基于非结构网格方法的重叠网格算法研究
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摘要
多体间具有相对运动的非定常绕流问题是航空工程中一类常见的问题。在这类问题中,物体间存在着较强的气动干扰,而这种气动干扰常常是非线性和非定常的,并对飞行器的气动性能有较大的影响,甚至会对飞行安全构成威胁。近年来,随着数值方法的不断发展以及计算机软硬件的突飞猛进,采用计算流体力学方法模拟多体间具有相对运动的非定常绕流问题已成为可能。Nakahashi提出的基于非结构的重叠网格思想结合了非结构网格方法和结构重叠网格方法的优点,适合应用于多体间具有大幅相对运动的复杂外形非定常绕流问题模拟研究,具有较大的实际工程应用前景。但是,与非结构网格技术和结构重叠网格技术相比,基于非结构的重叠网格方法还处于起步发展阶段,其中的一些关键技术,如网格间插值边界定义方法、适用于非结构重叠网格的网格间插值方法、高效宿主单元搜索算法、向任意网格类型的推广、基于非结构重叠网格方法的分布式并行计算算法以及适用于多体相对运动非定常绕流流场模拟的动态非结构重叠网格算法等方面都需要进行深入研究。因此,本文的主要工作是开展基于非结构网格方法的重叠网格算法研究,其目的是发展出适合于多体相对运动非定常绕流问题模拟的高效计算算法,并开发出相应的非定常计算软件。
本文首先讨论了所采用的流动控制方程以及数值求解方法。控制方程采用非定常可压缩Euler/N-S方程,空间离散采用有效体积方法,通量计算采用Jameson中心格式,时间离散采用双时间步长方法,在伪时间上采用多步Runge-Kutta迭代,湍流模拟中采用Spalart-Allmaras一方程湍流模型计算湍流粘性系数,其物面距计算采用了一种基于阵面推进的高效计算方法。
其次,开展了非结构重叠网格的网格间边界定义方法研究,并在Nakahashi的网格间边界定义方法的基础上,提出了一种能够处理包含任意多块子网格、任意单元类型子网格的重叠网格系统的优化网格间边界定义算法;为提高非结构重叠网格系统的网格间边界定义效率,在宿主单元搜索中,发展了一种适合于非结构网格数据结构的基于阵面推进与ADT方法相结合的相邻单元搜索算法,大大提高了大型非结构重叠网格系统的网格间边界定义的速度;为适应混合非结构重叠网格的网格间信息交换,在进行非结构重叠网格的网格间插值方法研究中提出了适合于混合类型单元网格的网格间插值方法。
然后,为把非结构重叠网格方法推广应用到多体间具有相对的非定常绕流问题模拟中,开展了基于动态非结构重叠网格的非定常Euler/N-S方程求解算法研究,提出了一种适合于多体相对运动模拟的动态非结构重叠网格算法,并且开展数值实验研究,表明该算法在非定常问题模拟中不但具有较高的计算效率和较强的鲁棒性,而且不需任何人工干预,具有很高的自动化程度。
最后,开展了基于动态非结构重叠网格方法的非定常Euler/N-S方程分布式并行算法研究。在采用区域分裂算法并行求解Euler/N-S方程时,提出了一种子网格独立分区的非结构重叠网格分区策略,并在子网格分区时根据网格节点的性质(活动节点、非活动节点或者插值点)进行加权分区,使得每个进程上的计算负载达到平衡。进程间通信通过调用MPI标准库函数实现。为测试所发展的基于动态非结构重叠网格的并行计算算法的正确性和并行效率,开展了一系列的数值实验研究,结果表明该并行算法不但能够得到与串行一样的正确结果,而且具有较高的并行计算效率。
The unsteady flow field past multiple bodies in relative motion is a common-faced engineering problem, in which there is a strong aerodynamic interaction among bodies. The aerodynamic interaction which is, in nature, always unsteady and nonlinear can make a serious impact on aerodynamic characteristics of flying vehicle and sometimes can threaten the safety of flight. Recently, with the rapid development of numerical simulation methods and computer technologies, computational fluid dynamics (CFD) method has been used to handle these problems. Overset unstructured grids method which was introduced by Nakahashi has the advantages of unstructured grid method and Chimera grid method and is very suitable to deal with unsteady flow fields past complex geometries and/or multiple bodies in relatively moving. However, the overset unstructured grids method is relatively unexplored and it has many problems such as automatic inter-grid definition, efficient algorithm for donor searching, interpolation between subgrids, general type element overlapping grids, dynamic overset grids assembling, parallel computation algorithm, etc. In this thesis, a new efficient and reliable dynamic overset unstructured grids method is proposed and a distributed memory parallel unsteady solver based on the method is developed to predict unsteady flow fields with multiple bodies in relative motion.
First of all, the numerical methods which are used in this thesis are discussed. The unsteady compressible Euler/Navier-Stokes equations are solved using the finite volume method in spatial discretization and the explicit multistage dual time-stepping scheme in temporal discretization. The low speed preconditioning method is applied to inner iteration of the dual-time stepping to accelerate the solution of the governing equations. In the simulation of turbulence flows, the Spalart-Allmaras one-equation turbulence model is implemented to evaluate the turbulent viscosity and the wall distance of grid nodes is evaluated by an efficient advancing front method.
Secondly, the inter-grid boundary definition method of overset unstructured grids is investigated. Nakahashi's method is extended to any type element and any number of overlapping grids. To improve the computational efficiency, a neighbour-to-neighbour searching algorithm coupled with advancing front method and ADT algorithm is used to search donor cells for all grid nodes in other component grids and as a consequence, the time used in inter-grid boundary definition is reduced. A general interpolation method which can deal with any element type is presented to realize information transfer between the overlapping grids. Many test cases were considered to validate the developed overset unstructured grids method and the numerical results indicate that the method is efficient and robust.
Then, a new dynamic overset unstructured grids algorithm is proposed and by coupling the six degree of freedom motion equations, it can be used to handle the unsteady flow problems with multiple bodies in relatively moving. To evaluate the capability of the dynamic overset unstructured grids algorithm for these problems, it was applied to a number of numerical test cases (3D store separation, Caradonna rotor in hover and flight forward, and Robin helicopter with a four-blade rotor). The results show that the dynamic overset unstructured grids method developed in the thesis is not only efficient and reliable but also automatic.
At last, a distributed memory parallel computation strategy for unsteady Euler/Navier-Stokes solver based on dynamic overset unstructured grids method is proposed and a parallel software was developed to predict unsteady flow fields with moving geometries. The parallel computation is based on the dynamic domain decomposition method which is performed by using METIS system at each physical time step. Load balance is achieved by respectively partitioning each component grid according to the number of CPUs and weighting the active nodes and inactive nodes. Communication between processors is implemented by calling MPI standard library. Numerical test results on the developed distributed memory parallel strategies indicate that a good parallel performance is achieved.
本文首先讨论了所采用的流动控制方程以及数值求解方法。控制方程采用非定常可压缩Euler/N-S方程,空间离散采用有效体积方法,通量计算采用Jameson中心格式,时间离散采用双时间步长方法,在伪时间上采用多步Runge-Kutta迭代,湍流模拟中采用Spalart-Allmaras一方程湍流模型计算湍流粘性系数,其物面距计算采用了一种基于阵面推进的高效计算方法。
其次,开展了非结构重叠网格的网格间边界定义方法研究,并在Nakahashi的网格间边界定义方法的基础上,提出了一种能够处理包含任意多块子网格、任意单元类型子网格的重叠网格系统的优化网格间边界定义算法;为提高非结构重叠网格系统的网格间边界定义效率,在宿主单元搜索中,发展了一种适合于非结构网格数据结构的基于阵面推进与ADT方法相结合的相邻单元搜索算法,大大提高了大型非结构重叠网格系统的网格间边界定义的速度;为适应混合非结构重叠网格的网格间信息交换,在进行非结构重叠网格的网格间插值方法研究中提出了适合于混合类型单元网格的网格间插值方法。
然后,为把非结构重叠网格方法推广应用到多体间具有相对的非定常绕流问题模拟中,开展了基于动态非结构重叠网格的非定常Euler/N-S方程求解算法研究,提出了一种适合于多体相对运动模拟的动态非结构重叠网格算法,并且开展数值实验研究,表明该算法在非定常问题模拟中不但具有较高的计算效率和较强的鲁棒性,而且不需任何人工干预,具有很高的自动化程度。
最后,开展了基于动态非结构重叠网格方法的非定常Euler/N-S方程分布式并行算法研究。在采用区域分裂算法并行求解Euler/N-S方程时,提出了一种子网格独立分区的非结构重叠网格分区策略,并在子网格分区时根据网格节点的性质(活动节点、非活动节点或者插值点)进行加权分区,使得每个进程上的计算负载达到平衡。进程间通信通过调用MPI标准库函数实现。为测试所发展的基于动态非结构重叠网格的并行计算算法的正确性和并行效率,开展了一系列的数值实验研究,结果表明该并行算法不但能够得到与串行一样的正确结果,而且具有较高的并行计算效率。
The unsteady flow field past multiple bodies in relative motion is a common-faced engineering problem, in which there is a strong aerodynamic interaction among bodies. The aerodynamic interaction which is, in nature, always unsteady and nonlinear can make a serious impact on aerodynamic characteristics of flying vehicle and sometimes can threaten the safety of flight. Recently, with the rapid development of numerical simulation methods and computer technologies, computational fluid dynamics (CFD) method has been used to handle these problems. Overset unstructured grids method which was introduced by Nakahashi has the advantages of unstructured grid method and Chimera grid method and is very suitable to deal with unsteady flow fields past complex geometries and/or multiple bodies in relatively moving. However, the overset unstructured grids method is relatively unexplored and it has many problems such as automatic inter-grid definition, efficient algorithm for donor searching, interpolation between subgrids, general type element overlapping grids, dynamic overset grids assembling, parallel computation algorithm, etc. In this thesis, a new efficient and reliable dynamic overset unstructured grids method is proposed and a distributed memory parallel unsteady solver based on the method is developed to predict unsteady flow fields with multiple bodies in relative motion.
First of all, the numerical methods which are used in this thesis are discussed. The unsteady compressible Euler/Navier-Stokes equations are solved using the finite volume method in spatial discretization and the explicit multistage dual time-stepping scheme in temporal discretization. The low speed preconditioning method is applied to inner iteration of the dual-time stepping to accelerate the solution of the governing equations. In the simulation of turbulence flows, the Spalart-Allmaras one-equation turbulence model is implemented to evaluate the turbulent viscosity and the wall distance of grid nodes is evaluated by an efficient advancing front method.
Secondly, the inter-grid boundary definition method of overset unstructured grids is investigated. Nakahashi's method is extended to any type element and any number of overlapping grids. To improve the computational efficiency, a neighbour-to-neighbour searching algorithm coupled with advancing front method and ADT algorithm is used to search donor cells for all grid nodes in other component grids and as a consequence, the time used in inter-grid boundary definition is reduced. A general interpolation method which can deal with any element type is presented to realize information transfer between the overlapping grids. Many test cases were considered to validate the developed overset unstructured grids method and the numerical results indicate that the method is efficient and robust.
Then, a new dynamic overset unstructured grids algorithm is proposed and by coupling the six degree of freedom motion equations, it can be used to handle the unsteady flow problems with multiple bodies in relatively moving. To evaluate the capability of the dynamic overset unstructured grids algorithm for these problems, it was applied to a number of numerical test cases (3D store separation, Caradonna rotor in hover and flight forward, and Robin helicopter with a four-blade rotor). The results show that the dynamic overset unstructured grids method developed in the thesis is not only efficient and reliable but also automatic.
At last, a distributed memory parallel computation strategy for unsteady Euler/Navier-Stokes solver based on dynamic overset unstructured grids method is proposed and a parallel software was developed to predict unsteady flow fields with moving geometries. The parallel computation is based on the dynamic domain decomposition method which is performed by using METIS system at each physical time step. Load balance is achieved by respectively partitioning each component grid according to the number of CPUs and weighting the active nodes and inactive nodes. Communication between processors is implemented by calling MPI standard library. Numerical test results on the developed distributed memory parallel strategies indicate that a good parallel performance is achieved.
引文
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