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    The purpose of this thesis is to study dissipativity of delay functional differential dynamical systems and their corresponding numerical dissipativity of one-leg θ-method.
    We first establish a sufficient condition under which a class of delay functional differential dynamical systems is dissipative. Then we construct a one-leg θ-method to solve such dissipative dynamical systems and prove that the one-leg θ-method is dissipative if θ ∈ [1/2, 1].
    We consider another class of delay functional differential dynamical systems and establish a sufficient condition under which such delay functional differential dynamical systems are dissipative.
    The purpose of this thesis is to study dissipativity property of Runge-Kutta methods solving delay differential equations.
    本学位论文旨在研究Runge-Kutta方法求解滞时微分动力系统的数值耗散性。 主要内容包括:
    A sufficient condition is given to ensure that a class of linear delay differential equations is dissipative. We then apply Runge-Kutta methods combined with Lagrange interpolation procedure to these dissipative equations and investigate the numerical dissipativity of numerical solution.
    We study the numerical dissipativity of (k, l)-algebraically stable Runge-Kutta methods and give some numerical examples to demonstrate our theory.
    在已有的非线性滞时微分动力系统耗散的条件下,讨论了(k,l)-代数稳定的Runge-Kutta方法求解此耗散系统的数值耗散性。 最后同样给出数值例子验证我们的结论。
    It can avoid excessive numerical diffusion and difficulty in capturing moving boundaries in Euler coordinates, it also can avoid severe gird deformation in the Lagrange coordinates, yet it remains sharp resolution of slip lines.
    In this algorithm we introduce a free parameter δ, which may control the decay of amplitude and effectively filter the high mode response from the solution. When δ= 1/6, the basic equations of the algorithm have no numerical dissipation.
    It can be concluded that the numerical damping effect in computation is insignificant,the modified characteristics procedure for treatment of the convection has more accuracy than the upwind scheme.
    通过数值解与精确解的比较,表明本方法的数值耗散很小,用改型特征线方法处理对流算子较迎风离散格式有更高的精度; 两种处理对流算子的方法都没有伪振荡现象发生。
    It is shown that cubic spline method is effective for restraining numerical dispersion in numerical simulation of hydrodynamic dispersion equations with radioactive decay.
    To solve numerical dissipation and dispersion in numerical solution of convection-diffuson equation, a numerical procedure for simulating the convection-diffusion movement has been developed. The procedure is based on a governing equation which can be divided into Euler type convection equation and Lagrange type diffusion equation.
    In this paper a new approach for desgining upwind type schemes-the charac-terizing-integral method and its applied skills are introduced. The method is simple, convenient and effective.
    The numerical dissipation and dispersion of Hybrid Finite Analytic Method are investigated by using four-point implicit scheme of HFAM.
    It is found that the numerical dissipation is second order and the numerical dispersion is third order.
    In order to reduce the numerical viscosities of TVD schemes and improve their resolution, this paper suggests a new TVD scheme of Harten form with less numerical dissipation. Numerical experiments show that such a TVD scheme is better than Harten TVD scheme [1] and modified Harten scheme (Harten-Yee TVD scheme [2] ) in simulating boundary layer and vortices.
    为了减小TVD格式的数值粘性,提高TVD格式的分辨度,提出了一种 具有较小数值耗散的Harten型TVD格式.数值模拟结果表明,这种Harten型TVD 格式比原来的Harten格式[1]及其改进形式Harten—Yee[2]的TVD格式能更好地模拟 出边界层及涡流。
    The completed calculations of the flows in a dust-gas shock tube show that the quasicharacteristic method has the advantages of high precision and small numerical dissipation and dispersion.
    The SOUCUP scheme of Zhu and Rodi is used to decrease thenumerical dispersion.
    Here the LF scheme is a specified form of B-grid center difinite scheme used in MM4. We also simulate a heavy rain case of June 19, 1982 with the model′s water transport options of B-grid center scheme, Upstream scheme and Prather scheme, respectively.
    这些格式都是正定的,在理想风场的数值实验中几乎无数值耗散,无计算频散。 我们在B网格中央差格式(原MM4中的格式)、Upstream格式和Prather格式等模式选择项下,对1982年6月的一次梅雨期暴雨过程进行了数值对比实验。
    The paper also presents the basic ideas on reconstruction of numerical solution distribution,based on the proposed TVD requirements,to reduce numerical dissipation and improve resolution of the contact discontinuities and head/tail of rarefaction waves.
    An expression for the numerical damping and dispersion of panel method calculating ship wave-making problem is derived from Fourier analysis, It can be used to analyse not only the order of magnitude of er-rors concerned and their coupling effects in calculating ship wavemaking problem but also the errors in calculating other steady free-surface flows by panel method in principle.
    本文利用Fourier分析导出了船舶兴波问题面元法计算中的数值耗散及数值色散误差表达式. 该公式不仅可用于从量级上分析船波问题计算的有关误差及其耦合影响,原则上亦可用于其它具有自由表面的稳态流动问题面元法计算的误差分析.


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