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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格上，本文对跨、超、高超声速绕流进行了数值模拟。计算实践表明现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。
In this paper, an implicit inverse wind finite element scheme for solving two-dimensional Euler equations is developed. The second-order precision upwind method is applied to approximate the space, and the implicit scheme of the finite element is derived based on the linearization of the numerical flux function. To reduce numerical oscillations, a limiting factor based on eigenvalues was introduced. In the adaptively treated unstructured grid, this paper simulates the flow around the transonic, hypersonic and hypersonic flows. The calculation practice shows that the present implicit finite element format has higher computational efficiency and stronger adaptability than the explicit format.