ALE and Space–Time Variational Multiscale Isogeometric Analysis of Wind Turbines and Turbomachinery

2020 ◽  
pp. 195-233 ◽  
Author(s):  
Yuri Bazilevs ◽  
Kenji Takizawa ◽  
Tayfun E. Tezduyar ◽  
Ming-Chen Hsu ◽  
Yuto Otoguro ◽  
...  
Keyword(s):  
Wind Turbines ◽  
Isogeometric Analysis ◽  
Space Time ◽  
Variational Multiscale

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.

scholarly journals Space–Time Variational Multiscale Isogeometric Analysis of a tsunami-shelter vertical-axis wind turbine

2020 ◽  
Vol 66 (6) ◽  
pp. 1443-1460 ◽  
Author(s):  
Yuto Otoguro ◽  
Hiroki Mochizuki ◽  
Kenji Takizawa ◽  
Tayfun E. Tezduyar
Keyword(s):  
Unsteady Flow ◽  
Wind Turbine ◽  
Mesh Generation ◽  
Isogeometric Analysis ◽  
Flow Analysis ◽  
Vertical Axis ◽  
Moving Mesh ◽  
Vertical Axis Wind Turbine ◽  
Accurate Representation ◽  
Variational Multiscale

AbstractWe present computational flow analysis of a vertical-axis wind turbine (VAWT) that has been proposed to also serve as a tsunami shelter. In addition to the three-blade rotor, the turbine has four support columns at the periphery. The columns support the turbine rotor and the shelter. Computational challenges encountered in flow analysis of wind turbines in general include accurate representation of the turbine geometry, multiscale unsteady flow, and moving-boundary flow associated with the rotor motion. The tsunami-shelter VAWT, because of its rather high geometric complexity, poses the additional challenge of reaching high accuracy in turbine-geometry representation and flow solution when the geometry is so complex. We address the challenges with a space–time (ST) computational method that integrates three special ST methods around the core, ST Variational Multiscale (ST-VMS) method, and mesh generation and improvement methods. The three special methods are the ST Slip Interface (ST-SI) method, ST Isogeometric Analysis (ST-IGA), and the ST/NURBS Mesh Update Method (STNMUM). The ST-discretization feature of the integrated method 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. The moving-mesh feature of the ST framework enables high-resolution computation near the blades. The ST-SI enables moving-mesh computation of the spinning rotor. The mesh covering the rotor spins with it, and the SI between the spinning mesh and the rest of the mesh accurately connects the two sides of the solution. The ST-IGA enables more accurate representation of the blade and other turbine geometries and increased accuracy in the flow solution. The STNMUM enables exact representation of the mesh rotation. A general-purpose NURBS mesh generation method makes it easier to deal with the complex turbine geometry. The quality of the mesh generated with this method is improved with a mesh relaxation method based on fiber-reinforced hyperelasticity and optimized zero-stress state. We present computations for the 2D and 3D cases. The computations show the effectiveness of our ST and mesh generation and relaxation methods in flow analysis of the tsunami-shelter VAWT.

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

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.

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