发表机构
Indian Institute of Petroleum and Energy-Visakhapatnam（印度石油能源大学-维沙卡帕特南）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究将瓦苏德瓦·穆尔蒂松弛方法拓展至多类松弛系统，建立其积分不变量，采用三种二阶数值方案验证了模型能保留积分不变量、稳定且精确的特性。
AI 中文摘要
瓦苏德瓦·穆尔蒂的松弛方法[A.S. Vasudeva Murthy, J. Comput. Appl. Math., 203(2), pp. 437-443, 2007]最初针对金-辛（Jin-Xin）松弛模型提出，提供了一种具有不变性质的替代公式，与标准公式相比具有一致性且保留了半线性结构。本研究针对多种松弛系统提出了瓦苏德瓦·穆尔蒂松弛方法，包括浅水方程、布罗德韦尔（Broadwell）模型、带热传递的欧拉方程以及二维金-辛模型。对于所提出的松弛模型，在理论层面严格建立了相关的积分不变量。积分不变量的主要优势在于，它通过纳入向量形式中解变量的耦合贡献，为松弛系统提供了一个守恒量。为验证分析结果，采用三种二阶数值方案对每个模型进行数值模拟：CS-EBT2，一种适用于带松弛源项的双曲系统的半隐式二阶中心有限体积方案[S. Sahu, E. Macca, and R. Samala, J. Comput. Phys., 563, 115100, 2026]；UCS2，一种有限体积中心松弛型方案[S. F. Liotta, V. Romano, and G. Russo, SIAM J. Numer. Anal., 38(4), 1337-1356, 2000]；以及IMEX-RK2，一种二阶隐式-显式龙格-库塔方案[Pareschi and Russo, J. Sci. Comput., 25, 129-155, 2005]。与精确解或精细解析的参考解相比，数值结果证实这些模型能保留积分不变量，在CFL条件限制下保持稳定，且在所有测试的基准系统中表现出稳健且精确的特性。
英文摘要
Vasudeva Murthy's relaxation approach [A.S. Vasudeva Murthy, J. Comput. Appl. Math., 203(2), pp. 437-443, 2007], originally proposed for the Jin-Xin relaxation model, provides an alternative formulation with invariant properties that is consistent and retains the semilinear structure incomparison to the standard one. In this work, Vasudeva Murthy's relaxation approach for various relaxation systems are proposed such as the shallow water equations, the Broadwell model, the Euler equations with heat transfer and two-dimensional Jin-Xin model. For proposed relaxation models, the associated integral invariants are rigorously established at the theoretical level. The main advantage of the integral invariant is that it provides a conserved quantity for the relaxation system by incorporating the coupled contributions of the solution variables in vector form. To validate the analytical results, numerical simulations are carried out for each model using three second-order numerical schemes: CS-EBT2, a semi-implicit second-order central finite-volume scheme for hyperbolic systems with relaxation source terms [S. Sahu, E. Macca, and R. Samala, J. Comput. Phys., 563, 115100, 2026]; UCS2, a finite-volume central relaxation-type scheme [S. F. Liotta, V. Romano, and G. Russo, SIAM J. Numer. Anal., 38(4), 1337-1356, 2000]; and IMEX-RK2, a second-order Implicit-Explicit Runge-Kutta scheme [Pareschi and Russo, J. Sci. Comput., 25, 129-155, 2005]. Numerical results, compared to exact or finely resolved reference solutions, confirm that the models preserve integral invariants, remain stable under CFL restrictions, and exhibit robust and accurate behavior across all benchmark systems tested.
Comments26 pages, 14 figures, 15 Tables
