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详细介绍了无网格伽辽金法(EFGM)基本原理,并将其应用于非均质多孔介质中的稳定地下水流问题,用具体算例将无网格伽辽金法计算结果与传统有限元法(LFEM)计算结果作比较,计算表明无网格伽辽金法具有较高的精度。 相似文献
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大体积混凝土温度裂缝扩展过程模拟 总被引:1,自引:0,他引:1
大体积混凝土的温度裂缝是关系到水电工程中混凝土大坝安全的重要问题,它贯穿混凝土坝的施工期直至运行期。重点探讨了应用无网格法求解大体积混凝土温度裂缝扩展过程的模拟方法。无网格法采用节点来离散求解域,特别适用于裂缝开裂过程的模拟。结合混凝土热传导问题推导了伽辽金无网格方法控制方程和基本算法步骤,编制了混凝土温度场计算和温度裂缝扩展过程模拟的无网格法程序,通过具体的算例验证了所编制的伽辽金无网格程序的正确性。数值算例的计算结果表明,无网格法能够有效地模拟混凝土块在温度应力作用下的开裂发展过程,计算结果符合大体积混凝土块在均匀温降和基础强约束条件下的裂缝分布规律。 相似文献
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无单元法(element free galerkin method)是一种基于滑动最小二乘法构造插值函数的无网格数值方法。以该方法中插值函数及其导函数为基础,从变分原理出发,建立了弹性地基上正交各向异性Mindlin板的无单元法求解控制方程,其中弹性地基采用Winkler地基模型。对该理论方法进行了相应的程序实现,最后通过算例分析表明了提出方法用于水工结构中弹性地基板问题分析的可行性和有效性。 相似文献
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用双曲线切线模量方程计算地基非线性沉降 总被引:10,自引:1,他引:9
提出了一种利用原位试验成果求解非均质非线弹性地基最终沉降的新方法。对分层原状土载荷试验或螺旋板试验成果进行双曲线拟合,建立分层原状土切线模量与竖向附加应力的关系方程;在沉降计算公式中引入附加应力修正系数,以考虑基础埋深、地基非均质非线性特征等因素对应力分布的影响;利用双曲线切线模量方程及附加应力弹性解,可准确求解地基的总沉降。通过对几个压板载荷试验成果的拟合分析,得出了各土类的双曲线切线模量方程,用于求解地基在各级荷载下的沉降。计算结果表明,计算值与实测值吻合得很好。该方法原理简单、参数可靠、结果准确,为地基沉降计算开辟了一条新途径。 相似文献
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利用扩展精细积分法求解横观各向同性地基的平面应变问题。扩展精细积分法具有高精度和较高计算效率的特点,是求解微分方程的有效方法,相比于解析法可以节省大量理论推导工作量。从直角坐标下弹性力学控制方程出发,推导出Fourier变换域内地基的常微分矩阵方程;之后对地基微层元进行消元合并,进一步得到荷载作用在地基内部时层状地基的扩展精细积解。与已有文献的对比验证了方法的精确性,并分析了横观各向同性参数、层状性质和荷载作用点对计算结果的影响。结果表明:土体竖向位移随着横观各向同性参数n的增大而减小,而随着横观各向同性参数m的增大而增大;荷载作用点 的变化只对作用点以上的土体有影响,而上层土体的模量对竖向位移计算结果的影响更为显著,土体成层性对沉降的影响要比对竖向应力的影响更为显著。 相似文献
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讨论了高阶Duffing型微分方程周期解的存在性,此类方程是二阶Duffing型方程的推广,具有重要的理论意义。利用同胚延拓和不动点方法,构造处理了一类比文献所述条件更弱的Duffing型方程。通过构造一个先验界,利用Schaud-er不动点方法得到解的存在性结论,所使用的方法能广泛适用于各种边界条件。 相似文献
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在有较厚沉积物覆盖的地洼盆地中,如何利用已有的重力资料研究被掩埋目的层的分布、厚皮等,是沉积盆地及能源研究等方面的一个重要任务。本文的电子计算机正、反演处理,正是这方面的一个尝试。 相似文献
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由于非饱和土的渗透系数是基质吸力的函数,使得控制方程带有强非线性的特征,进而使得控制方程的解析求解变得十分困难。同伦分析法对级数基函数和辅助线性算子的选择具有更大的自由性、灵活性,且收敛性的控制和调节更加容易实现,求解强非线性微分方程时在选择线性算子以及辅助参数上具有明显的优势。因此,针对非饱和土固结方程的非线性特征,对于处于地表浅层的非饱和土层,假设孔隙气压力为大气压力,在Richard经验公式与非饱和土一维固结理论的基础上,推导了非饱和一维固结无量纲控制方程;应用同伦分析法,通过选取适当的初始猜测解与辅助参数,将该非线性方程转换为线性的微分方程组并求解得到固结问题的级数解。此外,以压实高岭土为研究对象,在收集相关试验参数基础之上,将由同伦分析法求得的固结问题的近似解析解与有限差分法数值结果相对比,分析结果验证了解析解的正确性。 相似文献
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We compared diurnal variations in dissolved gaseous mercury (DGM) concentration and in losses of dissolved organic carbon fluorescence (DOCF) in four boreal Canadian Shield lakes, in one beaver pond, and in filtered and unfiltered water from a wetland in Lake St. Pierre, a fluvial lake of the St. Lawrence River. These systems were chosen to represent a spectrum of DOC. We also determined the contribution of UVB, UVA and visible light on DGM photo-induced production in the four lakes. Our results showed a strong relationship between DGM concentrations and light intensity and between DGM production and losses in DOCF, in all study sites. We also observed higher rates of DGM formation and of DOCF bleaching in the presence of UV radiation. Under UVB light, production of DGM was higher in clear lakes than in the humic ones. Inversely, in the UVA range, DGM production tended to be higher in humic lakes. We suggest that DOCF bleaching can be used as a proxy for the rate of formation of reactive species that may alter the redox state of mercury in surface waters. We also have indications that DGM production is more important in clear than in humic waters. 相似文献
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格点法是在计算流体力学中首先发展起来的数值模拟新方法,共根本思想是对问题重新建模,建立直接模拟流体运动的离散格点模型。本文以一阶拟线性双典型方程及Kdv方程为例,推广这种求解一般偏微分方程的。它是运用多尺度分析方法,构造出格点模型的演化方程的局部平衡分布函数。数值试验表明,该方法程序实现简单,求解速度快,数值结果令人满意。 相似文献
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正演数值模拟是反演成像的基础。为了实现磁法勘探精细化反演成像与定量解释,本文利用把一个大问题分解为多个小问题的思路,提出一种基于泊松方程的高效、高精度空间波数混合域二度体磁异常数值模拟方法。该方法利用傅里叶变换把二度体磁位偏微分方程转换为一维常微分方程,并采用基于二次插值的一维有限单元法求解该方程,进而通过反傅里叶变换得到空间域磁异常。在模型算例中,分别设计截面为矩形的常磁化率和变磁化率二度体模型,针对本文算法的计算精度和计算效率进行了验证。模型算例结果表明:该算法计算精度高,相对误差绝对值均小于1%;计算速度快,网格节点剖分2 501×2 501的模型模拟时间为4.18 s;适用于任意复杂地形模型。 相似文献
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Piret Cécile Dissanayake Nadun Gierke John S. Fornberg Bengt 《Mathematical Geosciences》2020,52(4):477-497
Mathematical Geosciences - A robust, high order modeling approach is introduced, based on the finite difference-based radial basis functions method, for solving the groundwater flow equation in the... 相似文献
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Aqueous production and water-air exchange of elemental mercury (Hg0) are important features of the environmental cycling of Hg. We investigated Hg0 cycling in ten Arctic Alaskan lakes that spanned a wide range in physicochemical characteristics. Dissolved gaseous Hg (DGM, dominated by Hg0) varied from 40 to 430 fM and averaged 200 fM. All surface waters were supersaturated relative to the atmosphere. DGM averaged 3 ± 2% of dissolved (i.e., filter passing) dissolved total mercury (DTM) and 15 ± 6% of dissolved labile Hg (DLM). In-lake DGM profiles generally followed the vertical distribution of light, indicating photoreduction of Hg(II) complexes as a source of Hg0. Additionally, DGM correlated linearly with DLM (r2 = 0.82, p < 0.0001) in the lake surface, signifying that Hg complexes (mostly organic Hg associations) in dissolved phase are photoreducible and contribute to production of DGM. Further, a positive relation between DGM/DTM and both Ka (light attenuation coefficient; r2 = 0.73, p < 0.02) and DOC (r2 = 0.60, p = 0.02) suggests that solar radiation and dissolved organic matter control DGM production and its cycling. An average rate of DGM formation (0.6 ± 0.2% of DTM d−1; range, 0.20.8) was estimated by assuming steady state with the evasional rate. In-lake DGM formation occurs at lower rates in waters with greater suspended particulate matter and dissolved organic carbon (DOC), pointing to the significant role of organic matter plays in controlling DGM formation in these aquatic systems. Estimated evasional fluxes of Hg0 (average, 140 ± 50 pmol m−2 d−1; range, 60-200) were comparable to those of temperate lakes (e.g., Wisconsin, Michigan). In arctic lakes, the rate of evasion during ice-free periods (7 ± 3 nmol m−2 yr−1) is similar to the atmospheric input of Hg (wet + dry) to the lakes based on levels in summertime precipitation but not including additional sources, e.g., springtime depletion. 相似文献
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考虑表皮效应竖向非均匀分布,建立各向异性承压层3D稳态井流数学模型,为求得问题的解,首先将表皮效应系数视为分段连续函数,再根据该分段函数将承压层划分成N层,然后通过差分法将问题转化为求解矩阵微分方程边界值问题,最后通过矩阵理论求得相应问题的解。应用数学软件对所求得解进行编程,并应用于实例计算和分析中。结果表明,在距竖井较近处,承压层水头降和流量沿竖向分布均与表皮效应系数函数变化趋势相反,即承压层某深度处的表皮效应系数越大(小),则相应位置的水头降和流量越小(大);而距竖井较远处,仅当竖向渗透系数相对于水平渗透系数较小时,才仍具有前述变化规律;承压层不同深度处的水头降沿径向的分布曲线的幅度值,不仅取决于该处的表皮效应系数大小,而且取决于竖向渗透系数与水平渗透系数相对值大小 相似文献
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M. H. Hashemi 《Geomechanics and Geoengineering》2015,10(4):243-248
One of the significant problems in geo-environmental and geotechnical engineering is the unsaturated flow of soil in unsaturated soils. The model of this phenomenon in porous media is governed by the Richards equation. In this paper a new, efficient, iterative method is used to handle the Richards equation. This new technique is obtained from the variational iteration method by a simple reconstruction that is the Laplace iteration method (LIM). In order to evaluate the efficiency and accuracy of the solutions obtained by the proposed method, two representative examples were investigated. The obtained results show that the Laplace iteration method is a very effective method, simplifies the difficulty of classical techniques and is quite accurate for systems of partial differential equations. 相似文献