Well-Balanced Central-Upwind Schemes for $$2\,\times \,2$$ Systems of Balance Laws
Well-Balanced Central-Upwind Schemes for $$2\,\times \,2$$ Systems of Balance Laws
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DOI：
10.1007/978-3-319-91545-6_28
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发表时间：
2016-08
期刊：
影响因子：
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通讯作者：
Alina Chertock;M. Herty;Ș. Özcan
中科院分区：
文献类型：
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作者：
Alina Chertock;M. Herty;Ș. Özcan
在这项研究中，我们为平衡律系统，特别是具有源和交通流松弛到平衡速度的等温气体动力学模型，开发了一个良好平衡的二阶中心迎风方案。新方案基于对godunov型中心迎风方法的重建和演化步骤的修改。这种修正的第一步是引入一个平衡变量，该平衡变量是通过将源项并入通量而得到的。通过重建平衡变量并将其应用于良好平衡的演化过程，我们证明了所提出的方案是良好平衡的，即它保持了系统的稳态。
In this study, we have developed a well-balanced second-order central-upwind scheme forsystems of balance laws, in particular, the models of isothermal gas dynamics with source and traffic flow with relaxation to equilibrium velocities. The new scheme is based on modifications in the reconstruction and evolution steps of a Godunov-type central-upwind method. The first step of this modification is to introduce an equilibrium variable obtained from incorporating the source term into the flux. By reconstructing equilibrium variables and using them in the well-balanced evolution process, we have illustrated that the proposed scheme being well balanced, namely, it preserves steady states of the system.