高精度全速域拉格朗日-重映算法研究

项目名称： 高精度全速域拉格朗日-重映算法研究

项目编号： No.11502030

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 刘玉侠

作者单位： 北京应用物理与计算数学研究所

项目金额： 22万元

中文摘要： 高低速混合的全速域流动广泛存在于各种工程实际应用中。本项目探讨基于拉格朗日-重映两步方法构造全速域算法的基本原则，提出一类高低速流动统一计算的方法；研究基于三阶精度分段抛物化插值的全速域算法，拟证明算法对高低速流的渐近一致性质，验证和确认格式的计算精度、收敛性和准确性。研究基于网格自适应的全速域两步方法，编制大规模高效并行程序，分析算法对重点局部流场的分辨率，并验证方法的有效性。研究多介质流动中的高精度全速域两步算法，探讨动力学和热力学一致相容的多介质算法的设计准则，发展基于一般状态方程和弹塑性本构关系的多介质混合相容算法，拟模拟预测高低速混合的一般多介质流动。本研究不仅对核工程物理中复杂介质混合流动和发动机中燃料雾化燃烧等有重要价值，而且也是计算流体力学的前沿课题，有重要的科学意义。

中文关键词： 全速域流动；拉格朗日-重映；网格自适应；多介质；计算流体力学

英文摘要： Mixed compressible and incompressible all-speed flows widely exist in various practical applications. This project will explore the basic principles to construct all-speed Lagrangian-Remapping two-step methods, propose a class of unified numerical method for high-speed and low-speed regions, investigate the three-order-accurate all-speed method with piecewise parabolic interpolation, prove the asymptotic properties of the unified algorithm under low Mach number limit, verify and validate the convergence and accuracy of the numerical method. This project will investigate the all-speed two-step method with adaptive mesh refinement, build a high-efficient large-scale parallel program on modern computer architecture, analyze the resolution focus on the important local flowfield, and demonstrate the validity of the proposed method. This project will investigate the all-speed two-step methods for multi-material flow, explore the design criterion of multi-material algorithms with consistency of kinetics and thermodynamics, develop all-speed mixture-consistent numerical method for multi-material flow with general equations of state and elastoplastic constitutive relations, and predict the general multi-material flow with mixed compressible and incompressible regions. This research not only has important value for the complex all-speed multi-material flow in engineering nuclear physics and the fuel atomization and combustion in industrial engines, and also has important scientific significance due to its pioneering nature in computational fluid dynamics.

英文关键词： all-speed flow;Lagrangian-Remapping;adaptive mesh refinement;multi-material;computational fluid dynamics