共查询到19条相似文献，搜索用时 140 毫秒
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本文建立了一种求解地下水中污染质运移方程的有限体积法。通过定义一种三角形控制体并求控制方程的应变量在它上面的平均值,这种格式就将有限元法处理复杂几何内蕴的灵活性和有限差法的简洁性结合起来。用高密迎风格式对平流项进行了离散。这种方法以“单调插值”原理为基础保证单调性,以保护格式的性质,它也以相邻控制体界面上局部黎曼问题的精确解为基础。这样,对所有单元peclet数都完全避免了数值振荡。在对弥散通量离散化的同时,得到了一种局部一阶。整体二阶精度的近似解与普通的迎风格式相对比,当遇到浓度尖锋时会产生少量的数值粘滞性.一些数值检验表明它与解析解很一致。本文求解了一个含有非平衡反应项的假想问题,来说明所提出的求解地下水运移方程方法的适用性。 相似文献
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天然水体具有形状复杂的计算区域和水下地形。本文采用无结构的网格以适合这一情况,并能方便地根据工程应用的要求局部地和适应性地加密网格。相应地,对二维水流计算问题采用了有限体积法的数学表示。跨单元边界的法向数值通量通过用Osher格式求解黎曼问题得到。文中给出了适合于二维浅水方程组的有关单元界面和各种物理边界的法向数值通量公式。分析了这一格式所具有的优点,包括:普适性、守恒性、逆风性、单调保持性、高效性、对间断的高分辨率、边界处理和内部格式相容,以及不引入数值边界条件等。最后,通过长江口南支水流计算的实例,阐明其良好性能。 相似文献
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基于有限体积方法和结构化网格,建立了海底滑坡引起的波浪传播数值模型。模型控制方程为考虑了海床随时间变化的二维浅水方程。采用中心迎风格式计算控制体界面数值通量,采用线性重构技术、局部海床高程处理技术和全隐式离散底摩阻项,保证了格式的和谐性、守恒性和水深非负性,有效处理了海岸动边界问题。时间积分采用具有强稳定性质的二阶龙格-库塔方法（ssp RK）。针对滑坡体兴波经典算例开展数值模拟,将计算结果与解析解、实验结果及其他模型计算结果进行比较和分析。结果表明,对于所考虑的计算工况,模型能较合理地模拟滑坡兴波的产生、传播和爬高过程。 相似文献
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波动方程数值模拟是研究地震波传播机理的重要工具,有限差分求解波动方程是当前地震波数值模拟的主要方法之一。当地下介质中的地震波速度较低或地震波高频成分丰富时,常规有限差分技术常常产生严重的数值频散误差,这种误差会降低数值模拟的精度,影响对地震波传播机理的分析。为压制地震波数值模拟时产生的数值频散误差,提高波场模拟精度,提出了基于NAD算子的时间四阶精度波动方程差分格式。根据对应的差分格式,分析了该差分格式的数值频散关系。与常规四阶精度差分算法的频散曲线相比,基于NAD时间四阶精度差分方法不但能够实现时间频散的有效压制,同时其基于更多网格点的位移分量和位移梯度分量空间微分求解方法还能够实现空间频散的有效压制。另外在相同模型条件下,基于NAD算法的声波方程时间四阶差分解法可采用大网格对模拟空间进行差分离散,减少网格数,提高计算效率。 相似文献
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在有限体积法框架下应用通量向量分裂(FVS)格式进行平面二维水流 水质模拟。通过对偏微分方程进行有限体积的积分离散、利用通量的旋转不变性,把二维问题转化为一系列局部的一维问题进行求解,采用FVS格式计算各跨单元边界的水量、动量及污染物输运等通量。应用该格式计算了理想条件下的浓度输移,其结果与精确解拟合很好;模拟了长江江苏靖江段的水质及污染带,计算结果与水质监测值相当吻合,为长江江苏干流段水质评价提供了科学依据。 相似文献
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采用一维-二维耦合数学模型对溃堤洪水进行模拟,可以发挥两者优势,提高计算效率。将基于黎曼近似解Godunov格式的一维、二维水流数学模型通过堰流公式进行耦合,实现交界面的水力要素交互;一维、二维模型均采用中心形式的有限体积法求解,分别采用HLL格式和Roe格式计算界面通量,具有一致的空间同步性。通过经典算例验证了模型的可靠性和稳定性,应用耦合模型对1998年松花江干流胖头泡溃堤洪水进行了模拟计算,较好地模拟了溃堤洪水的演进过程与淹没范围,对200年一遇洪水的分洪效果进行了分析,为此区域的分洪利用及松花江中上游防洪调度提供参考依据。 相似文献
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基于结构网格,采用有限体积法建立了二维水动力学模型,模拟溃坝洪水在复杂实际地形条件下的流动过程。该模型采用中心迎风格式求解界面通量,并结合对界面变量的线性重构,使其具有空间上的二阶精度。分别采用中心差分方法和半隐式方法对底床坡度项和摩擦阻力项进行离散,保证了模型的和谐性和稳定性。对于复杂地形条件下溃坝洪水的模拟,负水深的产生是影响模型稳定的关键因素。当库朗特数小于0.25时,模型能够保证任何时刻的计算水深都是非负的,而无需对负水深单元进行特殊处理。因此,相比于现有的大部分溃坝洪水模型,该模型具有更强的鲁棒性和稳定性。 相似文献
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Piyang Liu Gary Douglas Couples Jun Yao Zhaoqin Huang Wenhui Song Jingsheng Ma 《Computational Geosciences》2018,22(5):1187-1201
The two-scale continuum model is widely used in simulating the reactive dissolution process and predicting the optimum injection rate for carbonate reservoir acidizing treatment. The numerical methods of this model are currently based on structured grids, which are not applicable for complicated geometries. In this study, a general numerical scheme for simulating a reactive flow problem on both structured and unstructured grids is presented based on the finite volume method (FVM). The convection and diffusion terms involved in the reactive flow model are discretized by using the upwind scheme and two-point flux approximation (TPFA), respectively. The location of the centroid node inside each control volume is moved by using an optimization algorithm to make the connections with the surrounding elements as orthogonal as possible, which systematically improves the accuracy of the TPFA scheme. Additionally, in order to avoid the computational complexity resulting from the discretization of the non-linear term, the mass balance equation is only discretized in the spatial domain to get a set of ordinary differential equations (ODEs). These ODEs are coupled with the reaction equations and then solved using the numerical algorithm on ODEs. The accuracy and efficiency of the proposed method are studied by comparing the results obtained from the proposed numerical method with previous experimental and numerical results. This comparison indicates that, compared with the previous methods, the proposed method predicts the wormhole structure more accurately. Finally, the presented method is used to check the effect of the domain geometry, and it is found that the geometry of the flow domain has no effect on the optimum injection velocity, but the radial domain requires a larger breakthrough volume than the linear domain when other parameters are fixed. 相似文献
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针对溃坝水流数值模拟面临的复杂地形和不规则边界等问题,基于结构网格建立了适应复杂地形和不规则边界的溃坝水流数值模拟有限体积模型（HydroM2D）。模型基于具有守恒特性的二维浅水方程,利用HLLC格式的近似Riemann解计算网格界面通量,利用MUSCL-Hancock法不断向前积分,使模型在时空上具有二阶精度;对源项进行离散处理确保模型的稳定性;模型引入有效干湿边界和不规则地形边界处理方法,准确模拟了干湿单元的动态交替和复杂边界上的水流特性。最后分别利用水槽试验、物理模型和实际算例对模型进行验证。结果表明,该模型对不同情景下的溃坝洪水模拟结果和实测资料以及现有模型模拟结果具有较高的一致性,模拟精度较高,稳定性较好,具有推广应用价值。 相似文献
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建立了基于高阶Boussinesq水波方程的一维波浪破碎数值模型。基于一组具有二阶完全非线性特征的Boussinesq水波方程,建立了交错网格下的高精度差分格式,推导了适用于该组方程的永形波解析解,其和松弛造波技术相结合实现了数值波浪水槽中(强)非线性波浪的无反射入射。通过模拟封闭容器内水体晃动问题对数值格式进行了验证,通过模拟孤立波在斜坡海岸上的浅化过程说明了将方程从弱非线性发展到完全非线性的必要性。采用涡粘方法处理波浪破碎,利用物理模型实验数据,分析了模型中各波浪破碎参数对数值结果的影响并对参数进行了率定。应用该模型对规则波在斜坡海岸上的传播、变浅以及破碎过程进行了数值模拟研究,数值结果同实验数据吻合良好,验证了模型的有效性。 相似文献
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A numerical procedure is described for the analysis of the vertical deformation and the stress distribution of the strip footings
on layered soil media. Three layers of soil with different stiffness are considered with the middle soil layer the thinnest
and most stiff layer. The soil media is discretized and using the theory of elasticity, the governing differential equations
are obtained in terms of vertical and horizontal displacements. These equations along with appropriate boundary and continuity
conditions are solved by using the finite difference method. The vertical and horizontal displacements, strains and stresses
are found at various nodes in the soil media. Parametric studies are carried out to study the effect of the placement depth
of the middle soil layer, the relative ratios of the moduli of deformation of the soil layers on the vertical displacement
of the footing and the vertical stress distribution. These studies reveal that the middle thin but very stiff layer acts like
a plate and redistributes the stresses on the lower soft soil layer uniformly. The displacement on the top and bottom of the
middle soil layer is almost the same showing that the compression of the middle layer is negligible as it is very stiff. 相似文献
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This paper presents a complete finite‐element treatment for unsaturated soil problems. A new formulation of general constitutive equations for unsaturated soils is first presented. In the incremental stress–strain equations, the suction or the pore water pressure is treated as a strain variable instead of a stress variable. The global governing equations are derived in terms of displacement and pore water pressure. The discretized governing equations are then solved using an adaptive time‐stepping scheme which automatically adjusts the time‐step size so that the integration error in the displacements and pore pressures lies close to a specified tolerance. The non‐linearity caused by suction‐dependent plastic yielding, suction‐dependent degree of saturation, and saturation‐dependent permeability is treated in a similar way to the elastoplasticity. An explicit stress integration scheme is used to solve the constitutive stress–strain equations at the Gauss point level. The elastoplastic stiffness matrix in the Euler solution is evaluated using the suction as well as the stresses and hardening parameters at the start of the subincrement, while the elastoplastic matrix in the modified Euler solution is evaluated using the suction at the end of the subincrement. In addition, when applying subincrementation, the same rate is applied to all strain components including the suction. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
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平面波的传播问题通常可以归结为一维波动方程的定解问题。在非均匀介质中,即使简单的一维波动方程也需要借助于数值方法获得近似解。3层5点古典差分格式是计算偏微分方程一种常用算法,作为一种显式迭代格式,需要满足稳定性条件 ,其中 为波速, 为空间采样间隔, 为时间采样间隔。当 时, ,古典差分格式达到临界稳定状态。在这种情况下,平面波在 时间内的传播距离恰好等于空间采样间隔,差分格式真实地反映了平面波的传播原理,因而可以得到一维波动方程的精确解。但是,由于在非均匀介质中存在不连续的波阻抗界面,此方法不适于计算非均匀介质的波场。为了将临界稳定情况下的古典差分格式推广应用至非均匀层状介质,提出了一种能够处理波阻抗界面的有限差分格式,并应用傅里叶分析法得到其稳定性条件。模型算例验证了此算法的正确性。 相似文献
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Fluid injection–induced tensile opening is modeled using an extended finite volume method (XFVM). An embedded fracture strategy is used for the flow problem, that is, the fractures are discretized using finite volume segments without resolving the grid around them. Further, the discontinuities across fractures are modeled using special basis functions. The fracture openings due to enhanced fluid pressure and the associated shear slip due to traction free boundary condition on the fracture segments are both modeled using these special discontinuity basis functions. Mass transfer between fractures and matrix is modeled using the pressure difference. The enhancement of fracture storativity due to tensile opening leads to stronger coupling between flow and mechanics. An iterative scheme relying on the fixed-stress approach for fractures, which conserves the stress dependent terms over each iteration of the flow problem, has been introduced. Tensile opening has been simulated for single fractures embedded in two- and three-dimensional matrices. The convergence criterion for sequentially implicit fixed-stress scheme for fractures embedded in elastic media is established and has been validated numerically. Further, for 2D simulations, the effect of the matrix permeability for fracture propagation due to tensile opening has been studied. 相似文献