共查询到16条相似文献,搜索用时 125 毫秒
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动力学问题通常采用微分方程来描绘,但由于工程实际问题的复杂性,微分方程模型常伴随着解的不连续性、刚性或激波间断奇异性特点,传统方法很难求解,奇异性问题是计算动力学难点,同时也是国内外学者研究的热点.伪弧长数值算法是针对计算动力学中的奇异性问题所提出的,其基本思想为通过在解曲线上引入伪弧长参数,并增加一个约束方程,在伪弧长参数作用下,使得原始离散单元发生扭曲形变,从而达到消除或减弱奇异性的目的.本文首先介绍伪弧长方法求解定常对流-扩散方程的奇异性问题,并提出针对双曲守恒定律的局部伪弧长算法,其思想在于首先通过间断解的梯度变换来确定强间断所处位置,进而通过局部网格点重构以及数值修正来达到强间断处奇异性消除与降低的目的.针对高维问题,提出全局伪弧长方法,通过对整个计算区域内的网格点进行重构,使得所有网格点向奇异间断点处移动,从而降低间断点的影响域,达到降低奇异性的目的.重点讨论了三维全局伪弧长算法问题的计算难点,即三维空间网格扭曲大变形导致的数值算法不收敛,并提出在算法设计过程中采用分块重构与整体计算相结合的策略,实现了三维空间中的伪弧长数值算法,最后通过数值实验来验证伪弧长算法对于奇异性问题的有效性. 相似文献
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为了提高对冲击波强间断处的分辨率,通过引入弧长参数,使网格自适应地朝着间断处移动,并结合高精度WENO数值格式,进而达到了对大梯度物理量的高分辨率捕捉。针对网格移动造成的非均匀和非正交现象,通过坐标变换,使得计算过程在均匀正交的计算空间中进行。通过和有限体积下的数值结果对比,结合数值误差分析,可以看到高阶伪弧长数值算法不仅保证了高精度而且对间断的捕捉更加明显,在间断附近解的整体光滑性较好,网格的自适应移动使得解的奇异性得到了削弱,因此可以削弱高阶格式容易引起数值振荡这个缺点。最后采用高阶伪弧长算法计算了化学反应流问题,结果表明高阶伪弧长算法有着较快的收敛率,对于解决爆炸与冲击强间断问题有着较为明显的优势。 相似文献
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爆炸与冲击问题的大规模高精度计算 总被引:1,自引:0,他引:1
爆炸与冲击问题的数值模拟在国防和民用安全领域具有重要的工程实用价值.由于爆炸与冲击问题是一个多物质在高应变率、高温及高压条件下的强非线性的瞬态动力学问题,给数值模拟带来了很多的困难,为此,针对爆炸与冲击问题数值模拟中的一些关键和难点问题开展了研究.提出了三维非线性双曲守恒系统的伪弧长自适应网格算法,分析了算法的实现过程,数值结果表明该算法有效地提高了冲击波强间断处的分辨率.发展了针对气相爆轰数值模拟的附加龙格-库塔方法,对非线性对流项进行显示计算,化学反应源项进行半隐式计算,有效地解决了源项引起的刚性问题,计算结果表明该算法可以准确地捕捉和描述爆轰波的复杂结构和典型特征.针对三维工程实际物理问题中的大规模计算需求,给出了三维多物质流体动力学欧拉数值方法的并行化方法,开发了三维爆炸与冲击问题并行计算程序,并给出了针对该并行程序的测试方法.上述工作有利地解决了爆炸与冲击问题大规模、高精度计算中的一些难题.最后,开展了大口径聚能射流侵彻混凝土靶问题的数值模拟和实验研究,通过典型爆炸与冲击工程问题的计算验证了所研究数值方法的有效性. 相似文献
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重点研究了局部伪弧长方法在处理偏微分方程,尤其是双曲型偏微分方程出现激波间断的奇异性问题,对比分析了全局伪弧长方法空间转化的形式及其网格自适应的性质。为提高求解效率,提出了局部伪弧长方法,利用激波间断的性质,给出了判断奇异点位置以及模板选择的方法,涉及如何处理激波振荡,如何引入弧长参数,以及怎样求解间断等问题。通过数值算例验证了局部伪弧长在激波捕捉和追踪方面的可行性,通过比较局部伪弧长方法与Godunov方法处理不同初值条件的双曲问题,显示出局部伪弧长方法处理双曲偏微分方程的优越性,为伪弧长方法应用到物理问题奠定基础。 相似文献
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基于带化学反应的二维Euler方程,对圆柱形爆轰波的直接起爆和传播过程进行了二维数值模拟研究,拟分析起爆条件和初始压强对圆柱形爆轰波形成和传播的影响。研究发现,圆柱形爆轰波起爆成功向外传播的过程中,新的三波结构的生成标志着爆轰波进入稳定传播阶段。在起爆能量足够的情况下,起爆半径(曲率)的大小决定着三波结构初始形成时的数目和传播半径,起爆压强对其基本不产生影响;起爆半径大(曲率小)时,三波结构初始形成时的传播半径大、数目多,圆柱形爆轰波进入稳定传播阶段的传播距离长;数值模拟中,初始压强的提高,有助于圆柱形爆轰在较短的传播距离内进入稳定传播阶段。 相似文献
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A hyperbolic conservation equation can easily generate strong discontinuous solutions such as shock waves and contact discontinuity. By introducing the arc-length parameter, the pseudo arc-length method(PALM) smoothens the discontinuous solution in the arc-length space. This in turn weakens the singularity of the equation. To avoid constructing a high-order scheme directly in the deformed physical space, the entire calculation process is conducted in a uniform orthogonal arc-length space. Furthe... 相似文献
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The existence of a secondary discontinuity at the rear of a detonation front shown in experiments by Peraldi and Veyssiere
(1986) in stoichiometric hydrogen-oxygen mixtures with suspended 20-m starch particles has not been explained satisfactorily. Recently Veyssiere et al. (1997) analyzed these results using a
one-dimensional (1-D) numerical model, and concluded that the heat release rate provided by the burning of starch particles
in gaseous detonation products is too weak to support a double-front detonation (DFD), in contrast to the case of hybrid mixtures
of hydrogen-air with suspended aluminium particles in which a double-front detonation structure was observed by Veyssiere
(1986). A two-dimensional (2-D) numerical model was used in the present work to investigate abovementioned experimental results
for hybrid mixtures with starch particles. The formation and propagation of the detonation has been examined in the geometry
similar to the experimental tube of Peraldi and Veyssiere (1986), which has an area change after 2 m of propagation from the
ignition point from a 69 mm dia. section to a 53 mm 53 mm square cross section corresponding to a 33% area contraction. It is shown that the detonation propagation regime in
these experiments has a different nature from the double-front detonation observed in hybrid mixtures with aluminium particles.
The detonation propagates as a pseudo-gas detonation (PGD) because starch particles release their heat downstream of the CJ
plane giving rise to a non-stationary compression wave. The discontinuity wave at the rear of the detonation front is due
to the interaction of the leading detonation front with the tube contraction, and is detected at the farthest pressure gauge
location because the tube length is insufficient for the perturbation generated by the tube contraction to decay. Thus, numerical
simulations explain experimental observations made by Peraldi and Veyssiere (1986).
Received 5 July 1997 / Accepted 13 July 1998 相似文献
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Xu-Dong Zhang Bao-Chun Fan Ming-Yue Gui Zhen-Hua Pan Gang Dong 《Acta Mechanica Sinica》2012,28(1):66-72
Gaseous detonation propagating in a toroidal chamber was numerically studied for hydrogen/oxygen/nitrogen mixtures. The numerical method used is based on the three-dimensional Euler equations with detailed finiterate chemistry. The results show that the calculated streak picture is in qualitative agreement with the picture recorded by a high speed streak camera from published literature. The three-dimensional flow field induced by a continuously rotating detonation was visualized and distinctive features of the rotating detonations were clearly depicted. Owing to the unconfined character of detonation wavelet, a deficit of detonation parameters was observed. Due to the effects of wall geometries, the strength of the outside detonation front is stronger than that of the inside portion. The detonation thus propagates with a constant circular velocity. Numerical simulation also shows three-dimensional rotating detonation structures, which display specific feature of the detonationshock combined wave. Discrete burning gas pockets are formed due to instability of the discontinuity. It is believed that the present study could give an insight into the interesting properties of the continuously rotating detonation, and is thus beneficial to the design of continuous detonation propulsion systems. 相似文献
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波阻是飞行器超音速飞行的关键设计因素,精确捕捉激波在流场中的位置,是数值模拟含激波流场和精确计算波阻的一个重要研究内容.本文基于网格节点有限体积空间离散方法,采用AUSM格式与FVS格式的混合格式(MAUSM方法)计算对流通量,从而抑制在数值模拟流场出现的激波处振荡和过冲现象,确保AUSM准确捕获接触间断的特性和FVS格式捕捉激波的能力.本文使用MAUSM方法分别计算了在跨声速和超声速条件下的NACA0012翼型流场,并与中心差分格式的计算结果进行比较.结果表明,对于存在激波的翼型流场,MAUSM方法是有效的. 相似文献
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The propagation speed of a shock or detonation wave in a shock or detonation tube is usually determined by a time-of-flight
method by dividing the distance between two transducers with the propagation time of the disturbance signal. Some arbitrariness
is inherent in determining the propagation time by this method. A new method based on Haar and Morlet wavelet transforms is
reported. The method was applied to shock and detonation waves representing a step and a decaying spike discontinuity. The
wavelet methods can be applied to the step discontinuity provided that the SNR ratio is good. The wavelet methods worked well
for a decaying spike in the presence of noise. 相似文献
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陈少军 《应用数学和力学(英文版)》1993,14(6):545-554
In order to use the second-order5-point difference scheme mentioned to computethe solution of one dimension unsteady equations of the direct reflection of the strongplane detonation wave meeting a solid wall barrier,in this paper,we technicallyconstruct the difference schemes of the boundary and sub-boundary of the problem,and deduce the auto-analogue analytic solutions of the initial value problem,and at thesame time,we present a method for the singular property of the initial value problem,from which we can get a satisfactory computation result of this difficult problem.The difference scheme used in this paper to deal with the discontinuity problemsof the shock wave are valuable and worth generalization. 相似文献