非结构网格上欧拉方程的自适应逆风隐式有限元解法

本文发展了一种解二维欧拉方程的隐式逆风有限元格式。空间近似应用的是二阶精度逆风方法；时间近似上根据数值通量函数的线性化处理导出了有限元的隐格式。为减少数值振荡，引入了基于特征变量的限制因子。在经自适应处理的非结构网络上，本文对跨、超、高超声速绕流进行了数值模拟。计算实践表明发展的隐式有限元格式与显格式相比具有较高的计算效率和较强的适应性。

Implicit Finite Element Adaptive Upwind Methods for Euler Equations on Unstructured Meshes

A class of implicit finite element upwind schemes for solving 2-D Euler equations is developed in this paper.Second-order upwind methods are used for the spatial approximation with some limters based on characteristic variables to reduce numerical oscillations.For the advancing in time,an implicit scheme relying on a linearization of fluxes is built.Transonic,supersonic and hypersonic flows are simulated on seif-adaptive unstructured meshes.Numerical experiments show the implicit finite element upwind schemes is more efficient and robust than explicit schemes.