A 3-D pseudo-arc-length moving-mesh method for numerical simulation of detonation wave propagation
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ORIGINAL ARTICLE
A 3-D pseudo-arc-length moving-mesh method for numerical simulation of detonation wave propagation T. Ma1
· J. Zhao1 · J. Ning1
Received: 31 October 2019 / Revised: 31 July 2020 / Accepted: 8 August 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this paper, we propose a robust pseudo-arc-length moving-mesh method (PALM) which adopts the strategy of overall movement and block calculation for numerical simulation of detonation wave propagation in three dimensions. The pseudoarc-length moving-mesh method involves governing equations’ evolution, mesh redistribution, and positivity-preserving analysis. Second-order finite-volume schemes and multistage total-variation-diminishing Runge–Kutta methods are used for governing equations’ evolution, while mesh redistribution is an iterative procedure that includes mesh point redistribution and cell average conservative interpolation. In addition, positivity-preserving analysis is discussed to avoid the density or pressure becoming negative in the process of numerical calculation. Finally, several numerical examples show that our method is feasible and effective. The advantage of the PALM scheme is that we can get similar results as the Monotonic Upstreamcentered Scheme for Conservation Laws (MUSCL) which requires more cells and computational run time. It is demonstrated that the computational grids using the PALM scheme can capture the detonation front. Keywords Pseudo-arc-length moving-mesh method · Numerical simulation · Three-dimensional · Positivity-preserving analysis
1 Introduction Detonation involves complex interaction between reactive chemical kinetics and fluid dynamics. Numerical simulation of detonation wave propagation is an important research field, and many references can be found in the literature [1,2]. How to accurately capture and track the propagation of shock waves is a difficult problem in detonation simulations. One of the conventional methods is to increase the number of computational cells. However, as the number of grid cells increases, the computational cost increases rapidly. Therefore, capturing the detonation wave with high accuracy and keeping the computational cost within acceptable limits is a Communicated by G. Ciccarelli. This paper is based on work that was presented at the 25th International Colloquium on the Dynamics of Explosions and Reactive Systems, Beijing, China, July 28–August 2, 2019.
B 1
T. Ma [email protected] State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing, People’s Republic of China
major challenge. In order to achieve this, mesh adaptation is an essential tool for solving such problems. There are three types of mesh adaptation methods, namely h-methods [3], p-methods [4], and r-methods [5,6]. The r-methods, which are also called moving-mesh methods, relocate mesh point positions while maintaining the total number of mesh points and mesh connectivity [7]. Tang and Tang [8] proposed a moving-mesh method for oneand two-dimen
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