The pseudoplastic circular Couette flow （CCF） in annuli is investigated. The viscosity is dependent on the shear rate that directly affects the conservation equations solved by the spectral method in the present stu...The pseudoplastic circular Couette flow （CCF） in annuli is investigated. The viscosity is dependent on the shear rate that directly affects the conservation equations solved by the spectral method in the present study. The pseudoplastic model adopted here is shown to be the suitable representative of nonlinear fluids. Unlike the previous studies, where only the square of the shear ered to ease the numerical manipulations, quadratic power is also taken into account. rate term in the viscosity expression is consid- in the present study, the term containing the The curved streamlines of the CCF can cause the centrifugal instability leading to toroidal vortices, known as the Taylor vortices. It is further found that the critical Taylor number becomes lower as the pseudoplastic effect increases. The comparison with the existing measurements on the pseudoplastic CCF results in good agreement.展开更多
We investigate numerical approximations based on polynomials that are orthogonal with respect to a weighted discrete inner product and develop an algorithm for solving time dependent differential equations.We focus on...We investigate numerical approximations based on polynomials that are orthogonal with respect to a weighted discrete inner product and develop an algorithm for solving time dependent differential equations.We focus on the family of super Gaussian weight functions and derive a criterion for the choice of parameters that provides good accuracy and stability for the time evolution of partial differential equations.Our results show that this approach circumvents the problems related to the Runge phenomenon on equally spaced nodes and provides high accuracy in space.For time stability,small corrections near the ends of the interval are computed using local polynomial interpolation.Several numerical experiments illustrate the performance of the method.展开更多
文摘The pseudoplastic circular Couette flow （CCF） in annuli is investigated. The viscosity is dependent on the shear rate that directly affects the conservation equations solved by the spectral method in the present study. The pseudoplastic model adopted here is shown to be the suitable representative of nonlinear fluids. Unlike the previous studies, where only the square of the shear ered to ease the numerical manipulations, quadratic power is also taken into account. rate term in the viscosity expression is consid- in the present study, the term containing the The curved streamlines of the CCF can cause the centrifugal instability leading to toroidal vortices, known as the Taylor vortices. It is further found that the critical Taylor number becomes lower as the pseudoplastic effect increases. The comparison with the existing measurements on the pseudoplastic CCF results in good agreement.
文摘We investigate numerical approximations based on polynomials that are orthogonal with respect to a weighted discrete inner product and develop an algorithm for solving time dependent differential equations.We focus on the family of super Gaussian weight functions and derive a criterion for the choice of parameters that provides good accuracy and stability for the time evolution of partial differential equations.Our results show that this approach circumvents the problems related to the Runge phenomenon on equally spaced nodes and provides high accuracy in space.For time stability,small corrections near the ends of the interval are computed using local polynomial interpolation.Several numerical experiments illustrate the performance of the method.
基金the Deutsche Forschungsgemeinschaft in the French-German DFG-CNRS research program 'Numerische Strmungssimulation-Simulation Numérique d'Ecoulements'National Nataral Science Foundation of China under granted number 10772044
文摘为轴的电流通过的液体金属的一口圆柱的喷气的捏不稳定性被调查。除从表面紧张发源的捏效果以外， Lorentz 力量，由轴的电流密度和相应方位角的磁场创造了，引起电磁的捏效果。这效果在电力工程引起了注意，因为它能与 self-healing 性质在液体金属水流限制 ers 的构造被使用。在这篇论文，一个简单模型用浅水近似被导出：描述完整的系统的方程为轴的速度和喷气的半径被归结为二个一个维的进化方程。为这个减少的系统的稳定性分析被执行为不稳定性产出批评电流密度和生长率。为有限不安模拟调查捏不稳定性的非线性的行为，浅水模型被执行。
