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研究并行算法解决应用并行计算机完成规模尽可能大的偏微分方程的数值求解问题。利用Hopf-Cole变换,将一维非线性Burgers方程转化为线性扩散方程,基于第二类Saul’yev型非对称格式和Crank-Nicolson格式对扩散方程进行差分离散,建立解Burgers方程的交替分段并行差分格式,并讨论该方法的稳定性,给出了数值算例。此算法把剖分节点分成若干组,在每组上构造能够独立求解的差分方程,因此具有并行本性,适合在高性能多处理器的并行计算机上使用。数值试验的结果表明此方法是有效的,且有较高的精度。 相似文献
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讨论交替蛙跳格式在二维POM的运用。这个交替蛙跳格式是在z坐标下开发的针对线性浅水波方程的一种新的高效无耗散的格式。首先通过一维问题的试验,给出了σ坐标下非线性浅水波的演化特性及其交替蛙跳格式的数值特性,证实该格式的可行性以及优于传统格式的计算效率、守恒性及稳定性。其次,针对该格式二维问题运用讨论了科氏项相应的数值处理,给出了一套完整的数值计算方法,并应用于正压方程和POM外模的数值计算。研究表明,交替蛙跳格式具有两倍于传统蛙跳格式的计算效率,且不再需要Assenlin时间滤波,由此避开了时间滤波带来的数值衰减,具有良好的数值守恒性能。 相似文献
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杨宗严 《中国海洋大学学报(自然科学版)》1994,(2)
利用Ｂ－样条函数．文中发展了一个对流扩散方程欧拉－拉格朗日方法的插值格式．改善了其数值频散性。算例表明，此格式优于一次和二次插值格式。文中给出了Ｂ－样条插值格式的二维及三维推广。 相似文献
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二维非线性浅水波的数值模拟 总被引：3，自引：0，他引：3
研究工作的目的在于建立一个能够模拟二维潮流、洪水波(长波)和浅水波浪(短波)的综合数学模型.基本模型建立在非线性的Boussinesq方程基础之上.本文主要讨论浅水波浪即短波的数值模拟.模型可以考虑必要的外力项,如柯氏力、风应力、大气压力和底摩阻力等.针对Boussinesq方程提出了一个全隐的二维差分格式,讨论了人工开边界的处理方法.模型被用来计算了突然扩张渠槽中的环流和单突堤后的水波绕射,取得了满意的结果. 相似文献
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一种基于Roe格式的有限体积法在二维溃坝问题中的应用 总被引：3，自引：0，他引：3
溃坝属于典型的非恒定含间断的浅水问题。应用有限体积法离散二维浅水控制方程的守恒型方程组,将基于近似黎曼解的Roe格式用于数值计算溃坝问题,并利用MUSCL方法构造二阶空间积分格式和预测-校正二步法构造二阶时间格式,从而使数值解的整体达到二阶,提高了精度。文中算法在一维溃坝的Stoker问题的数值结果与解析解进行对比,结果证明了此方法的可行性。应用此方法在二维溃坝问题上的结果,说明了此算法可有效模拟溃坝水流的演进过程。 相似文献
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海洋流体动力学的一种交替方向隐式二维数值模式 总被引：5，自引：2，他引：5
本文提出一种计算浅海潮汐、风暴潮及其他长周期波动的二维数值模式.动力学方程用建立在交错网格上的二步差分子方程近似,两步均为隐格式,其中一步用于计算水位和x方向速度分量,另一步计算水位和y方向速度分量.两步交替进行以获得每一时间步长的值,该格式具有二阶精度.文章用Von Neumann方法证明了该计算格式的线性差分方程是无条件稳定的.为检验数值模式的可靠性,本文作了一系列数值实验.在有一开边界的长方形平底和斜底水域中以开边界处周期性振动和海面处定常风应力驱动下,数值模拟所得结果与解析解完全一致;在水深不连续,边界封闭的矩形水域中,水位对定常风响应的数值解也与Leendertse模式计算结果完全一致.模式还用于对南海风暴潮进行后报,良好地再现了风暴增水过程. 相似文献
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将跳点法的基本思想应用于求解二维水位抛物型方程，从而构造了一种用于风暴潮数值预报的高效率差分格式。文中给出了这一格式的稳定性证明，并通过对实际风暴潮过程的模拟，证实了这一格式的稳定性和时效性 相似文献
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Motoyoshi Ikeda 《Journal of Oceanography》2003,59(1):79-86
An approximate variational method is proposed to assimilate an oceanographic data set with a numerical ocean model. In the
approximate method, the adjoint equation to a governing equation is derived and then converted to a finite difference form,
in contrast to the ordinary, exact variational method which is composed of a finite difference equation adjoint to the finite
difference governing equation. A cumbersome derivation of the adjoint equation is avoided, and finite difference schemes used
for the original governing equation are easily utilized for the adjoint equation. This method has been verified with twin
experiments. The flow field in the twin experiments is composed of dipole eddies in a two-layer quasi-geostrophic model. Initial
and boundary conditions are control variables. The descent converges towards the exact field within 50 iterations, showing
that the fundamental problem of the method (an unstable descent with a large number of iterations) does not appear. The approximate
method is promising and should be tried with real data.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
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N-S方程的数值解法及其在水波动力学中应用的综述 总被引：7，自引：0，他引：7
对于描述流体运动的基本方程N-S方程,现已开发出了多种不同的数值求解方法。其中以MAC法和VOF法为代表的网格数值方法较为成熟,并被逐渐用于实际工程的水动力研究中：以SPH和MPS为代表的粒子方法则刚刚起步．具有很大的发展空间。针对N-S方程中的能量耗散问题,采用雷诺时均化的方程形式仍是目前解决水动力问题的主要途径,但需要引入相应湍流模型,以封闭方程。本文首先对N-S方程求解方法的发展过程进行简要回顾,对一些重要的计算方法进行评述,简要介绍其在水波动力学中的应用;然后对时均化的N-S方程的主要封闭模式进行总结介绍;最后对数值求解N-S方程的发展趋势进行展望。 相似文献
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Lin Mingchung Hsiao Sungshan Hsu Yungcheng
Professor Dept. of Naval Architecture Ocean Engineering National Taiwan University Taiwan. Doctor Course Student Dept. of Naval Architecture Ocean Engineering National Taiwan University Taiwan 《中国海洋工程》1994,(3)
-Wave refraction-diffraction due to a large ocean structure and topography in the presence of a 'current are studied numerically. The mathematical model is the mild-slope equation developed by Kirby (1984). This equation is solved using a finite and boundary element method. The physical domain is devid-ed into two regions: a slowly varying topography region and a constant water depth region. For waves propagating in the constant water depth region, without current interfering, the mild- slope equation is then reduced to the Helmholtz equation which is solved by boundary element method. In varying topography region, this equation will be solved by finite element method. Conservation of mass and energy flux of the fluid between these two regions is required for composition of these two numerical methods. The numerical scheme proposed here is capable of dealing with water wave problems of different water depths with the main characters of these two methods. 相似文献
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The elliptic mild slope equation is used to simulate linear wave propagation over variable seabed topography with mild slopes.The governing equation is discretized by the finite difference method.Ba-sed on the BI-CGSTAB technique.an attractive variant of BI-Conjugate Gradients(BI-CG)method,theobtained linear algebraic system of equations is solved.Numerical experiments show that the BI-CGSTABmethod is efficient for solving the elliptic mild slope equation.The results obtained by the BI-CGSTAB-Ba-sed method are much the same as those obtained by other authors with different solution methods,but theconvergence rate is much faster than that of other methods. 相似文献
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A Fast Multipole Method (FMM) is developed as a numerical approach to the reduction of the computational cost and requirement memory capacity for a large in solving large-scale problems. In this paper it is applied to the boundary integral equation method (BIEM) for current diffraction from arbitrary 3D bodies. The boundary integral equation is discretized by higher order elements, the FMM is applied to avoid the matrix/vector product, and the resulting algebraic equation is solved by the Generalized Conjugate Residual method (GCR). Numerical examination shows that the FMM is more efficient than the direct evaluation method in computational cost and storage of computers. 相似文献
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C.C. Tung 《Applied Ocean Research》1979,1(4):209-212
The solution to the non-linear, stochastic, ordinary differential equation governing the dynamic response of offshore structures to random waves, hitherto achieved by the statistical equivalent linearization method, is approached in a different manner. It is shown that the correlation function of the response is governed by a non-linear integral equation which can be solved successively. To the first order of approximation, the solution coincides with that of the statistical equivalent linearization method. This equation is solved up to the second order. 相似文献
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应用内外解匹配的方法和驻相法推导了柱坐标系下地震引起的水面波动方程的解,即推导了地震海啸波生成与传播的理论方程,并对越洋地震海啸理论方程进行了求解。基于Boussinesq方程出发,建立了二维越洋海啸波传播数学模型,并对越洋海啸进行了数值计算,计算方法采用有限差分方法,差分格式采用交替方向隐格式(Alternating Direction Implicit即ADI方法)。利用越洋海啸计算模式对发生在大洋中的地震海啸进行了模拟,将数值模拟结果与地震海啸波理论方程的计算结果进行了比较,两种计算结果吻合较好。 相似文献
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《Ocean Engineering》1999,26(3):255-276
A Eulerian–Lagrangian method (ELM) is employed for the simulation of wave propagation in the present research. The wave action conservation equation, instead of the wave energy balance equation, is used. The wave action is conservative and the action flux remains constant along the wave rays. The ELM correctly accounts for this physical characteristic of wave propagation and integrates the wave action spectrum along the wave rays. Thus, the total derivative for wave action spectrum may be introduced into the numerical scheme and the complicated partial differential wave action balance equation is simplified into an ordinary differential equation. A number of test cases on wave propagation are carried out and show that the present method is stable, accurate and efficient. The results are compared with analytical solutions and/or other computed results. It is shown that the ELM is superior to the first-order upwind method in accuracy, stability and efficiency and may better reflect the complicated dynamics due to the complicated bathymetry features in shallow water areas. 相似文献
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利用有限元方法求解双曲型缓坡方程 总被引：4，自引：1，他引：4
本文提出了一种双曲型缓坡方程的有限元计算方法 ,在建立有限元积分方程时通过在造波线处加入脉动源项来实现内部造波 ,并在开边界处利用阻尼层吸波 ,减少了在边界处由于数值处理引起的误差。数值计算结果与实测值吻合良好。本方法可用于大区域波浪场的计算中 相似文献