一类流固耦合问题的数值算法及风场中摇曳树木的物理仿真
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摘要
本文针对耦合作用发生在两相交界面上的柔性结构流固耦合问题,选择两种可以优势互补的数值算法进行了研究并作出改进,使其能适用于风场中摇曳树木的物理仿真。进而系统地提出了一种风场中摇曳树木的物理仿真方法,用该方法分别模拟了风场中阔叶树和无叶树的摇曳,还将该方法应用于风场中摇曳树木的基于物理的计算机动画生成。
文中选择任意拉格朗日—欧拉法(ALE法)和基于固定笛卡尔网格的切割单元法(CCC法)进行深入研究。在ALE法方面,本文提出了一种管道中活门运动的整体耦合模拟和网格处理方法,并使其可用于二维流场中树叶周围流场的模拟和树叶阻力系数的计算。在CCC法方面,因原算法通常用于二维问题的模拟,在处理三维问题时因切割单元成型困难而较少采用。本文针对风场中的阔叶树运动模拟的需求,提出了通过适当降低三维的CCC法求解精度而极大简化切割单元的成型过程的改进方法,这不仅有效提高计算速度,而且使算法特别适用于风场中摇曳树木的仿真分析。
在改进算法的基础上,论文系统地提出了一种风场中摇曳树木的物理仿真方法。该方法包括树木有限元模型的生成、树叶的材料特性和空气动力学特性的仿真模拟、将树水分为阔叶树和无叶树两种模式进行风荷载计算,以及基于上述技术思路建立对风场中的树木流固耦合物理仿真的方法。该仿真模拟方法,首次提出了用虚拟壳结构代替阔叶树的树冠的建模、考虑树枝本身运动速度和流场中圆柱体上的脉动涡脱作用力的双向流固耦合模拟,以及材料参数的不对称性会影响树木的动力学特性的假设和物理仿真与验证。
本文还将仿真分析应用于计算机图形学领域,首次提出了基于模拟结果数据库的风场中摇曳树木基于物理的计算机动画的生成方法。针对计算机动画数据量大和精度要求远低于工程设计的特点,提出了两种有效方法:一种方法是用简化的单向耦合算法来代替双向耦合算法,用人工阻尼代替双向耦合算法的物理阻尼来对单向耦合算法进行修正,使得简化的单向耦合模拟的结果更接近双向耦合算法的模拟结果;另一种方法是虚拟材料法,通过虚拟地改变材料参数来加快动力学有限元显式求解的速度。采用了上述两种方法后,所需计算时间大大缩短,能够适应动画制作的要求。
A Class of fluid-structure interaction (FSI) problems with flexible structures immersed in fluid fields and fluid-structure interfaces between fluid and solid were studied in this paper and simulation of swaying trees in wind field were carried out based on the investigation of FSI numerical algorithms. Two typical numerical algorithms were deeply studied and some improvements were made to accommodate the simulation of swaying tree in wind field. A systematic simulation approach for swaying tree in wind field was proposed, and swaying behaviors of broad-leaf tree and no-leaf tree in wind field were simulated. The simulation method for wind-induced swaying tree simulation proposed in this paper was also implemented to physics-based animation generation.
Two FSI algorithms that deeply studied were Arbitrary Lagrangian-Eulerian (ALE) method and Cartersian Cut Cell (CCC) method. For ALE method, a monolothic coupling approach and a mesh updating approach for valves in pipes was put forward, and 2D flow field near the leaf and the drag coefficient of the leaf was calculated using the similar approach. For CCC method, the original method was merely powerful for 2D problems, however some difficulties will meet due to the variety of cut cells when extending to 3D problems. Based on the requirement of wind-induced broad-leaf tree simulation, a simplified 3D CCC method is proposed in this paper by properly lower down the precision requirement in exchange of greatly lesson the cut cell types. The simplified method is much faster than the original one, and very suitable for wind-induced broad-leaf tree simulation.
Based on the mended algorithms, a systematic approach of wind induced swaying tree simulation is proposed. This approach includes finite element tree model generation, estimation of material and aerodynamic property of tree leaves, different wind loading methods for broad-leaf tree and no-leaf tree, along with the FSI simulation methods for swaying trees in wind field. As an important part of the approach, a new method for calculating wind force exerting on the finite element broad-leaf tree model was given. The method was to establish a virtual shell structure as the fluid-structure interface surrounding the crown structure of the tree. Another important part of the approach is the two-way coupling simulation for no-leaf trees based on the experimental data of the fluctuating wind force on circular cylinders derived during the wind tunnel tests. The next point worth to mention was the investigation of a geometrically symmetric model for special purpose to investigate the influence of asymmetric material properties on tree motion.
The simulation approach proposed in this paper was also applied to computer graphics field and a new method for physics-based animation generation based on the resulting database of wind-induced swaying tree simulation is proposed. Considering that animation generation needs massive data but the requirement of simulation precision is much lower than any engineering simulation, two effective methods were bring forward to accelerate the simulation: The first method was to run the one-way coupling code instead of two-way coupling code to save the time, but artificial damping was added to compensate the physical damping of two-way coupling algorithm, the amendment of artificial damping may prevent the dropping of simulation precision. The second method was named as "virtual material method", this method can enhance the time step size of explicit code of the dynamic finite element simulation by virtually adjusting the material parameters of tree material. The combination of simplified FS1 simulation method and virtual material method can greatly reduce the time for running the simulation, and meets the requirement of physics-based animation generation.
文中选择任意拉格朗日—欧拉法(ALE法)和基于固定笛卡尔网格的切割单元法(CCC法)进行深入研究。在ALE法方面,本文提出了一种管道中活门运动的整体耦合模拟和网格处理方法,并使其可用于二维流场中树叶周围流场的模拟和树叶阻力系数的计算。在CCC法方面,因原算法通常用于二维问题的模拟,在处理三维问题时因切割单元成型困难而较少采用。本文针对风场中的阔叶树运动模拟的需求,提出了通过适当降低三维的CCC法求解精度而极大简化切割单元的成型过程的改进方法,这不仅有效提高计算速度,而且使算法特别适用于风场中摇曳树木的仿真分析。
在改进算法的基础上,论文系统地提出了一种风场中摇曳树木的物理仿真方法。该方法包括树木有限元模型的生成、树叶的材料特性和空气动力学特性的仿真模拟、将树水分为阔叶树和无叶树两种模式进行风荷载计算,以及基于上述技术思路建立对风场中的树木流固耦合物理仿真的方法。该仿真模拟方法,首次提出了用虚拟壳结构代替阔叶树的树冠的建模、考虑树枝本身运动速度和流场中圆柱体上的脉动涡脱作用力的双向流固耦合模拟,以及材料参数的不对称性会影响树木的动力学特性的假设和物理仿真与验证。
本文还将仿真分析应用于计算机图形学领域,首次提出了基于模拟结果数据库的风场中摇曳树木基于物理的计算机动画的生成方法。针对计算机动画数据量大和精度要求远低于工程设计的特点,提出了两种有效方法:一种方法是用简化的单向耦合算法来代替双向耦合算法,用人工阻尼代替双向耦合算法的物理阻尼来对单向耦合算法进行修正,使得简化的单向耦合模拟的结果更接近双向耦合算法的模拟结果;另一种方法是虚拟材料法,通过虚拟地改变材料参数来加快动力学有限元显式求解的速度。采用了上述两种方法后,所需计算时间大大缩短,能够适应动画制作的要求。
A Class of fluid-structure interaction (FSI) problems with flexible structures immersed in fluid fields and fluid-structure interfaces between fluid and solid were studied in this paper and simulation of swaying trees in wind field were carried out based on the investigation of FSI numerical algorithms. Two typical numerical algorithms were deeply studied and some improvements were made to accommodate the simulation of swaying tree in wind field. A systematic simulation approach for swaying tree in wind field was proposed, and swaying behaviors of broad-leaf tree and no-leaf tree in wind field were simulated. The simulation method for wind-induced swaying tree simulation proposed in this paper was also implemented to physics-based animation generation.
Two FSI algorithms that deeply studied were Arbitrary Lagrangian-Eulerian (ALE) method and Cartersian Cut Cell (CCC) method. For ALE method, a monolothic coupling approach and a mesh updating approach for valves in pipes was put forward, and 2D flow field near the leaf and the drag coefficient of the leaf was calculated using the similar approach. For CCC method, the original method was merely powerful for 2D problems, however some difficulties will meet due to the variety of cut cells when extending to 3D problems. Based on the requirement of wind-induced broad-leaf tree simulation, a simplified 3D CCC method is proposed in this paper by properly lower down the precision requirement in exchange of greatly lesson the cut cell types. The simplified method is much faster than the original one, and very suitable for wind-induced broad-leaf tree simulation.
Based on the mended algorithms, a systematic approach of wind induced swaying tree simulation is proposed. This approach includes finite element tree model generation, estimation of material and aerodynamic property of tree leaves, different wind loading methods for broad-leaf tree and no-leaf tree, along with the FSI simulation methods for swaying trees in wind field. As an important part of the approach, a new method for calculating wind force exerting on the finite element broad-leaf tree model was given. The method was to establish a virtual shell structure as the fluid-structure interface surrounding the crown structure of the tree. Another important part of the approach is the two-way coupling simulation for no-leaf trees based on the experimental data of the fluctuating wind force on circular cylinders derived during the wind tunnel tests. The next point worth to mention was the investigation of a geometrically symmetric model for special purpose to investigate the influence of asymmetric material properties on tree motion.
The simulation approach proposed in this paper was also applied to computer graphics field and a new method for physics-based animation generation based on the resulting database of wind-induced swaying tree simulation is proposed. Considering that animation generation needs massive data but the requirement of simulation precision is much lower than any engineering simulation, two effective methods were bring forward to accelerate the simulation: The first method was to run the one-way coupling code instead of two-way coupling code to save the time, but artificial damping was added to compensate the physical damping of two-way coupling algorithm, the amendment of artificial damping may prevent the dropping of simulation precision. The second method was named as "virtual material method", this method can enhance the time step size of explicit code of the dynamic finite element simulation by virtually adjusting the material parameters of tree material. The combination of simplified FS1 simulation method and virtual material method can greatly reduce the time for running the simulation, and meets the requirement of physics-based animation generation.
引文
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