独立覆盖流形法的精度分析
发布时间：2019-03-03 17:27
【摘要】：数值流形法采用两套相互独立的网格(数学网格和物理网格),具备了能够统一处理连续与非连续变形问题的能力,也解决了前处理工作量大的难题。但是目前采用有限元网格作为数学网格的流形法存在着关键部位计算精度不高、高阶情况下方程组线性相关、网格加密不方便等问题。针对这种完全重叠的覆盖方式带来的问题,长江科学院提出了基于独立覆盖的数值流形法(简称独立覆盖流形法),该法采用以独立覆盖分析为主的方式,在局部网格加密和特殊区域的快速收敛等方面相比现有方法优势突出,为解决上述问题提供了新的思路。但该方法在收敛性、精度分析、自适应等方面还有待进一步研究。考虑到计算精度问题是关系到新方法是否具有实用价值的关键性问题,所以本文基于独立覆盖的流形法开展精度分析和收敛性研究,具体包括以下内容:(1)通过几个算例对独立覆盖流形法现有的精度指标进行验证,在肯定其合理性的同时,指出独立覆盖内部误差不易控制的问题,以及裂尖奇异区精度指标不易满足、需要研究覆盖的合理布置问题。(2)针对独立覆盖内部误差不易控制的问题,提出了独立覆盖的子模型法,在单独的独立覆盖内进行覆盖函数的升阶操作,通过高低阶之间的相对误差获得新的误差指标,为将来实现逐点的误差控制打下基础。给出了考虑子模型法的自动计算实施步骤,用重力坝等算例验证了该方法能有效控制独立覆盖内部误差。(3)针对裂尖奇异区精度指标不易满足的问题,采用数值试验的方法探索了裂尖附近的覆盖布置方式,找出了裂尖处的解析覆盖和周边数值覆盖的分割界限(在一定大小的数值覆盖的前提下),并从裂纹体的应力解析解入手,说明了这种覆盖布置方式对Ⅰ型裂纹和Ⅱ型裂纹的普遍适用性,通过算例验证了采用合适的覆盖布置能够加快收敛,并使裂尖附近数值覆盖的精度指标得到满足。
[Abstract]:The numerical flow method adopts two sets of independent meshes (mathematical mesh and physical mesh), which has the ability to deal with continuous and discontinuous deformation problems in a unified way, and solves the difficult problem of large workload of pre-processing. But at present, the finite element mesh is used as the mathematical mesh in the flow form method, there are some problems, such as the accuracy of the key parts is not high, the linear correlation of the equations in the high-order case, the inconvenient mesh refinement and so on. In view of the problems caused by this completely overlapping coverage method, the Changjiang Academy of Sciences proposed a numerical fluidic method based on independent coverage (referred to as independent coverage fluidization method), which is mainly based on independent coverage analysis. Compared with the existing methods, local mesh encryption and fast convergence in special areas are superior to the existing methods, which provides a new way to solve the above-mentioned problems. However, the convergence, precision analysis, self-adaptation and other aspects of this method need to be further studied. Considering that the computational accuracy is a key problem related to the practical value of the new method, the accuracy analysis and convergence study based on the independent cover flow method is carried out in this paper. The main contents are as follows: (1) the existing accuracy indexes of the independent cover flow method are verified by several examples. While affirming its rationality, it is pointed out that the internal error of the independent cover is difficult to control, and that it is difficult to control the internal error of the independent coverage method. And the precision index of crack tip singular region is not satisfied, so it is necessary to study the reasonable arrangement of cover. (2) aiming at the problem that the internal error of independent cover is not easy to control, a sub-model method of independent cover is proposed. A new error index is obtained through the relative error between high and low order, which lays a foundation for the realization of point-by-point error control in the future. The steps of automatic calculation and implementation of the submodel method are given. Examples such as gravity dam show that the method can effectively control the internal error of independent coverage. (3) aiming at the problem that the precision index of the singular zone at the crack tip is not easily satisfied, the method can control the internal error of independent cover effectively. The method of numerical experiment is used to explore the covering arrangement near the crack tip, and the dividing boundary between the analytical cover and the surrounding numerical coverage is found (on the premise of a certain size of numerical coverage). Based on the analytical solution of the stress of the crack body, the universal applicability of the coverage arrangement to type I crack and type 鈪，
本文编号：2433935
[Abstract]:The numerical flow method adopts two sets of independent meshes (mathematical mesh and physical mesh), which has the ability to deal with continuous and discontinuous deformation problems in a unified way, and solves the difficult problem of large workload of pre-processing. But at present, the finite element mesh is used as the mathematical mesh in the flow form method, there are some problems, such as the accuracy of the key parts is not high, the linear correlation of the equations in the high-order case, the inconvenient mesh refinement and so on. In view of the problems caused by this completely overlapping coverage method, the Changjiang Academy of Sciences proposed a numerical fluidic method based on independent coverage (referred to as independent coverage fluidization method), which is mainly based on independent coverage analysis. Compared with the existing methods, local mesh encryption and fast convergence in special areas are superior to the existing methods, which provides a new way to solve the above-mentioned problems. However, the convergence, precision analysis, self-adaptation and other aspects of this method need to be further studied. Considering that the computational accuracy is a key problem related to the practical value of the new method, the accuracy analysis and convergence study based on the independent cover flow method is carried out in this paper. The main contents are as follows: (1) the existing accuracy indexes of the independent cover flow method are verified by several examples. While affirming its rationality, it is pointed out that the internal error of the independent cover is difficult to control, and that it is difficult to control the internal error of the independent coverage method. And the precision index of crack tip singular region is not satisfied, so it is necessary to study the reasonable arrangement of cover. (2) aiming at the problem that the internal error of independent cover is not easy to control, a sub-model method of independent cover is proposed. A new error index is obtained through the relative error between high and low order, which lays a foundation for the realization of point-by-point error control in the future. The steps of automatic calculation and implementation of the submodel method are given. Examples such as gravity dam show that the method can effectively control the internal error of independent coverage. (3) aiming at the problem that the precision index of the singular zone at the crack tip is not easily satisfied, the method can control the internal error of independent cover effectively. The method of numerical experiment is used to explore the covering arrangement near the crack tip, and the dividing boundary between the analytical cover and the surrounding numerical coverage is found (on the premise of a certain size of numerical coverage). Based on the analytical solution of the stress of the crack body, the universal applicability of the coverage arrangement to type I crack and type 鈪，
本文编号：2433935
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