天山上地幔对流与造山运动数值模拟
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摘要
大陆动力学是当今固体地球科学研究的主导方向之一,其核心问题是大陆构造变形及其动力学机制.造山带是大陆变形最强烈、地表形态最明显的构造,它所涉及的地表地质结构、地球物理场特征、深部作用过程以及地表作用,一直是人们关注的热点.造山动力学研究对推动大陆构造变形及其动力学机制研究具有不可替代的作用.
天山造山带远离板块边界,是现今世界上最为活跃的陆内造山带,被公认为研究陆内造山的天然实验场.刘启元(2004)提出了天山造山带动力学的10个关键科学问题.其中,塔里木板块的水平挤压与地幔对流作用对天山造山带的影响作用,以及二者之间相互关系是最核心的问题.
现今天山造山带的活动不属于原始的碰撞造山过程,而是在被剥蚀夷平的古老造山带上的“复活”过程.同时,深部地球物理探测显示,地幔对流可能对天山造山带的复活起到了相当重要的作用.因此,确定中国境内天山造山带下方地幔中是否存在对流,是天山陆内造山动力学研究需要首先解答的关键问题.随之,如果存在地幔对流,那么对流的形态如何?地幔对流对造山过程产生了什么影响?塔里木板块的水平挤压与地幔对流构成了怎样的相互关系?塔里木板块的水平挤压作用是否足以造就现今天山的变形?古老的天山造山带内部结构与物性在造山复活过程中起到了怎样的作用?这些问题都有待于在资料解释和定量分析的基础上进行深入探讨.
针对上述问题,本文首先确立了大陆构造变形及动力学定量研究的数学模型.采用热-流体连续介质的动量守恒方程、能量守恒方程和质量守恒方程,并引入了流体热力学的状态方程描述地幔对流和造山动力学过程.
实现了求解这些方程的“ALE FEM+MIC”方法,即“任意拉格朗日-欧拉(ALE)描述的有限单元方法(FEM)”和“网格-粒子(MIC)”技术相结合的数值求解新技术.在热-蠕变耦合的方程中,基本未知量是速度场和温度场.未知量通过ALE描述的有限单元方法求解.同时,方法中引入了“网格-粒子”技术,即在有限单元内部设置若干代表物质的“粒子”,通过粒子的移动跟踪物质的运动和变形.有限单元方法求解动量方程和连续性方程时采用了速度场和压力场等阶插值的压力场稳定化Petrov-Galerkin(PSPG)方法,求解能量方程时采用了流线迎风Petrov-Galerkin(SUPG)方法.ALE描述通过定义合理的网格移动方式跟踪计算区域边界的变化.网格-粒子算法中采用双线性插值与有限单元插值函数对应.有限单元计算与网格-粒子计算相对独立,两种方法计算的数据通过有限单元节点传递.ALE FEM+MIC方法使得包含边界变化的极其强烈的变形流动问题和强烈不连续边界条件问题均可以正常描述.算例表明计算程序具有较好的计算精度和数值稳定性.
Continental dynamics is one of the frontier fields in present earth sciences. The key problems of continental dynamics are the tectonic deformation and their mechanisms. As orogenic belts have strong deformation and apparent surface figures, orogenic dynamics research is an important branch of continental dynamics.
The Tianshan orogenic belt is a typical active intracontinental mountain belt, far from either the locus of collision between continents or a subduction zone. It is recognized as an outstanding natural laboratory of intra-continental deformation research. 10 key problems are presented by Liu Qiyuan (2004) about the Tianshan orogenic dynamics. The kernel problems of these are the influence of the horizontal compression of the Tarim plate and the mantle convection to the orogeny of Tianshan, as well as the relationship between these two different forces.
The activity of the Tianshan at present is not an original orogenic process of collision. It is a rejuvenation of an old orogenic belt which has been denuded and leveled off. Geophysical studies show that maybe mantle convection has played an important role in the uplift of Tianshan. So, it is the first problem to determine whether the mantle convection exists or not. If exists, how about the pattern and what is the influence of the mantle convection on the Tianshan orogenic process? What is the relationship between the horizontal compression of the Tarim plate and the mantle convection? What is the influence of the structures and properties of the ancient Tianshan? It is necessary to address these problems based on data interpretation and quantitative analysis.
Aiming at these issues, a mathematical model is established for the quantitative study of continental deformation and dynamics. The governing equations include the conservation equations of mass, momentum and energy, as well as the state equation.
The“ALE FEM + MIC”numerical method is accomplished which means the Arbitrary Lagrangian- Eulerian Finite Element Method combining with the Marker-in-cell technique. In particular, the unknown parameters (velocity and temperature) are calculated using the ALE FEM. The cell-markers in each element carry the material composition and history variables during the flowing process. The momentum and continuity equations are solved in terms of the pressure-stabilizing Petrov-Galerkin (PSPG) method with the equal-order interpolation of the velocity and pressure, and the energy equation is solved using the streamline upwind Petrov-Galerkin (SUPG) method. By means of ALE, the computational region can be tracked with moving boundaries. In the MIC algorithm, the bilinear interpolation corresponds to the interpolation function in the finite elements. The FEM and MIC algorithm are independent each other. The data in these two processes communicate through the nodal points. With the ALE FEM + MIC, the problems can be described for the variable boundary and extremely strong flow, as well as discontinuous boundary conditions. The numerical tests show that the precision and stability of the computational codes
天山造山带远离板块边界,是现今世界上最为活跃的陆内造山带,被公认为研究陆内造山的天然实验场.刘启元(2004)提出了天山造山带动力学的10个关键科学问题.其中,塔里木板块的水平挤压与地幔对流作用对天山造山带的影响作用,以及二者之间相互关系是最核心的问题.
现今天山造山带的活动不属于原始的碰撞造山过程,而是在被剥蚀夷平的古老造山带上的“复活”过程.同时,深部地球物理探测显示,地幔对流可能对天山造山带的复活起到了相当重要的作用.因此,确定中国境内天山造山带下方地幔中是否存在对流,是天山陆内造山动力学研究需要首先解答的关键问题.随之,如果存在地幔对流,那么对流的形态如何?地幔对流对造山过程产生了什么影响?塔里木板块的水平挤压与地幔对流构成了怎样的相互关系?塔里木板块的水平挤压作用是否足以造就现今天山的变形?古老的天山造山带内部结构与物性在造山复活过程中起到了怎样的作用?这些问题都有待于在资料解释和定量分析的基础上进行深入探讨.
针对上述问题,本文首先确立了大陆构造变形及动力学定量研究的数学模型.采用热-流体连续介质的动量守恒方程、能量守恒方程和质量守恒方程,并引入了流体热力学的状态方程描述地幔对流和造山动力学过程.
实现了求解这些方程的“ALE FEM+MIC”方法,即“任意拉格朗日-欧拉(ALE)描述的有限单元方法(FEM)”和“网格-粒子(MIC)”技术相结合的数值求解新技术.在热-蠕变耦合的方程中,基本未知量是速度场和温度场.未知量通过ALE描述的有限单元方法求解.同时,方法中引入了“网格-粒子”技术,即在有限单元内部设置若干代表物质的“粒子”,通过粒子的移动跟踪物质的运动和变形.有限单元方法求解动量方程和连续性方程时采用了速度场和压力场等阶插值的压力场稳定化Petrov-Galerkin(PSPG)方法,求解能量方程时采用了流线迎风Petrov-Galerkin(SUPG)方法.ALE描述通过定义合理的网格移动方式跟踪计算区域边界的变化.网格-粒子算法中采用双线性插值与有限单元插值函数对应.有限单元计算与网格-粒子计算相对独立,两种方法计算的数据通过有限单元节点传递.ALE FEM+MIC方法使得包含边界变化的极其强烈的变形流动问题和强烈不连续边界条件问题均可以正常描述.算例表明计算程序具有较好的计算精度和数值稳定性.
Continental dynamics is one of the frontier fields in present earth sciences. The key problems of continental dynamics are the tectonic deformation and their mechanisms. As orogenic belts have strong deformation and apparent surface figures, orogenic dynamics research is an important branch of continental dynamics.
The Tianshan orogenic belt is a typical active intracontinental mountain belt, far from either the locus of collision between continents or a subduction zone. It is recognized as an outstanding natural laboratory of intra-continental deformation research. 10 key problems are presented by Liu Qiyuan (2004) about the Tianshan orogenic dynamics. The kernel problems of these are the influence of the horizontal compression of the Tarim plate and the mantle convection to the orogeny of Tianshan, as well as the relationship between these two different forces.
The activity of the Tianshan at present is not an original orogenic process of collision. It is a rejuvenation of an old orogenic belt which has been denuded and leveled off. Geophysical studies show that maybe mantle convection has played an important role in the uplift of Tianshan. So, it is the first problem to determine whether the mantle convection exists or not. If exists, how about the pattern and what is the influence of the mantle convection on the Tianshan orogenic process? What is the relationship between the horizontal compression of the Tarim plate and the mantle convection? What is the influence of the structures and properties of the ancient Tianshan? It is necessary to address these problems based on data interpretation and quantitative analysis.
Aiming at these issues, a mathematical model is established for the quantitative study of continental deformation and dynamics. The governing equations include the conservation equations of mass, momentum and energy, as well as the state equation.
The“ALE FEM + MIC”numerical method is accomplished which means the Arbitrary Lagrangian- Eulerian Finite Element Method combining with the Marker-in-cell technique. In particular, the unknown parameters (velocity and temperature) are calculated using the ALE FEM. The cell-markers in each element carry the material composition and history variables during the flowing process. The momentum and continuity equations are solved in terms of the pressure-stabilizing Petrov-Galerkin (PSPG) method with the equal-order interpolation of the velocity and pressure, and the energy equation is solved using the streamline upwind Petrov-Galerkin (SUPG) method. By means of ALE, the computational region can be tracked with moving boundaries. In the MIC algorithm, the bilinear interpolation corresponds to the interpolation function in the finite elements. The FEM and MIC algorithm are independent each other. The data in these two processes communicate through the nodal points. With the ALE FEM + MIC, the problems can be described for the variable boundary and extremely strong flow, as well as discontinuous boundary conditions. The numerical tests show that the precision and stability of the computational codes
引文
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