三维Euler方程的隐式间断有限元算法

为了求解三维欧拉方程,对隐式时间离散格式间断有限元方法进行了研究。根据间断Galerkin有限元方法思想,构造内迭代SOR-LU-SGS隐式时间离散格式,结合当地时间步长技术、多重网格方法,实现了三维流场的计算。数值计算了ONERAM6机翼、大攻角尖前缘三角翼以及DLR-F4翼身组合体的亚声速绕流问题。结果表明,加入SOR内迭代步的LU-SGS隐式算法具有较大的优势,相较于GMRES算法所占用的内存少且收敛速度相当,是LU-SGS算法的三倍以上。针对三维算例,具有较好的稳定性和较高的收敛速度,能够给出准确的流场信息。与原方法相比,SOR-LU-SGS方法无论是在迭代步数上还是在CPU时间上,效率均有明显提高,适合于三维复杂流场计算。

Implicit discontinuous finite element algorithm for solving three-dimensional Euler equations

In order to solve three-dimensional Euler equations, this work investigated the implicit time discretization discontinuous finite element algorithm. According to discontinuous Galerkin finite element method ideology, this paper established SOR-LU-SGS time discretization discontinuous Galerkin finite element method for three-dimensional inviscid flow fluid coupled with implicit time discretization scheme, local time step technique and multi-grid method. Then, it calculated the classical three-dimensional examples, including subsonic flow around the ONERA M6 wing, delta wing with tip, and DLR-F4 wing-body geometry. The results show that the SOR-LU-SGS implicit algorithm has more advantages than GMRES with less memory, and the convergence rate is more than triple times of the traditional LU-SGS algorithm. For the three-dimensional examples, SOR-LU-SGS scheme not only has good stability and high convergence rate, but also can give accurate flow field information. Compared with the original method, the present scheme improves the efficiency both in iteration steps and in the CPU time, which is very suitable for solving three-dimensional complex flow field.