Identification of diffusion parameters in a nonlinear convection–diffusion equation using the augmented Lagrangian method

Numerical identification of diffusion parameters in a nonlinear convection–diffusion equation is studied. This partial differential equation arises as the saturation equation in the fractional flow formulation of the two-phase porous media flow equations. The forward problem is discretized with the finite difference method, and the identification problem is formulated as a constrained minimization problem. We utilize the augmented Lagrangian method and transform the minimization problem into a coupled system of nonlinear algebraic equations, which is solved efficiently with the nonlinear conjugate gradient method. Numerical experiments are presented and discussed. This work was partially supported by the Research Council of Norway (NFR), under grant 128224/431.     

On the scavenging of SO2 by cloud and raindrops: II. An experimental study of SO2 absorption and desorption for water drops in air

For the purpose of testing our previously described theory of SO₂ scavenging a laboratory investigation was carried out in the UCLA 33 m long rainshaft. Drops with radii between 250 and 2500 m were allowed to come to terminal velocity, after which they passed through a chamber of variable length filled with various SO₂ concentrations in air. After falling through a gas separating chamber consisting of a fluorocarbon gas the drops were collected and analyzed for their total S content in order to determine the rate of SO ₂ absorption.The SO₂ concentration in air studied ranged between 1 and 60% (v). Such relatively large concentrations were necessary due to the short times the drops were exposed to SO₂ in the present setup. The present experimental results were therefore not used to simulate atmospheric conditions but rather to test our previously derived theory which is applicable to any laboratory or atmospheric condition. Comparison of our studies with the results from our theory applied to our laboratory conditions led to predicted values for the S concentration in the drops which agreed well with those observed if the drops had radii smaller than 500 m. In order to obtain agreement between predicted and observed S concentrations in larger drops, an empirically derived eddy diffusivity for SO₂ in water had to be included in the theory to take into account the effect of turbulent mixing inside such large drops.In a subsequent set of experiments, drops initially saturated with S (IV) were allowed to fall through S-free air to determine the rate of SO ₂ desorption. The results of these studies also agreed well with the results of our theoretical model, thus justifying the reversibility assumption made in our theoretical models.In a final set of experiments, the effects of oxidation on SO₂ absorption was studied by means of drops containing various amounts of H₂O₂. For comparable exposure times to SO₂, the S concentration in drops with H₂O₂ was found to be up to 10 times higher than the concentration in drops in which no oxidation occurred.     

缓变地形下β效应的Rossby代数孤立波

正压流体中,从准地转位涡方程出发采用摄动方法和时空伸长变换推导了在缓变地形下β效应的Rossby代数孤立波方程,得到Rossby波振幅满足带有缓变地形非齐次Benjamin-Davis-Ono(BDO)方程的结论.通过分析孤立Rossby波振幅的演变,指出了β效应、地形效应是诱导Rossby孤立波产生的重要因素,说明了在缓变地形强迫效应和非线性作用相平衡的假定下,Rossby孤立波振幅的演变满足非齐次BDO方程,给出在切变基本气流下缓变地形和正压流体中Rossby波的相互作用.     

Perfectly matched layer-absorbing boundary condition for finite-element time-domain modeling of elastic wave equations

The perfectly matched layer (PML) is a highly efficient absorbing boundary condition used for the numerical modeling of seismic wave equation. The article focuses on the application of this technique to finite-element time-domain numerical modeling of elastic wave equation. However, the finite-element time-domain scheme is based on the second-order wave equation in displacement formulation. Thus, the first-order PML in velocity-stress formulation cannot be directly applied to this scheme. In this article, we derive the finite-element matrix equations of second-order PML in displacement formulation, and accomplish the implementation of PML in finite-element time-domain modeling of elastic wave equation. The PML has an approximate zero reflection coefficients for bulk and surface waves in the finite-element modeling of P-SV and SH wave propagation in the 2D homogeneous elastic media. The numerical experiments using a two-layer model with irregular topography validate the efficiency of PML in the modeling of seismic wave propagation in geological models with complex structures and heterogeneous media.     

地震波动方程的局部间断有限元方法数值模拟

近年来,随着地震波数值模拟对计算精度和效率的要求越来越高,间断有限元方法开始受到越来越多的关注.本文中,针对具有吸收边界条件的二维地震声波波动方程,作者提出了一种基于局部间断有限元方法的数值模拟算法.该算法在空间上使用局部间断有限元方法进行离散,在时间上采用了显式蛙跳格式.在这种时空离散的组合方式下,每个时间步上,此算法在空间剖分的每个单元上的求解计算是相互独立的,因而具有极高的并行性.通过数值算例,我们将该算法与连续有限元方法进行了比较.结果表明,本算法不仅具有对起伏构造的良好适应性,而且在计算效率和计算精度等方面,都具有优越性.     

Spatio-temporal variations of reference crop evapotranspiration and pan evaporation in the West Songnen Plain of China

Abstract

The spatio-temporal variations of reference crop evapotranspiration (ET_ref) reflect the combined effects of meteorological variables, primarily wind speed, relative humidity, net radiation and air temperature. This study investigated the spatial distribution and temporal trends of ET_ref (calculated by the FAO-56 Penman-Monteith equation), pan evaporation (E_pan) and pan coefficient (K_p) in a 140?×?10³ km² semi-humid to semi-arid area in China. The results show that: (i) although the spatial distributions of ET_ref and E_pan are roughly similar and their spatial correlation is high over the growing season, K_p varied considerably in space due to high humidity in the east of the region and low humidity in the southwest; (ii) the monthly variations of ET_ref and E_pan are similar to that of net radiation and opposite to that of relative humidity, while the monthly variation of K_p is similar to that of relative humidity and opposite to that of wind speed, and the long-term trend is slightly increasing for ET_ref and E_pan, while significantly (10% significance level) increasing for K_p; and (iii) generally, the time series of ET_ref and E_pan from 1951 to 2001 could be divided into three phases due to variations of meteorological variables.

Citation Liang, L.-Q., Li, L.-J. & Liu, Q. (2011) Spatio-temporal variations of reference crop evapotranspiration and pan evaporation in the West Songnen Plain of China. Hydrol. Sci. J. 56(7), 1300–1313.     

Fission of a weakly nonlinear interfacial solitary wave at a step

The transformation of a weakly nonlinear interfacial solitary wave in an ideal two-layer flow over a step is studied. In the vicinity of the step the wave transformation is described in the framework of the linear theory of long interfacial waves, and the coefficients of wave reflection and transmission are calculated. A strong transformation arises for propagation into shallower water, but a weak transformation for propagation into deeper water. Far from the step, the wave dynamics is described by the Korteweg-de Vries equation which is fully integrable. In the vicinity of the step, the reflected and transmitted waves have soliton-like shapes, but their parameters do not satisfy the steady-state soliton solutions. Using the inverse scattering technique it is shown that the reflected wave evolves into a single soliton and dispersing radiation if the wave propagates from deep to shallow water, and only dispersing radiation if the wave propagates from shallow to deep water. The dynamics of the transmitted wave is more complicated. In particular, if the coefficient of the nonlinear quadratic term in the Korteweg-de Vries equation is not changed in sign in the region after the step, the transmitted wave evolves into a group of solitons and radiation, a process similar to soliton fission for surface gravity waves at a step. But if the coefficient of the nonlinear term changes sign, the soliton is destroyed completely and transforms into radiation. The effects of cubic nonlinearity are studied in the framework of the extended Korteweg-de Vries (Gardner) equation which is also integrable. The higher-order nonlinear effects influence the amplitudes of the generated solitons if the amplitude of the transformed wave is comparable with the thickness of lower layer, but otherwise the process of soliton fission is qualitatively the same as in the framework of the Korteweg-de Vries equation.     

Radially convergent groundwater flow in sloping terrain

Abstract

The groundwater flow equation governing the elevation (h) of the steady-state phreatic surface in a sloping aquifer fed by constant recharge over a bi-circular sector is rhh′ ? r ² Bh′ + Pr ² ? PR ² = 0, where r is the radial coordinate, P is a constant involving recharge and aquifer properties, and B is the slope of the aquifer—bedrock boundary. The derived flow equation describes radially convergent flow through a sloping aquifer that discharges to a water body of fixed head. One important simplification is that in which the width of the bi-circular sector is constant, and the draining land becomes a rectangular aquifer. The bi-circular sector and rectangular-strip groundwater flow problems are solved in terms of implicit equations. The solutions for the steady-state phreatic surfaces depend on the ratio of recharge to hydraulic conductivity, the slope of the aquifer-bedrock, and the downstream constant-head boundary. Computational examples illustrate the application of the solutions.     

基于逆散射级数法的鬼波压制方法

鬼波问题是影响海上地震资料分辨率和保真度提高的最重要因素之一.详细论述了逆散射级数理论和逆散射级数法鬼波压制原理,说明了逆散射级数方法进行鬼波压制理论的完善性和对鬼波描述的精确性.实现了基于逆散射级数理论的鬼波压制方法,方法以波动方程和Lippmann-Schwinger方程为基础,在频率-波数-波数域内构造与鬼波相关的压制算子,在不需要对地下介质作任何假设条件下实现地震数据驱动鬼波压制,并通过改善消除鬼波的压制算子,提高算法的稳定性.资料处理试验与处理结果分析表明,基于逆散射级数鬼波压制方法能在实现鬼波压制的同时较好保留有效反射波的信息,从而补偿地震资料低频损失和提高地震数据的保真度.数据处理试验还表明,研究方法能对低信噪比的地震资料进行有效的鬼波压制处理.建立了基于逆散射级数鬼波压制处理流程.