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21.
Hisashi Mikami 《国际流体数值方法杂志》1987,7(6):603-619
The piecewise linear method (PLM) based on time operator splitting is used to solve the unsteady compressible Euler equations describing the two-dimensional flow around and through a straight wall inlet placed stationary in a rapidly rotating supersonic flow. The PLM scheme is formulated as a Lagrangian step followed by an Eulerian remap. The inhomogeneous terms in the Euler equations written in cylindrical coordinates are first removed by Sod's method and the resulting set of equations is further reduced to two sets of one-dimensional Lagrangian equations, using time operator splitting. The numerically generated flow fields are presented for different values of the back pressure imposed at the downstream exit of the inlet nozzle. An oblique shock wave is formed in front of the almost whole portion of the inlet entrance, the incoming streamlines being deflected towards the higher pressure side after passing through the oblique shock wave and then bending down to the lower pressure side. A reverse flow appears inside the inlet nozzle owing to the recovery pressure of the incoming streams being lower than the back pressure of the inlet nozzle. 相似文献
22.
Many recent algorithmic approaches involve the construction of a differential equation model for computational purposes, typically
by introducing an artificial time variable. The actual computational model involves a discretization of the now time-dependent differential system, usually
employing forward Euler. The resulting dynamics of such an algorithm is then a discrete dynamics, and it is expected to be
“close enough” to the dynamics of the continuous system (which is typically easier to analyze) provided that small – hence
many – time steps, or iterations, are taken. Indeed, recent papers in inverse problems and image processing routinely report
results requiring thousands of iterations to converge. This makes one wonder if and how the computational modeling process
can be improved to better reflect the actual properties sought.
In this article we elaborate on several problem instances that illustrate the above observations. Algorithms may often lend
themselves to a dual interpretation, in terms of a simply discretized differential equation with artificial time and in terms
of a simple optimization algorithm; such a dual interpretation can be advantageous. We show how a broader computational modeling
approach may possibly lead to algorithms with improved efficiency.
AMS subject classification (2000) 65L05, 65M32, 65N21, 65N22, 65D18 相似文献
23.
A convergent-barrel (CB) cold spray nozzle was designed through numerical simulation. It was found that the main factors influencing significantly particle velocity and temperature include the length and diameter of the barrel section, the nature of the accelerating gas and its pressure and temperature, and the particle size. Particles can achieve a relatively low velocity but a high temperature under the same gas pressure using a CB nozzle compared to a convergent-divergent (CD) nozzle. The experiment results with Cu powder using the designed CB nozzle confirmed that particle deposition can be realized under a lower gas pressure with a CB nozzle. 相似文献
24.
Summary We study the integration theory for general integral metrics when restricted to upper integrals q, finding improvements in the relation between the classes of the q-integrable and the ql-integrable functions. We give new results and notions which lead to the desirable characterizations of q-integrable functions as ql-integrable f with q(|f|) < ∞, and of ql-integrable functions via the integrability of their upper truncations, under natural conditions which are fulfilled in most
finitely additive integration theories. 相似文献
25.
本文针对一类非饱和土壤水流问题,提出了基于二次插值的特征差分格式,得到了严谨的L2模误差估计.并作了数值试验,指明方法的有效性. 相似文献
26.
A one-dimensional nanodusty plasma was modeled by self-consistently coupling a plasma model with nanoparticle growth, charging,
and transport models. As nanoparticles grow from subnanometer to tens of nm in diameter, the numerical results predict a rich
spatiotemporal structure, including four distinct temporal phases: a charge-limited phase, a charge accumulation phase, an
early ion drag phase, and a sheath interaction phase. 相似文献
27.
Chi-Kwong Li Ilya M. Spitkovsky 《Journal of Mathematical Analysis and Applications》2003,282(1):329-340
Existence of the fractional powers is established in Banach algebra setting, in terms of the numerical ranges of elements involved. The behavior of the spectra and (for Hermitian ∗-algebras satisfying some additional hypotheses) the ∗-numerical range under taking these powers also is investigated. 相似文献
28.
29.
魏嵬 《数学的实践与认识》2007,37(16):76-83
为给转炉设计提供依据,需要计算炉液倾动的重心.利用数学方法将实际问题进行简化,通过分析炉液倾动过程中变量间的相互关系,来确定每个倾动角度对应情况下的液面位置.利用数学中三重积分的有关应用,进一步得出转炉在每个倾动角度为α∈(0,π2)时的重心计算方法及相关结论,在理论上为工程计算重心的方法提供参考. 相似文献
30.
Adam B. Levy 《Mathematical Programming》2007,110(3):615-639
Numerical methods for solving constrained optimization problems need to incorporate the constraints in a manner that satisfies
essentially competing interests; the incorporation needs to be simple enough that the solution method is tractable, yet complex
enough to ensure the validity of the ultimate solution. We introduce a framework for constraint incorporation that identifies
a minimal acceptable level of complexity and defines two basic types of constraint incorporation which (with combinations)
cover nearly all popular numerical methods for constrained optimization, including trust region methods, penalty methods,
barrier methods, penalty-multiplier methods, and sequential quadratic programming methods. The broad application of our framework
relies on addition and chain rules for constraint incorporation which we develop here. 相似文献