超短脉冲激光作用下金属热响应的物质点法算法研究

发布时间：2018-06-19 08:35

本文选题：超短脉冲激光 + 金属　；参考：《浙江大学》2017年硕士论文

【摘要】：超短脉冲激光与金属相互作用的过程一般采用双温模型进行描述,求解时常用的是基于网格的数值计算方法,比如有限差分法和有限元法。但是在超短脉冲激光辐照下,金属内部不仅存在电子和晶格间的不平衡热状态,且可能导致目标靶的大变形甚至断裂。因此,采用基于网格的方法求解双温模型会出现网格畸变的问题。而物质点法(MPM)作为一种无网格法,结合了拉格朗日和欧拉方法的优点,已被证明适用于模拟这类涉及大变形的问题。最近,物质点法已用于研究傅里叶热传导过程。本文的主要工作是发展用于模拟超短脉冲激光作用下金属热响应的物质点法算法,并对其进行验证。首先从双温模型出发,建立电子和晶格能量方程的弱形式,将电子和晶格离散为物质点,构造出控制方程的离散形式;然后,仿照传统MPM,引入形函数,将物质点信息映射到背景网格进行方程求解,再由网格结点物理量映射回质点更新温度。分别采用提出的MPM算法和差分法,对一维和不规则二维模型条件下超短脉冲激光照射下金薄膜的热响应开展模拟,结果显示物质点法计算得到的电子和晶格温度与有限差分法的模拟结果差别都较小,验证了 MPM算法的准确性。此外,改变MPM计算的时间步长、网格间距、背景网格单元中物质点的数目和分布情况,验证了 MPM的收敛性和稳定性,且MPM能自动满足边界绝热条件,无需对边界做额外处理。所以,对于超短脉冲激光与金属相互作用中靶材的热力大变形,MPM算法较有网格方法具有优越性。最后,针对多维模型中存在的计算量大、模拟时间长的问题,提出了基于OpenMP的MPM并行算法等优化方法,研究节点更新的数据竞争问题的解决方案,并探讨与串行程序相比不同网格规模的提速效果。研究结果表明,降低计算精度和调整迭代机制能够对原MPM程序有加速效果,但会产生累积误差导致只能应用于对模拟结果的精度要求不高的场合。而采用OpenMP实现CPU多核并行计算,能够有效地提高计算效率且不影响计算结果,且对于越大规模的网格模型并行效率会稍高。为避免节点更新阶段出现的数据竞争问题,本文采用优化节点整合的背景网格区域分解法实现并行计算。
[Abstract]:The process of interaction between ultrashort pulse laser and metal is usually described by a two-temperature model, and the mesh-based numerical methods, such as finite difference method and finite element method, are commonly used to solve the problem. However, under ultrashort pulse laser irradiation, there is not only an unbalanced thermal state between electrons and lattices in the metal, but also a large deformation or even fracture of the target. Therefore, grid-based method is used to solve the problem of mesh distortion in the two-temperature model. As a meshless method, the material point method (MPM) combines the advantages of Lagrangian and Euler methods and has been proved to be suitable for simulating such problems involving large deformation. Recently, the material point method has been used to study the Fourier heat conduction process. The main work of this paper is to develop and verify the material point method for simulating the thermal response of metal under ultrashort pulse laser. Starting from the two-temperature model, the weak form of the energy equation of electron and lattice is established, and the discrete form of the governing equation is constructed by discrete the electron and lattice into the material point, and then the form function is introduced, which is similar to the traditional MPM. The material point information is mapped to the background grid to solve the equation, and then the mesh node physical quantity is mapped back to the particle renewal temperature. The thermal response of gold films irradiated by ultrashort pulse laser is simulated by the MPM algorithm and the difference method, respectively. The results show that the difference of electron and lattice temperature between the material point method and the finite difference method is small, which verifies the accuracy of the MPM algorithm. In addition, the convergence and stability of MPM are verified by changing the time step size, mesh spacing, the number and distribution of material points in the background meshes, and MPM can satisfy the boundary adiabatic condition automatically without the need for extra boundary treatment. Therefore, the MPM algorithm for large thermal deformation of targets in the interaction of ultrashort pulse laser with metal is superior to the grid method. Finally, aiming at the problems of large computation and long simulation time in the multidimensional model, an optimization method, such as MPM parallel algorithm based on OpenMP, is proposed to solve the data competition problem of node update. Compared with the serial program, the speedup effect of different grid scale is discussed. The results show that reducing the calculation accuracy and adjusting the iterative mechanism can accelerate the original MPM program, but the cumulative error can only be applied to the situation where the accuracy of the simulation results is not high. Using OpenMP to implement CPU multi-core parallel computing can effectively improve the computing efficiency without affecting the calculation results, and the parallel efficiency will be slightly higher for the larger grid model. In order to avoid the problem of data competition in the node update phase, the background grid domain decomposition method of optimizing node integration is used to realize parallel computing in this paper.
【学位授予单位】：浙江大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TG665

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