共查询到19条相似文献,搜索用时 125 毫秒
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本文给出了一种数值求解变系数对流扩散反应方程的指数型高精度紧致差分方法.我们首先将模型方程变形,借助常系数对流扩散方程的指数型高精度紧致差分格式,采用残量修正法得到变系数对流扩散反应方程的指数型高精度紧致差分格式;并从理论上分析了当Pelect数很大时,本文格式达到四阶计算精度时网格步长的限制条件;离散得到的代数方程组可采用追赶法直接求解.数值实验结果与理论分析完全吻合,表明了本文格式对于边界层问题或大梯度变化的物理量求解问题具有的高精度和鲁棒性的优点. 相似文献
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定常对流扩散反应方程非均匀网格上高精度紧致差分格式 总被引:1,自引:1,他引:0
本文构造了非均匀网格上求解定常对流扩散反应方程的高精度紧致差分格式.我们首先基于非均匀网格上函数的泰勒级数展开,给出了一阶导数和二阶导数的高阶近似表达式;然后将模型方程变形,借助于对流扩散方程高精度紧致格式构造的方法,结合原模型方程,得到定常对流扩散反应方程的高精度紧致差分格式;最后给出的数值算例验证了本文格式高精度和高分辨率的优点. 相似文献
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用基于特征线的算子分裂(CBOS)有限元法求解Naiver-Stokes方程:即在每一个时间层上,采用算子分裂法将N-S方程的对流项与扩散项分开求解,对流项离散采用特征线-Galerkin法,显式求解。流体自由表面跟踪采用浓度法,建立了新的水波模型。经过下游河床有水、无水溃坝模型的验证,表明该模型能精确模拟带自由表面流体运动问题。同时,研究了下游河床无水时溃坝模型自由水面运动特征;探讨了下游河床有水时溃坝模型中涌浪波形成原因、波浪翻卷形成过程,并分析了涌浪波与下游河床水体冲击接触瞬间,下游河床压力突然增大这一现象。 相似文献
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针对气泡在聚合物熔体内的等温长大过程,建立了其几何模型和有限元模型;采用幂律型流体本构关系描述聚合物流变性质;对控制方程进行无量纲化处理,采用Galerkin方法对对流扩散有限元控制方程进行数值求解;采用隐式差分法对扩散方程中的时间导数项进行离散,并在每个时间步进行网格重划分,确保计算结果的可靠性。计算获得了聚合物内发泡剂浓度分布规律及不同的特征无量纲量对气泡长大过程的影响。 相似文献
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本文对一类线性对流占优扩散问题提出了一种修正的特征混合有限元格式,该格式对方程的对流部分沿流体流动的方向即特征方向离散以保证格式在流动的锋线前沿逼近的高稳定性,消除数值弥散现象;对方程的扩散部分采用最低次混合有限元方法离散以同时高精度逼近未知函数及未知函数的梯度;为保证方法的整体守恒性,在格式中引入一修正项.数值分析表明,文中提出的修正的特征混合有限元方法具有所期望的稳定性,收敛性及整体守恒性. 相似文献
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对流扩散方程在工程计算中具有广泛应用.本文研究一维变系数对流扩散方程第三边值问题的高精度有限体积方法.通过在控制体积上积分导出了方程的积分守恒形式,然后对积分守恒形式利用泰勒公式和二次埃尔米特插值进行离散得到了紧有限体积格式.该格式导出的线性代数方程组具有三对角性质,因此可使用追赶法求解.进而,通过分析截断误差,采用能量方法证明了格式按照几种标准的离散范数四阶收敛.最后,数值算例验证了格式的正确性和有效性,这与理论分析结果是一致的. 相似文献
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研究了缓增分数阶扩散方程的高阶时间离散局部间断Galerkin (Local Discontinuous Galerkin, LDG)方法,不是直接求解缓增分数阶扩散方程,而是首先通过变换将其转化成Caputo型时间分数阶扩散方程。接着,采用L1-2差分逼近离散Caputo型分数阶导数,间断有限元离散空间变量,构造求解模型的全离散LDG格式。证明了所建立的全离散格式为无条件稳定的且具有最优误差阶,两个数值算了验证了所建立数值格式的精度和鲁棒性。数值实验结果表明所建立格式在时间和空间方向均具有高精度。 相似文献
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We propose and analyse a class of fully discrete schemes for the Cahn-Hilliard
equation with Neumann boundary conditions. The schemes combine large-time step
splitting methods in time and spectral element methods in space. We are particularly
interested in analysing a class of methods that split the original Cahn-Hilliard equation
into lower order equations. These lower order equations are simpler and less
computationally expensive to treat. For the first-order splitting scheme, the stability
and convergence properties are investigated based on an energy method. It is proven
that both semi-discrete and fully discrete solutions satisfy the energy dissipation and
mass conservation properties hidden in the associated continuous problem. A rigorous
error estimate, together with numerical confirmation, is provided. Although not
yet rigorously proven, higher-order schemes are also constructed and tested by a series
of numerical examples. Finally, the proposed schemes are applied to the phase field
simulation in a complex domain, and some interesting simulation results are obtained. 相似文献
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P.P. Peng Q. Wu Y.M. Cheng 《International journal for numerical methods in engineering》2020,121(1):146-164
In this paper, the dimension splitting reproducing kernel particle method (DSRKPM) for three-dimensional (3D) potential problems is presented. In the DSRKPM, a 3D potential problem can be transformed into a series of two-dimensional (2D) ones in the dimension splitting direction. The reproducing kernel particle method (RKPM) is used to solve each 2D problem, the essential boundary conditions are imposed by penalty method, and the discretized equation is obtained from Galerkin weak form of potential problems. Finite difference method is used in the dimension splitting direction. Then, by combining a series of the equations of the RKPM for solving 2D problems, the final equation of the DSRKPM for 3D potential problems is obtained. Five example problems on regular or irregular domains are selected to show that the DSRKPM has higher computational efficiency than the RKPM and the improved element-free Galerkin method for 3D potential problems. 相似文献
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Moon-Sun Chung Keun-Shik ChangSung-Jae Lee 《International Journal of Engineering Science》2002,40(7):789-803
Flux vector splitting method is applied to the two-fluid six-equation model of two-phase flow, which takes account of surface tension effect via the interfacial pressure jump terms in the momentum equations. The latter terms using the concept of finite-thickness interface are derived as a simple function of fluid bulk moduli. We proved that the governing equation system is hyperbolic with real eigenvalues in the bubbly, slug, and annular flow regimes. The governing equations do not need any conventional artificial stabilizing terms like the virtual mass terms. Sonic speeds obtained through characteristic analysis show excellent agreement with the existing experimental data. Edwards pipe problem is solved as a benchmark test of the present two-phase equation model. 相似文献
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Kenn K. Q. Zhang 《International journal for numerical methods in engineering》2005,64(3):285-303
The presence of the pressure and the convection terms in incompressible Navier–Stokes equations makes their numerical simulation a challenging task. The indefinite system as a consequence of the absence of the pressure in continuity equation is ill‐conditioned. This difficulty has been overcome by various splitting techniques, but these techniques incur the ambiguity of numerical boundary conditions for the pressure as well as for the intermediate velocity (whenever introduced). We present a new and straightforward discrete splitting technique which never resorts to numerical boundary conditions. The non‐linear convection term can be treated by four different approaches, and here we present a new linear implicit time scheme. These two new techniques are implemented with a finite element method and numerical verifications are made. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
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Chip splitting is a natural chip separation phenomenon that can significantly reduce cutting energy consumption. To reveal its occurrence mechanisms, a method for obtaining its critical conditions through cutting experiments and establishing its critical equation is proposed in this paper. Based on previous research results regarding the relationship between chip removal interference and chip splitting, the control variables that affect chip splitting are identified by analyzing a geometric model of the cutting process. A total of 366 experiments on turning a C45E4 disc workpiece with a high-speed steel double-edged turning tool based on the dichotomy method were conducted and 51 experimental data on chip splitting critical conditions were obtained. According to these experimental data, a critical equation expressed by a finite-degree polynomial with a cutting thickness equal to the other control variables was fitted. By analyzing the critical surface, it was determined that chip splitting followed a law in which the smaller the cutting thickness and the larger the absolute value of the negative rake angle, edge angle, and edge inclination of the tool, the more likely chip splitting was to occur. Through a verification experiment, it was determined that the derived critical equation could accurately predict the occurrence of 95.24% of chip splitting. It was also determined that the occurrence of chip splitting led to a cliff-like drop in the specific total cutting force with a maximum drop of 51.23%. This research lays a foundation for the rational utilization of chip splitting in tool structure parameter design and cutting parameter energy saving optimization.The full text can be downloaded at https://link.springer.com/article/10.1007/s40436-021-00378-7 相似文献
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Chongbin Zhao Tianyun Liu 《International journal for numerical methods in engineering》2003,58(10):1435-1456
This paper presents an exact non‐reflecting boundary condition for dealing with transient scalar wave propagation problems in a two‐dimensional infinite homogeneous layer. In order to model the complicated geometry and material properties in the near field, two vertical artificial boundaries are considered in the infinite layer so as to truncate the infinite domain into a finite domain. This treatment requires the appropriate boundary conditions, which are often referred to as the artificial boundary conditions, to be applied on the truncated boundaries. Since the infinite extension direction is different for these two truncated vertical boundaries, namely one extends toward x →∞ and another extends toward x→‐ ∞, the non‐reflecting boundary condition needs to be derived on these two boundaries. Applying the variable separation method to the wave equation results in a reduction in spatial variables by one. The reduced wave equation, which is a time‐dependent partial differential equation with only one spatial variable, can be further changed into a linear first‐order ordinary differential equation by using both the operator splitting method and the modal radiation function concept simultaneously. As a result, the non‐reflecting artificial boundary condition can be obtained by solving the ordinary differential equation whose stability is ensured. Some numerical examples have demonstrated that the non‐reflecting boundary condition is of high accuracy in dealing with scalar wave propagation problems in infinite and semi‐infinite media. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
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Manufacturing‐induced material properties of linear flow split and linear bend split profiles 下载免费PDF全文
E. Bruder L. Ahmels J. Niehuesbernd C. Müller 《Materialwissenschaft und Werkstofftechnik》2017,48(1):41-52
In this work the two massive forming processes linear flow splitting and linear bend splitting, which generate profiles from sheet metal, are evaluated with respect to characteristic manufacturing‐induced material properties of the produced parts. Resulting microstructural features such as grain size and shape as well as crystallographic textures are linked to mechanical properties such as strength, ductility and anisotropic elasticity and general rules for their evolution are defined. Residual stress distributions are detailed and discussed with regard to the causing geometrical and forming process related aspects. The aim of this paper is to give a comprehensive overview of the properties of profiles produced by linear flow splitting and linear bend splitting and to illustrate general rules for their evolution in order to provide guidelines for an optimized product development process which allows a beneficial use of the manufacturing‐induced properties. 相似文献
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This paper discusses the advantages of lot splitting in hybrid manufacturing environments where cellular and functional layouts are combined under Constant Work in Process (CONWIP) production control. The proposed model fills a research gap in the related literature by applying lot splitting and pull production simultaneously. A linear CONWIP control mathematical model that minimises the average flow time is developed in case of lot splitting. The developed model has sequence-dependent set-up times. The demand level, coefficient of variation (CV) impact and set-up time reduction effect on CONWIP production control are also investigated. The model is solved using GAMS21.6 optimisation software; the optimal backlog list, the number and size of sublots are reported. The proposed model is compared with lot production under push control in different settings as well as with two different heuristics from the literature. Experimental results indicate that in all settings, the lot splitting is more advantageous than lot production in terms of average flow time. CV has a greater effect than set-up time reduction on average flow time. 相似文献