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引用次数: 0
摘要
本文构建了平衡扩散极限下辐射流体力学方程(RHE)的任意拉格朗日-欧勒(ALE)正保有限体积方案。首先,介绍了 ALE 框架下的 RHE 积分方程。然后,应用算子分割法将方程分为双曲部分和抛物部分。此外,基于 MUSCL 重构,为双曲部分构建了二阶保正有限体积方案。顶点速度通过预测器-校正器策略获得。采用温斯洛方法提高拉格朗日网格的质量。此外,还针对抛物线部分提出了一种适用于扭曲网格的非线性保正值有限体积方案。最后,给出了一些数值示例,以说明数值方案的准确性和可靠性。
An arbitrary Lagrangian–Eulerian positivity-preserving finite volume scheme for radiation hydrodynamics equations in the equilibrium-diffusion limit
In this paper, an arbitrary Lagrangian–Eulerian (ALE) positivity-preserving finite volume scheme is constructed for radiation hydrodynamics equations (RHE) in the equilibrium-diffusion limit. Firstly, the integral form equations of RHE in the ALE framework are presented. Then, the operator-splitting method is applied to divide the equations into hyperbolic part and parabolic part. In addition, a second-order positivity-preserving finite volume scheme is constructed for the hyperbolic part based on MUSCL reconstruction. The vertex velocity is obtained by the predictor–corrector strategy. The Winslow method is applied to improve the quality of the Lagrangian mesh. Furthermore, a nonlinear positivity-preserving finite volume scheme suitable for distorted mesh is proposed for the parabolic part. Finally, some numerical examples are given to show the accuracy and reliability of the numerical scheme.
期刊介绍:
The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest.
The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.