
Keyword(s):  
Isogeometric Analysis ◽  
Evolution Equations ◽  
Space Time ◽  
Point Of View ◽  
Low Rank ◽  
Parabolic Problems ◽  
Computational Point ◽  
Varying Coefficients ◽  
Analysis Scheme ◽  
Parabolic Evolution Equations

AbstractIn this paper we present a space-time isogeometric analysis scheme for the discretization of parabolic evolution equations with diffusion coefficients depending on both time and space variables. The problem is considered in a space-time cylinder in {\mathbb{R}^{d+1}}, with {d=2,3}, and is discretized using higher-order and highly-smooth spline spaces. This makes the matrix formation task very challenging from a computational point of view. We overcome this problem by introducing a low-rank decoupling of the operator into space and time components. Numerical experiments demonstrate the efficiency of this approach.

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
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