共查询到19条相似文献,搜索用时 203 毫秒
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基于不可压Navier-Stokes方程, 采用计算流体力学方法, 数值模拟与分析了层流圆管潜射流在密度均匀黏性流体中的演化机理及其表现特征, 定量研究了蘑菇形涡结构无量纲射流长度L*、螺旋型涡环半径R*及其包络外形长度d*等几 何特征参数随无量纲时间t*的变化规律. 数值结果表明, 蘑菇形涡结构的形成与演化过程可分为三个不同的阶段: 启动阶段、发展阶段和衰退阶段. 在启动阶段, L*和d*随t* 线性变化, 而R*则近似为一个常数; 在发展阶段, 蘑菇形涡结构的演化具有自相似性, L*, R*和d*与t*1/2均为同一正比关系, 而且雷诺数和无量纲射流时间不影响该正比关系; 在衰退阶段, L* 和R* 正比于t*1/5, 而d*则近似为一个常数. 此外, 还对蘑菇形涡结构二次回流点、 动量源作用中心及其几何中心的速度变化规律、垂向涡量分布特征和 涡量-流函数关系进行了分析.
关键词:
圆管潜射流
蘑菇形涡结构
演化机理 相似文献
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在高维情况下,首先研究了无单元Galerkin方法的形函数构造方法——移动最小二乘法在Sobolev空间Wk,p(Ω)中的误差估计.然后,在势问题的无单元Galerkin方法的基础上,研究了势问题的通过罚函数法施加本质边界条件的无单元Galerkin方法在Sobolev空间中的误差估计.当节点和形函数满足一定条件时,证明了该误差估计是最优阶的.从误差分析中可以看出,数值解的误差与权函数的影响半径密切相关.最后,通过算例验证了结论的正确性.
关键词:
无网格方法
无单元Galerkin方法
势问题
误差估计 相似文献
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利用QCISD(T),SAC-CI方法和cc-pVQZ,aug-cc-pVTZ,6-311++G及6-311++G(3df,2pd)基组,对MgH分子的基态X2Σ+,第一简并激发态A2Π和第二激发态B2Σ+的结构进行优化计算.通过对4个基组计算结果进行比较,得出6-311++G(3df,2pd)基组为最优基组.使用
关键词:
分子结构与势能函数
激发态
Murrell-Sorbie函数
C6函数')" href="#">Murrell-Sorbie+C6函数 相似文献
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用密度泛函理论B3LYP方法计算研究AuZn和AuAl分子基态与低激发态的结构与势能函数,导出分子的光谱数据.结果表明,AuZn和AuAl分子基态分别为X2Σ和X1Σ,基态与低激发态的势能函数均可用Murrell-Sorbie函数来表达.AuZn分子低激发态a4Σ的绝热激发能为43529kJ/mol,AuAl分子低激发态a3Σ的绝热激发能为19991kJ/mol.计算固体AuZn和AuAl的内能和熵时,近似以气体分子的电子能和振动能代替固体分子的内能,用电子熵和振动熵代替固体分子的熵.在此近似下,计算得到AuZn和AuAl基态与低激发态固态分子生成反应热力学性质与温度的关系.
关键词:
AuZn和AuAl
B3LYP
热力学性质
势能函数 相似文献
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利用单双激发多参考组态相互作用方法获得了LiAl分子基态X1∑+及七个激发态a3∏, A1∏, b3∑+, c3∑+, B1∏, C1∑+, d3∏的势能曲线, 通过势能曲线得到各态的平衡核间距Re, 进而求得绝热激发能和垂直激发能.计算结果表明:c3∑+ 电子态是一个不稳定的排斥态, A1∏态是一个较弱的束缚态, 其余6个电子态均为束缚态; b3∑+与 c3∑+态之间存在预解离现象; 8个电子态分别解离到两个通道, 即Li(2S)+Al(2P0)与Li(2P0)+Al(2P0). 接着将势能曲线拟合到Murrel-Sorbie解析势能函数形式, 据此获得各态的光谱数据:基态X1∑+的平衡键长为0.2863 nm, 谐振频率为316 cm-1, 解离能De为1.03 eV, 激发态a3∏, A1∏, b3∑+, c3∑+, B1∏, C1∑+, d3∏的垂直激发能依次为0.27, 0.83, 1.18, 1.14, 1.62, 1.81, 2.00 eV; 解离能依次为1.03, 0.82, 0.26, 排斥态, 1.54, 1.10, 0.93 eV, 相应谐振频率 ωe为339, 237, 394, 排斥态, 429, 192, 178 cm-1. 通过求解核运动的薛定谔方程找到了J=0时 LiAl分子7个束缚电子态的振动能级和转动惯量.
关键词:
LiAl
光谱常数
势能曲线
振动能级 相似文献
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基于移动最小二乘法在Sobolev空间Wk,p(Ω)中的误差估计以及弹性力学问题的变分弱形式中出现的双线性形式的连续性和强制性,研究了弹性力学问题的无单元Galerkin方法的误差分析以及数值解的误差和影响域半径之间的关系,给出了弹性力学问题的无单元Galerkin方法在Sobolev空间中的误差估计定理,并证明了当节点和形函数满足一定条件时该误差估计是最优阶的.从误差分析中可以看出,数值解的误差与权函数的影响域半径密切相关.最后,通过算例验证了结论的正确性.
关键词:
无网格方法
无单元Galerkin方法
弹性力学
误差估计 相似文献
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Zhendong Luo 《advances in applied mathematics and mechanics.》2014,6(5):615-636
A semi-discrete scheme about time for the non-stationary Navier-Stokes equations is presented firstly, then a new fully discrete finite volume element (FVE) formulation based on macroelement is directly established from the semi-discrete scheme about time. And the error estimates for the fully discrete FVE solutions are derived by means of the technique of the standard finite element method. It is shown by numerical experiments that the numerical results are consistent with theoretical conclusions. Moreover, it is shown that the FVE method is feasible and efficient for finding the numerical solutions of the non-stationary Navier-Stokes equations and it is one of the most effective numerical methods among the FVE formulation, the finite element formulation, and the finite difference scheme. 相似文献
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给出数值求解一维双曲守恒律方程的新方法——龙格-库塔控制体积间断有限元方法(RKCVDFEM),其中空间离散基于控制体积有限元方法,时间离散基于二阶TVB Runge-Kutta技术,有限元空间选取为分段线性函数空间.理论分析表明,格式具有总变差有界(TVB)的性质,而且空间和时间离散形式上具有二阶精度.数值算例表明,数值解收敛到熵解并且对光滑解的收敛阶是最优的,优于龙格-库塔间断Galerkin方法(RKDGM)的计算结果. 相似文献
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In this work, two-level stabilized finite volume formulations for the
2D steady Navier-Stokes equations are considered.
These methods are based
on the local Gauss integration technique and the lowest equal-order
finite element pair. Moreover, the two-level
stabilized finite volume methods involve solving one small Navier-Stokes
problem on a coarse mesh with mesh size $H$, a large general Stokes problem for the Simple and
Oseen two-level stabilized finite volume methods on the fine mesh with mesh size $h$=$\mathcal{O}(H^2)$ or a large general Stokes equations for the Newton two-level stabilized finite
volume method on a fine mesh with mesh size $h$=$\mathcal{O}(|\log h|^{1/2}H^3)$.
These methods we studied provide an
approximate solution $(\widetilde{u}_h^v,\widetilde{p}_h^v)$ with the convergence rate of same order
as the standard stabilized finite volume method, which involve solving one large
nonlinear problem on a fine mesh with mesh size $h$. Hence, our methods
can save a large amount of computational time. 相似文献
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Unified a Priori Error Estimate and a Posteriori Error Estimate of CIP-FEM for Elliptic Equations
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Jianye Wang & Rui Ma 《advances in applied mathematics and mechanics.》2016,8(4):517-535
This paper is devoted to a unified a priori and a posteriori error analysis of
CIP-FEM (continuous interior penalty finite element method) for second-order elliptic
problems. Compared with the classic a priori error analysis in literature, our technique
can easily apply for any type regularity assumption on the exact solution, especially
for the case of lower $H^{1+s}$ weak regularity under consideration, where 0 ≤$s$≤ 1/2.
Because of the penalty term used in the CIP-FEM, Galerkin orthogonality is lost and
Céa Lemma for conforming finite element methods can not be applied immediately
when 0≤$s$≤1/2. To overcome this difficulty, our main idea is introducing an auxiliary $C^1$ finite element space in the analysis of the penalty term. The same tool is also utilized
in the explicit a posteriori error analysis of CIP-FEM. 相似文献
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This paper is concerned with a stabilized finite element method
based on two local Gauss integrations for the two-dimensional
non-stationary conduction-convection equations by using the lowest
equal-order pairs of finite elements. This method only offsets the
discrete pressure space by the residual of the simple and symmetry
term at element level in order to circumvent the inf-sup condition.
The stability of the discrete scheme is derived under some
regularity assumptions. Optimal error estimates are obtained by
applying the standard Galerkin techniques. Finally, the numerical
illustrations agree completely with the theoretical expectations. 相似文献
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考察非饱和水流问题的模型方程,利用线性迎风有限体积元方法建立非饱和流动的守恒形式,并获得该方法形式为O(Δt+h)的误差估计,最后给出数值模拟. 相似文献
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Cell Conservative Flux Recovery and a Posteriori Error Estimate of Vertex-Centered Finite Volume Methods
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Long Chen & Ming Wang 《advances in applied mathematics and mechanics.》2013,5(5):705-727
A cell conservative flux recovery technique is developed here for vertex-centered
finite volume methods of second order elliptic equations.
It is based on solving a local Neumann problem on each control volume using mixed
finite element methods. The recovered flux is used to
construct a constant free a posteriori error estimator which is proven to be
reliable and efficient. Some numerical tests are presented
to confirm the theoretical results. Our method works for general order finite volume
methods and the recovery-based and residual-based
a posteriori error estimators are the first result on
a posteriori error estimators for high
order finite volume methods. 相似文献
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针对非齐次和齐次体积约束的非局部扩散问题设计了新的有限元方法——加罚有限元方法,并给出该方法的误差分析.数值算例验证了加罚有限元方法的稳定性和有效性. 相似文献