非结构网格上Euler方程有限体积解法的改进

对二维非结构三角形网格上Euler方程有限体积解法的格点格式进行了一些改进，重点在于提高数值解的精度，细致处理人工粘性项的尺度因子以及对该项建立适当的边界条件；发展一种新的基于最长边剖分的三角形网格自适应加密方法。采取多步Runge—Kutta格式推进、当地时间步长、隐式残值光顺等措施加速迭代收敛。文末给出的数值结果非常接近于参考文献中结构网格上的结果，验证了所发展数值方法的精确性。

Improvements of a Finite Volume Method for Euler Equations on Unstructured Meshes

Some improvements are performed by vertex scheme for Euler equations on unstructured triangular meshes in two dimensions. Special emphasis is placed on the accuracy of solutions. High accuracy is achieved by careful scaling of the artificial dissipation term, and reformulating the inner and outer boundary conditions for dissipative operator, and by mesh adaptation based on the longest edge bisection algorithm. Convergence is accelerated by using Runge Kutta multistage time stepping scheme and implicit residual smoothing. Numerical results are very close to those on structural meshes and validate the accuracy of the improved scheme.