High order conservative Lagrangian scheme for three-temperature radiation hydrodynamics
High order conservative Lagrangian scheme for three-temperature radiation hydrodynamics
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DOI：
10.1016/j.jcp.2023.112595
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发表时间：
2023-10
期刊：
影响因子：
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通讯作者：
Juan Cheng;Chi-Wang Shu
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文献类型：
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作者：
Juan Cheng;Chi-Wang Shu
三温度（3-T）辐射流体动力学（RH）方程被广泛用于各种光学厚高能量密度物理环境的建模，如天体物理和惯性约束聚变（ICF）。本文讨论了求解3- trh方程的高阶保守拉格朗日格式的构造方法。具体来说，首先定义了三个新的能量变量，将3-T RH方程的三个能量方程改写为3-T RH方程的形式。该公式的主要优点是便于设计既具有保守性又具有任意高阶精度的格式。以一维为出发点，基于多分辨率WENO重构和强稳定保持（SSP）高阶时间离散化为例，设计了空间和时间上的三阶保守拉格朗日格式。为了确定3- trh方程中保守平流项的数值通量，我们提出了一个适用于具有理想气体状态方程的多物质问题的严格的由散度定理导出的HLLC数值通量。然后，我们讨论了如何设计一类高阶保正显式拉格朗日格式来求解空间中只包含保守平流项的3-T RH方程。本文还考虑了对二维情况的初步推广。最后，通过数值实验验证了高阶拉格朗日格式的高阶精度、非振荡性、守恒性和对多材料问题的适应性。
The three-temperature (3-T) radiation hydrodynamics (RH) equations are widely used in modeling various optically thick high-energy-density-physics environments, such as those in astrophysics and inertial confinement fusion (ICF). In this paper, we will discuss the methodology to construct a high order conservative Lagrangian scheme solving 3-T RH equations. Specifically, the three new energy variables are defined first, in the form of which the three energy equations of the 3-T RH equations are rewritten. The main advantage of this formulation is that it facilitates the design of a scheme with both conservative property and arbitrary high order accuracy. Starting from one dimension and based on the multi-resolution WENO reconstruction and the strong stability preserving (SSP) high order time discretizations, taken as an example, we design a third order conservative Lagrangian scheme both in space and time. To determine the numerical flux for the conservative advection terms in the 3-T RH equations, we propose a HLLC numerical flux which is derived from the divergence theorem rigorously and is suitable for multi-material problems with the ideal-gas equations of state. After that, we discuss how to design a class of high order positivity-preserving explicit Lagrangian schemes to solve the 3-T RH equations which only contain the conservative advection terms in space. Preliminary extension to the two dimensional case is also considered. Finally, various numerical tests are given to verify the desired properties of the high order Lagrangian schemes such as high order accuracy, non-oscillation, conservation and adaptation to multi-material problems.