2-D Modeling and Calculations of Stratospheric Ozone and Influences of Convection, Diffusion, and Time

An engineering system approach of 2-D cylindrical model of transient mass balance calculations of ozone and other concerned chemicals along with fourteen photolysis, ozone-generating and ozone-depleting chemical reaction equations was developed, validated, and used for studying the ozone concentrations, distribution and peak of the layer, ozone depletion and total ozone abundance in the stratosphere. The calculated ozone concentrations and profile at both the Equator and a 60˚N location were found to follow closely with the measured data. The calculated average ozone concentration was within 1% of the measured average, and the deviation of ozone profiles was within 14%. The monthly evolution of stratospheric ozone concentrations and distribution above the Equator was studied with results discussed in details. The influences of slow air movement in both altitudinal and radial directions on ozone concentrations and profile in the stratosphere were explored and discussed. Parametric studies of the influences of gas diffusivities of ozone DO3 and active atomic oxygen DO on ozone concentrations and distributions were also studied and delineated. Having both influences through physical diffusion and chemical reactions, the diffusivity (and diffusion) of atomic oxygen DO was found to be more sensitive and important than that of ozone DO3 on ozone concentrations and distribution. The 2-D ozone model present in this paper for stratospheric ozone and its layer and depletion is shown to be robust, convenient, efficient, and executable for analyzing the complex ozone phenomena in the stratosphere. .

上海市气象场与SO_2浓度数值模拟

采用地形坐标系下适合于复杂地形且满足地—气耦合的静力学三维中 - β尺度气象预报模式 ,使用 0 8时的实测流场经变分法初始化后得到的初始流场 ,模拟研究了上海地区的局地流场时空演变特征。模式较细致地考虑了湍流、长短波辐射、凝结、蒸发、地表热力平衡等因子 ,在此基础上 ,使用有限元法数值求解一阶闭合的三维欧拉平流扩散方程 ,模拟了上海地区的 SO2 浓度分布。结果表明 :上海的局地流场具有明显的日变化特征 ,受海陆温差的影响明显 ,日间风速较夜间风速大 ,风向呈顺时针旋转 ;在不稳定层结情况下 ,高架点源排放的高空污染物对地面的污染物浓度有贡献 ,会造成地面污染物浓度升高。

A Vertex-Centered and Positivity-Preserving Finite Volume Scheme for Two-Dimensional Three-Temperature Radiation Diffusion Equations on General Polygonal Meshes

Two-dimensional three-temperature(2-D 3-T)radiation diffusion equa-tions are widely used to approximately describe the evolution of radiation energy within a multimaterial system and explain the exchange of energy among electrons,ions and photons.In this paper,we suggest a new positivity-preserving finite volume scheme for 2-D 3-T radiation diffusion equations on general polygonal meshes.The vertex unknowns are treated as primary ones for which the finite volume equations are constructed.The edgemidpoint and cell-centered unknowns are used as auxiliary ones and interpolated by the primary unknowns,which makes the final scheme a pure vertex-centered one.By comparison,most existing positivity-preserving finite volume schemes are cell-centered and based on the convex decomposition of the co-normal.Here,the conormal decomposition is not convex in general,leading to a fixed stencil of the flux approximation and avoiding a certain search algo-rithm on complex grids.Moreover,the new scheme effectively alleviates the nu-merical heat-barrier issue suffered by most existing cell-centered or hybrid schemes in solving strongly nonlinear radiation diffusion equations.Numerical experiments demonstrate the second-order accuracy and the positivity of the solution on various distorted grids.For the problem without analytic solution,the contours of the nu-merical solutions obtained by our scheme on distorted meshes accord with those on smooth quadrilateral meshes.

A Numerical Simulation of Air Flow in the Human Respiratory System Based on Lung Model

The lung is an important organ that takes part in the gas exchange process. In the study of gas transport and exchange in the human respiratory system, the complicated process of advection and diffusion (AD) in airways of human lungs is considered. The basis of a lumped parameter model or a transport equation is modeled during the inspiration process, when oxygen enters into the human lung channel. The quantitative measurements of oxygen are detached and the model equation is solved numerically by explicit finite difference schemes. Numerical simulations were made for natural breathing conditions or normal breathing conditions. The respiratory flow results for the resting conditions are found strongly dependent on the AD effect with some contribution of the unsteadiness effect. The contour of the flow rate region is labeled and AD effects are compared with the variation of small intervals of time for a constant velocity when breathing is interrupted for a negligible moment.

山区复杂地形上区域大气质量模式的试验研究

由于复杂地形上的气流多变，所以，进行区域空气质量模拟是比较困难的。根据大气污染总量控制和环境规划的需要，发展了一种可适用于山谷城市的大气质量模式。该模式的主要特点：（１）采用目前应用尚少的复杂地形上的三维边界层模式作为大气扩散模式所需的三维边界层要素场；（２）用复杂地形上的三维平流扩散模式和高斯扩散模式分别模拟低架源（包括面源）和高架源所造成的地面ＳＯ２浓度，然后将两者的模拟浓度在相应网格上叠加。验证结果表明，该混合模式可以较好地模拟山区复杂地形上的大气污染物浓度。

河流混合污染物浓度二维移流扩散方程的解析计算及其简化计算的条件Ⅰ:顺直宽河流不考虑边界反射

在恒定连续点源条件下,从移流扩散方程的二维解析解出发,给出了顺直宽河渠无边界反射情况下,污染混合区的二维解析计算方法和等浓度曲线方程,分析了污染混合区的形状变化规律。以简化二维移流扩散条件下的污染混合区长度为特征长度L、流速U和纵向扩散系数EL,定义了贝克来数Pe=UL/EL,给出了污染混合区无量纲上、下游长度、最大宽度及相应纵坐标和面积的试算公式及诺莫图。结果表明,污染混合区的无量纲长度主要取决于贝克来数,而无量纲最大宽度和面积既取决于贝克来数也与横向与纵向扩散系数的比值λy有关。在此基础上,给出了非保守物质污染混合区的修正计算方法,以及保守与非保守物质的计算分区图。系统地提出了二维移流扩散方程的简化计算条件。

时间分数阶二维对流扩散方程多点源强的数值反演

对于一类带有多个点源的二维反常扩散问题,基于Caputo意义下时间分数阶导数的离散,给出了一个有限差分求解格式.在已知点源个数及位置的前提下,根据终止时刻的浓度观测数据,应用最佳摄动量正则化算法对源强度识别反问题进行了有效的数值反演,并讨论了正则参数、分数微分阶数及数据扰动等因素对反演算法的影响.

Riesz空间分数阶对流-扩散方程的一种新型Crank-Nicolson有限体积法

分数阶微分方程作为整数阶微分方程的推广,近年来被广泛应用于科学和工程领域,从而受到越来越多学者的关注.本文提出一种新型Crank-Nicolson有限体积方法求解具有Dirichlet齐次边界的Riesz空间分数阶对流-扩散方程.为了得到Riesz空间分数阶对流-扩散方程的离散格式,在时间层上,利用Crank-Nicolson方法对一阶时间偏导数进行离散.在空间层上,利用有限体积法近似对流项的一阶空间偏导数和扩散项的Riesz空间分数阶偏导数.更进一步,我们也得到了该Crank-Nicolson有限体积离散格式的稳定性和收敛性两个主要理论结果.证明了该离散格式是无条件稳定的,以及在离散L2-范数下的收敛阶为O(h2+τ2),其中h和τ分别为空间和时间上的步长.最后,通过数值试验验证了该离散格式理论结果的正确性.