标题： 高阶通量分裂格式用于气体动力学的欧拉方程 显示英文标题

标题： High-Order Flux Splitting Schemes for the Euler Equations of Gas Dynamics

摘要： 我们为气体动力学的一维和二维欧拉方程开发了高阶通量分裂格式。 所提出的格式是现有的一阶通量分裂格式的高阶扩展，这些格式在[ E. F. Toro, M. E. Vázquez-Cendón, Comput. & Fluids, 70 (2012), pp. 1--12]中引入，其中将气体动力学的欧拉方程分解为两个子系统：对流和压力系统。 在本文中，我们在半离散框架内提出了TV分裂，首次将其扩展到更高精度。 通过使用分段线性插值来重构未知数的一侧点值，得到二阶扩展。 三阶和五阶格式是利用有限差分替代加权本质无振荡（A-WENO）框架开发的，该框架在处理多维问题时特别有效，并提供了构建更高阶WENO格式更直接的方法。 这些扩展通过一系列一维和二维气体动力学欧拉方程的数值实验显著提高了不连续性的分辨率和数值解的准确性。 显示英文摘要

摘要： We develop high-order flux splitting schemes for the one- and two-dimensional Euler equations of gas dynamics. The proposed schemes are high-order extensions of the existing first-order flux splitting schemes introduced in [ E. F. Toro, M. E. V\'azquez-Cend\'on, Comput. \& Fluids, 70 (2012), pp. 1--12], where the Euler equations of gas dynamics are split into two subsystems: the advection and pressure systems. In this paper, we formulate the TV splitting within the semi-discrete framework to extend it to higher orders of accuracy for the first time. The second-order extension is obtained by using piecewise linear interpolant to reconstruct the one-sided point values of the unknowns. The third- and fifth-order schemes are developed using the finite-difference alternative weighted essentially non-oscillatory (A-WENO) framework, which is particularly effective in handling multidimensional problems and provides a more straightforward approach to constructing higher-order WENO schemes. These extensions significantly improve the resolution of discontinuities and the accuracy of numerical solutions, as demonstrated by a series of numerical experiments of both the one- and two-dimensional Euler equations of gas dynamics.