航空学报 > 2011, Vol. 32 Issue (9): 1608-1615   doi: CNKI:11-1929/V.20110120.1732.007

任意多面体网格上的欧拉方程数值算法

李书杰, 杨国伟   

  1. 中国科学院 力学研究所 高温气体动力学重点实验室, 北京 100190
  • 收稿日期:2010-11-30 修回日期:2010-12-26 出版日期:2011-09-25 发布日期:2011-09-16
  • 通讯作者: 杨国伟(1967-) 男,博士,研究员,博士生导师。主要研究方向:计算流体力学,包括定常流,非定常流,流体/结构干扰,动稳定性,气动优化设计,计算方法,气动激光等。 Tel: 010-82544006 E-mail: gwyang@imech.ac.cn E-mail:gwyang@imech.ac.cn
  • 作者简介:李书杰(1983-) 男,博士研究生。主要研究方向:计算流体力学,高阶格式及无网格算法。 Tel: 010-82544010 E-mail: xpoly.sj@gmail.com
  • 基金资助:

    中国科学院研究生科技创新与社会实践资助专项(2009)

Numerical Algorithm of Euler Equations on Arbitrary Polyhedral Grids

LI Shujie, YANG Guowei   

  1. Laboratory of High Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
  • Received:2010-11-30 Revised:2010-12-26 Online:2011-09-25 Published:2011-09-16

摘要: 发展并验证了一种新的支持多面体网格的欧拉方程离散算法,采用Fortran 95编写了支持任意网格拓扑及三维复杂外形的通用求解器。在空间离散上,基于径向基函数理论提出了一种新的梯度计算方法,并采用动能通量分裂格式来得到准确并且稳定的二阶精度重构。该方法不依赖于网格几何形状,因此对网格质量不敏感。由于在时间方向采用了点隐松弛推进方法,使得该求解器在大时间步长上仍能保持稳定性。最后通过若干数值算例对本文所发展的算法进行了验证,证明了本文的算法及求解器具有稳定、准确的特性及宽广的网格类型适应性。

关键词: 多面体网格, 蜂窝网格, 径向基函数, 动能通量分裂, 非结构, 复杂外形, 可压缩流动

Abstract: A new algorithm for solving Euler equations on polyhedral grids is developed and validated in this paper. A general solver which supports arbitrary mesh topology and three-dimensional complex geometry is constructed by using Fortran 95 language. For spatial discretization, a new improved radial basis function method is proposed for gradient calculation. An accurate and robust second-order reconstruction is achieved by using the kinetic flux vector splitting scheme. The new method does not depend on the geometry of the grid. Thus it is much less sensitive to grid quality. With a point implicit relaxation time marching strategy, the solver remains stable at large time steps. The test cases indicate that the algorithm and the solver developed in this paper are stable, accurate while exhibiting good flexibility on mesh universality.

Key words: polyhedral grid, honeycomb grid, radial basis function, kinetic flux vector splitting, unstructured, complex geometry, compressible flow

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