Semidiscrete central-upwind schemes for hyperbolic conservation laws and Hamilton-Jacobi equations
Semidiscrete central-upwind schemes for hyperbolic conservation laws and Hamilton-Jacobi equations
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DOI：
10.1137/s1064827500373413
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发表时间：
2001-10-01
影响因子：
3.1
通讯作者：
Petrova, G
中科院分区：
文献类型：
--
作者：
Kurganov, A;Noelle, S;Petrova, G
本文对双曲型守恒律方程组和汉密尔顿Jacobi方程组引入新的Godunov型半离散中心格式。该方案是基于使用更精确的信息，当地的传播速度，可以看作是一个推广的计划，从[A。Kurganov和E. Tadmor，J. Comput. Phys. 160（2000），pp. 241-282; A. Kurganov和D. Levy，SIAM J. Sci. Comput. 22（2000），pp. 1461-1488; A. Kurganov和G. Petrova双曲守恒律及相关问题的三阶半离散真多维中心格式。数学、[A]和[B]。Kurganov和E. Tadmor，J. Comput. Phys. 160（2000），pp. 720-742].所提出的中心格式的主要优点是高分辨率，由于较小的数值耗散量，和简单。没有黎曼解和特征分解，这使得他们成为一个通用的工具，为各种各样的应用程序。同时，开发的计划有一个逆风的性质，因为他们尊重波的传播方向，通过测量单侧当地的速度。这就是为什么我们称它们为中心迎风格式的原因，所构造的格式被应用于各种问题，如气体动力学的欧拉方程，具有凸和非凸Hamilton算子的汉密尔顿雅可比方程，以及不可压缩的欧拉和Navier Stokes方程。后者方程中的不可压缩性条件使我们能够以守恒形式和输运形式处理它们。我们适用于这些问题的中心迎风格式，分别为他们每个人，并计算相应的数值解。
We introduce new Godunov-type semidiscrete central schemes for hyperbolic systems of conservation laws and Hamilton Jacobi equations. The schemes are based on the use of more precise information about the local speeds of propagation and can be viewed as a generalization of the schemes from [A. Kurganov and E. Tadmor, J. Comput. Phys. 160 (2000), pp. 241-282; A. Kurganov and D. Levy, SIAM J. Sci. Comput. 22 (2000), pp. 1461-1488; A. Kurganov and G. Petrova A third-order semidiscrete genuinely multidimensional central scheme for hyperbolic conservation laws and related problems Numer. Math., to appear] and [ A. Kurganov and E. Tadmor, J. Comput. Phys. 160 (2000), pp. 720-742].The main advantages of the proposed central schemes are the high resolution, due to the smaller amount of the numerical dissipation, and the simplicity. There are no Riemann solvers and characteristic decomposition involved, and this makes them a universal tool for a wide variety of applications.At the same time, the developed schemes have an upwind nature, since they respect the directions of wave propagation by measuring the one-sided local speeds. This is why we call them central-upwind schemes.The constructed schemes are applied to various problems, such as the Euler equations of gas dynamics, the Hamilton Jacobi equations with convex and nonconvex Hamiltonians, and the incompressible Euler and Navier Stokes equations. The incompressibility condition in the latter equations allows us to treat them both in their conservative and transport form. We apply to these problems the central-upwind schemes, developed separately for each of them, and compute the corresponding numerical solutions.