非对称不定问题双线性元的超收敛和外推

本文主要讨论非对称不定问题的双线性有限元逼近.在不需要引入Ritz投影的前提下直接利用单元上的插值并借助于该元已有的高精度分析和平均值技巧,得到在H1模意义下O(h2)阶的超逼近和整体超收敛结果.同时给出两个新的误差渐近展开式,导出比传统有限元误差高两阶的O(h3)阶的外推解.

非对称不定椭圆方程的两网格内罚间断有限元方法

针对一类非对称或不定椭圆方程的内罚间断有限元方法,设计和分析了相应的两网格求解算法.首先给出了内罚间断有限元解的适定性,及其在L2和间断H1范数下的先验估计;其次设计了相应的两网格求解算法,并给出算法的误差分析;最后,数值实验结果验证了算法的高效性.

非对称不定问题Mortar型旋转Q_1元的多重网格方法

讨论了mortar型旋转Q1元求解非对称不定问题,给出了求解离散问题的多重网格算法,证明了多重网格方法的最优收敛性,即收敛速度与网格大小和层数无关.最后,数值结果验证了本文的理论分析.

以Richardson迭代为光滑化的非对称不定椭圆边值问题的多重网格法的收敛性

在两个基本算子假设下,以Richardson为光滑迭代,通过对算子在能量范数下作巧妙地估计,证明了以Richardson迭代为光滑化在无椭圆正则性假设前提下的非对称不定椭圆边值问题的多重网格方法是收敛的.

非对称不定问题的非协调多重网格法

In this note, we extend the results in [6] [7] [10] to more general problems andto other nonconforming elements.

非对称不定问题类Wilson元的超收敛和外推

讨论了非对称不定问题的类Wilson有限元逼近.利用该元的特殊性并借助于双线性元已有的高精度分析结果和平均值技巧,得到了O(h^2)阶的超逼近和整体超收敛结果,同时给出了新的渐进展开式,导出了O(h^3)阶的外推解,这比传统的误差估计高两阶.

Primary instabilities and bicriticality in fiber suspensions between rotating cylinders

The linear stability of fiber suspensions between two concentric cylinders rotating independently is studied. The modified stability equation is obtained based on the fiber orientation model and Hinch-Leal closure approximation. The primary instabilities and bicritical curves have been calculated numerically. The critical Reynolds number,wavenumber and wave speeds of fiber suspensions as functions of the aspect ratio,volume concentration of the fibers and the gap width of cylinders are obtained.

Non-axisymmetric instability in the Taylor-Couette flow of fiber suspension

An analysis of the instability in the Taylor-Couette flow of fiber suspensions with respect to the non-axisymmetric disturbances was performed. The constitutive model proposed by Ericksen was used to represent the role of fiber additives on the stress tensor. The generalized eigenvalue equation governing the hydrodynamic stability of the system was solved using a direct numerical procedure. The results showed that the fiber additives can suppress the instability of the flow. At the same time, the non-axisymmetric disturbance is the preferred mode that makes the fiber suspensions unstable when the ratio of the angular ve- locity of the outer cylinder to that of the inner cylinder is a large negative number.

两阶不定椭圆问题混合元和投影非协调元的区域分解法

对两阶非对称不定椭圆边值问题 ,在最小正则性假设下 ,对非拟一致网格 ,讨论了最低阶Raviart Thomas三角形元的混合元方法和投影非协调元方法的区域分解法 ,并得到了 GMRES方法收敛率的最优估计 .

The effects of asymmetric potential vorticity forcing on the instability of South Asia High and Indian summer monsoon onset

Based on the theory of potential vorticity(PV),the unstable development of the South Asia High(SAH)due to diabatic heating and its impacts on the Indian Summer Monsoon(ISM)onset are studied via a case diagnosis of 1998.The Indian Summer Monsoon onset in 1998 is related to the rapidly strengthening and northward moving of a tropical cyclone originally located in the south of Arabian Sea.It is demonstrated that the rapid enhancement of the cyclone is a consequence of a baroclinic development characterized by the phase-lock of high PV systems in the upper and lower troposphere.Both the intensification of the SAH and the development of the zonal asymmetric PV forcing are forced by the rapidly increasing latent heat released from the heavy rainfall in East Asia and South East Asia after the onsets of the Bay of Bengal(BOB)monsoon and the South China Sea(SCS)monsoon.High PV moves southwards along the intensified northerlies on the eastern side of the SAH and travels westwards on its south side,which can reach its northwest.Such a series of high PV eddies are transported to the west of the SAH continuously,which is the main source of PV anomalies in the upper troposphere over the Arabian Sea from late spring to early summer.A cyclonic curvature on the southwest of the SAH associated with increasing divergence,which forms a strong upper tropospheric pumping,is generated by the anomalous positive PV over the Arabian Sea on 355 K.The cyclone in the lower troposphere moves northwards from low latitudes of the Arabian Sea,and the upper-layer high PV extends downwards and southwards.Baroclinic development thus occurs and the tropical low-pressure system develops into an explosive vortex of the ISM,which leads to the onset of the ISM.In addition,evolution of subtropical anticyclone over the Arabian Peninsula is another important factor contributing to the onset of the ISM.Before the onset,the surface sensible heating on the Arabian Peninsula is very strong.Consequently the subtropical anticyclone which dominated the Arabian Sea in spring retreats westwards to the Arabian Peninsula and intensifies rapidly.The zonal asymmetric PV forcing develops gradually with high PV eddies moving southwards along northerlies on the eastern side of the anticyclone,and a high PV trough is formed in the middle troposphere over the Arabian Sea,which is favorable to the explosive barotropic development of the tropical cyclone into the vortex.Results from this study demonstrate that the ISM onset,which is different from the BOB and the SCS monsoon onset,is a special dynamical as well as thermodynamic process occurring under the condition of fully coupling of the upper,middle,and lower tropospheric circulations.

Roles of forced and inertially unstable convection development in the onset process of Indian summer monsoon

The NCEP/NCAR R1 reanalysis data are employed to investigate the impact of forced and inertial instability in the lower troposphere over the Arabian Sea on the onset process of Indian summer monsoon(ISM),and to reveal the important role of zonal advection of zonal geostrophic momentum played in the forced unstable convection.Results show that during the ISM onset the zero absolute vorticity contour(??=0)shifts northward due to the strong cross-equatorial pressure gradient in the lower troposphere over southern Arabian Sea.Thus a region with negative absolute vorticity is generated near the equator in the northern hemisphere,manifesting the evident free inertial instability.When a southerly passes through this region,under the influence of friction a lower convergence that facilitates the convection flourishing at the lower latitudes appears to the north of zero absolute vorticity contour.However,owing to such a traditional inertial instability,the convection is confined near the equator which does not have direct influence on the ISM onset.On the contrary in the region to the north of the zero absolute vorticity contour and to the south of the low pressure center near the surface,although the atmosphere there is inertially stable,the lower westerly jet can develop and bring on the apparent zonal advection of zonal geostrophic momentum.Both theoretical study and diagnosing analysis present that such a zonal advection of geostrophic momentum is closely associated with the zonal asymmetric distribution of meridional land-sea thermal contrast,which induces a convergence center near and further north of the westerly jet in the lower troposphere over the southwestern coast of the Indian Peninsula,providing a favorable lower circulation for the ISM onset.It illustrates that the development of convection over the Arabian Sea in late spring and early summer is not only due to the frictional inertial instability but also strongly affected by the zonal asymmetric distribution of land-sea thermal contrast.Moreover,before the ISM onset due to the eastward development of the South Asian High(SAH)in the upper troposphere,high potential vorticity is transported to the region over the Arabian Sea.Then a local trumpet-shaped stream field is generated to cause the evident upper divergence-pumping effect which favors the ISM onset.When the upper divergence is vertically coupled with the lower convergence resulted from the aforementioned forced unstable convection development near the southwestern coast of Indian Peninsula,the atmospheric baroclinic unstable development is stimulated and the ISM onset is triggered.

CRITERION FOR SL(2,Z)-MATRIX TO BE CONJUGATE TO ITS INVERSE

This paper gives a necessary and sufficient condition for a matrix in SL(2, Z) to be conjugateto its inverse. This condition reduces the determination of the conjugation to solving some indeterminate equation of second degree. It yields an algorithm to determine this conjugation in finite steps based on the elementary number theory.