爆炸力学高精度数值模拟研究进展

High-resolution numerical simulation of explosion problems is of significant theoretical value owing to the numerous potential applications in both national defense and civilian projects, such as ammunition design, damage assessment, target protection, and industrial gas explosion prevention. In this paper, we review the research history of explosion mechanics and present the highest-order numerical simulation in decades. Building upon the author’s research work in recent years, we specifically discuss the development of high-order positivity-preserving schemes, high-order boundary treatment, an adaptive mesh method, and multi-material interface treatment. We extended the WENO and RKDG methods and constructed conservative positivity-preserving high-order schemes. The problems of negative density and pressure were solved through the simulation of complex detonation propagation. The detonation wave front structure and flow characteristics were captured clearly. In this paper, a high-order inverse Lax-Wendroff method on a Cartesian mesh is presented to treat the complex boundary. The main principle is that the first-order normal derivative can be obtained by the inverse Lax-Wendroff method, while all the higher-order normal derivatives can simply be obtained by fifth-order WENO-type extrapolation. The efficient implementation in the detonation process further indicates that the inverse Lax-Wendroff method is stable and robust when applied to a complex-geometry boundary. An a posteriori error estimate, which is often used as a refinement criterion, is applied to solve the Euler equations. To achieve mesh refinement, WENO and Hermite interpolations are used to prolong the solutions from coarse to fine grid in space and time, respectively. For mesh merging, the direct point value replacement method is employed to update the solutions of coarse grids. For this study, a local level-set tracking method was developed to treat the multi- material interface, and the velocity field in the computational domain was modified in order to effectively avoid errors caused by velocity field discontinuity when the interface position was solved. The method presented in this paper combines the GFM (Ghost Fluid Method) with the RGFM (Real Ghost Fluid Method) to deal with the material interface, thereby avoiding non-physical solutions when the GFM is used to deal with a strong discontinuity, and the CPU running time is increased when RGFM is employed to deal with a weak discontinuity in solving the Riemann problem repeatedly. Finally, the future of high-order numerical simulation of explosion mechanics is discussed.