用隐式高精度间断伽辽金方法模拟可压层流和湍流

摘要

为了提高隐式高阶间断伽辽金数值方法的稳定性,发展了一种基于解析精确Jacobian矩阵的GMRES隐式方法,用于求解可压缩层流和湍流问题.在GMRES的求解中,无黏通量和黏性通量的Jacobian矩阵采用链式法则解析精确求解,并用于线性系统方程的LU-SGS预处理和GMRES矩阵矢量生成;与此同时,对修正的负Spalart-Allmaras湍流模型的生成源项进行了修正,以避免隐式化求导时出现非物理解.通过典型层流和湍流算例对发展的方法进行了验证,研究结果表明:基于精确Jacobian矩阵的隐式GMRES方法,不仅能够提高隐式高精度间断伽辽金方法计算的稳定性,而且还能够提高计算效率.%In order to improve the stability of the implicit higher order discontinuous Galerkin (DG)method,an implicit GMRES method based on analytic exact Jacobian matrix is developed for simulating compressible laminar and turbulent flow.In the process of the GMRES,Jacobians of inviscid and viscous flux,which are solved by the chain rule,are used for the LU-SGS preconditioning and GMRES matrix-vector product. The source of the Spalart-Allmaras turbulence model is modified to avoid unphysical solution that occurs at implicit derivative.The developed method is validated by benchmark laminar and turbulent flow cases.The results show that the implicit GMRES method based on exact Jacobian possesses significant advantages in reducing computational cost and improving the stability of the implicit high order discontinuous Galerkin method.