航空科学技术2025，Vol.36Issue(7)：41-48,8.DOI:10.19452/j.issn1007-5453.2025.07.006
热化学非平衡Navier-Stokes方程组GMRES算法研究
Study on GMRES Algorithm for Non-Equilibrium Thermal and Chemical Navier-Stokes Equations
摘要
Abstract
Efficiently solving the non-equilibrium thermal and chemical Navier-Stokes equations is essential for hypersonic projects.To improve stability and convergence efficiency of GMRES algorithim applied to numerical solving three-dimensional non-equilibrium thermal and chemical Navier-Stokes equations which is subjected to strong numerical stiffness induced by vibrational energy and chemical source terms,a type of preconditioning matrix is constructed from lower order numerical schemes and diagonalized source term Jacobian matrix.Diagonalized methods which are originally used in chemical source are extended to both vibrational energy and chemical source terms and preconditioning matrix is deduced in detail.Through matrix approximate factorization,a LU-SGS based GMRES algorithm is developed with calculation processes.Numerical results show that,the hypersonic flow predicted by preconditioning method developed in this paper is coincide with reference datum.As to source term Jacobian diagonalization,even with large CFL number,the Kim method is convergence.So,Kim method is more stable and robust than Eberhardt and Ju methods.关键词
化学反应源项/振动能源项/数值刚性/雅可比矩阵对角化/GMRES算法预处理/热化学非平衡效应Key words
chemical source/vibrational energy source/numerical stiffness/Jacobian diagonalized/preconditioning GMRES/thermal-chemical non-equilibrium分类
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朱海涛,吴耕宇,李岩..热化学非平衡Navier-Stokes方程组GMRES算法研究[J].航空科学技术,2025,36(7):41-48,8.
