Positivity-preserving Lagrangian scheme for multi-material compressible flow
Positivity-preserving Lagrangian scheme for multi-material compressible flow
复制标题
多材料可压缩流保正拉格朗日格式
DOI：
10.1016/j.jcp.2013.09.047
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发表时间：
2014-01
影响因子：
4.1
通讯作者：
Chi-Wang Shu
中科院分区：
文献类型：
--
作者：
Juan Cheng;Chi-Wang Shu
数值方法的鲁棒性引起了计算流体力学界越来越多的兴趣。数值方法鲁棒性的一个数学方面是保正性。在高马赫数或接近真空的情况下，求解保守欧拉方程可能会产生负密度或负内能，从而导致程序的非线性失稳和崩溃。对于高阶方法、多材料流和移动网格问题，如拉格朗日方法，这种困难尤其深刻。本文用一般状态方程（EOS）构造了一阶和一致高阶精确保守拉格朗日格式，这些格式保持了密度和内能等物理正变量的正性。我们首先开发了一个保正的近似黎曼解，用于求解具有理想和非理想EOS的可压缩欧拉方程的拉格朗日格式。然后利用基本无振荡（ENO）重构、强稳定保持（SSP）高阶时间离散化和保正尺度限制器设计了一类高阶保正保守拉格朗日格式，证明了该格式保持守恒性和一致的高阶精度，并且易于实现。给出了保正拉格朗日格式的一维和二维数值实验，证明了这些方法的有效性。
Robustness of numerical methods has attracted an increasing interest in the community of computational fluid dynamics. One mathematical aspect of robustness for numerical methods is the positivity-preserving property. At high Mach numbers or for flows near vacuum, solving the conservative Euler equations may generate negative density or internal energy numerically, which may lead to nonlinear instability and crash of the code. This difficulty is particularly profound for high order methods, for multi-material flows and for problems with moving meshes, such as the Lagrangian methods. In this paper, we construct both first order and uniformly high order accurate conservative Lagrangian schemes which preserve positivity of physically positive variables such as density and internal energy in the simulation of compressible multi-material flows with general equations of state (EOS). We first develop a positivity-preserving approximate Riemann solver for the Lagrangian scheme solving compressible Euler equations with both ideal and non-ideal EOS. Then we design a class of high order positivity-preserving and conservative Lagrangian schemes by using the essentially non-oscillatory (ENO) reconstruction, the strong stability preserving (SSP) high order time discretizations and the positivity-preserving scaling limiter which can be proven to maintain conservation and uniformly high order accuracy and is easy to implement. One-dimensional and two-dimensional numerical tests for the positivity-preserving Lagrangian schemes are provided to demonstrate the effectiveness of these methods.
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DOI：
10.1016/j.jcp.2009.09.001
发表时间：
2009-12
期刊：
J. Comput. Phys.
影响因子：
--
作者：
Wei Liu;Juan Cheng;Chi-Wang Shu
通讯作者：
Wei Liu;Juan Cheng;Chi-Wang Shu
DOI：
10.1088/0031-9112/11/6/008
发表时间：
1960-06
期刊：
Physics Bulletin
影响因子：
--
作者：
L. Howarth
通讯作者：
L. Howarth
影响因子：
4.1
作者：
J. Dukowicz;B. Meltz
通讯作者：
J. Dukowicz;B. Meltz
影响因子：
4.1
作者：
Jiang, GS;Shu, CW
通讯作者：
Shu, CW
DOI：
10.1007/s000330050150
发表时间：
1999-03
期刊：
Zeitschrift für angewandte Mathematik und Physik ZAMP
影响因子：
--
作者：
Tao Tang;Kun Xu
通讯作者：
Tao Tang;Kun Xu