凝聚态炸药爆轰研究在国防军事发展和国民经济建设中具有重要的应用价值。由于凝聚态炸药的物理化学性质较为复杂，其反应过程极其短暂且能量释放剧烈，通过实验难以获取全面且细致的物理信息，因此数值模拟成为了凝聚态炸药爆轰的主要研究方法。

爆轰波的传播和发展是爆轰研究中的重要内容，爆轰波兼具了激波和界面两类间断类型的间断问题，因而需要发展具有强鲁棒性的高精度算法，同时由于凝聚态炸药复杂的状态方程和爆轰模型，基于具有强劲的浮点数运算能力的计算设备（如图形处理器GPU），发展适合爆轰研究的高性能数值模拟方法及程序更具有实际意义。

本文的主要工作包括：

（1）方程组共用权WENO格式是指对方程组中的每个分量方程的通量，均共用同一组权值来进行加权以获得相应的数值通量。本文提出一种新的共用函数来计算Euler方程组中的共用权。该函数主要是基于一般的状态方程（不局限于理想气体状态方程），考虑到其声速包含了更多的介质信息，因而用声速来代替原来所用的压力，从而发展了相应的共用权WENO格式。利用数值试验验证了本文所发展的格式具有较高的精度与分辨率和较低的耗散，与全局Lax-Friedrichs通量分裂使用时能较好的处理流场中的间断结构。

（2）图形处理器(Graphics processing unit，GPU)在并行处理及高密集运算等方面具有突出的优势，近年来在计算流体力学中得到了越来越多的关注和应用。归约算法是并行计算的基本算法之一，常应用于数组求和、数组求极值等压缩数组的行为，其在基于GPU的可压缩流动数值模拟中关于流通矢量分裂、计算时间步长等步骤中具有重要的应用。本文利用一种改进型的归约算法，并将其实现在可压缩流动并行程序中，并利用CUDA编程模式的特点，利用内存补齐技术和线程块内归约的思想，最大程度上保留了基于GPU开发的并行CFD程序优异的加速性能,同时拓展了算法的通用性,智能化了基于GPU开发的可压缩流动并行程序。

（3）爆轰波是高速化学反应流动中最为常见的物理现象之一，它是由前沿的以超声速传播的诱导激波和紧随其后的化学反应区组成，化学反应区为诱导激波提供能量以自持。诱导激波前为未反应区，激波后为产物区，而化学反应是典型的一类界面问题，因此爆轰波属于结合了激波和界面两种类型的间断问题。本文利用发展的三阶共用权WENO格式，模拟了凝聚态钝感炸药PBX-9502炸药的圆形散心爆轰波相互作用和LX-17炸药二维爆轰波衍射问题，数值结果表明本文使用的格式能够无振荡的计算爆轰波的起爆和传播，能准确的模拟出爆轰波传播、相互作用、衍射等物理现象，表明了本文所发展的格式具有模拟复杂爆轰现象的高效、高精度性质。

The research on the detonation of condensed explosives is important in the military

and the economic.

Due to the complex physical and chemical properties of condensed explosives, the

reaction process is extremely short and releases huge energy, so it is hard to

obtain detailed information through experiments. Therefore,

numerical simulation has become the main means in condensed explosives

detonation research.

The propagation and development of detonation waves is an important content

in detonation research. Detonation wave combines two types of discontinuity

problems: shock wave and interface. Therefore, it is necessary to develop

high-precision algorithms with strong robustness. At the same time, due to

the complex equation of state and detonation model of condensed explosives,

it is of great importance to develop high-performance numerical simulation

methods and programs suitable for detonation research on computing equipment

with strong floating-point operation ability (such as graphics processor unit).

The main work of this paper includes:

(1)A common weights WENO (co-WENO) scheme for solving Euler equations

is developed. This method proposes a new function to calculate the weights of

each sub-template in the WENO scheme. All components in the equation

group use this set of weights for the weighting combination. Compared with the

traditional schemes, this method not only greatly improves the calculation

efficiency, but also improves the robustness of the calculation. Numerical

experiments show that the new scheme has high accuracy, resolution and low

dissipation. When used with global L-F flux splitting, it can better deal

with the discontinuous structure in the flow field.

(2) GPU has outstanding performance in parallel processing and high performance

computing. In recent years, it has received more and more attention

and application in computational fluid dynamics.The reduction algorithm is one

of the basic algorithms of parallel computing. It is often used to

compress arrays. It's appllied in the flow vector splitting and time advancing

step in the numerical simulation of compressible flow based on GPU.

The reduction algorithm based on the classical tree-base can achieve an excellent

speedup ratio after multi-level optimization, but it has a certain

limit on the number of grids in application. It has a good speedup effect for

the given grid , and for the arbitrary grid, it often has serious

consequences such as thread divergence or even unable to calculate, Therefore,

it limits the generality and intelligence of compressible flow parallel

programs. In this paper, an improved protocol algorithm is used and implemented

in a compressible flow parallel program. By using the features of

CUDA Programming mode, memory completion technology and the idea of a reduction

in a block, the excellent acceleration performance of parallel CFD program

based on GPU is retained to the greatest extent, and the generality of the

algorithm is expanded, the compressible flow parallel program based on GPU

becomes more intelligentized.

(3)The detonation wave is one of the most common physical phenomena

in high-speed chemical reaction flow. It is composed of the leading shock

wave propagating at supersonic speed and the following chemical reaction

zone. The chemical reaction zone provides energy for the shock wave to sustain

itself.There is an unreacted zone before the induced shock wave and a

product zone after the shock wave.The chemical reaction is a typical kind of

interface problem. Therefore,the detonation wave belongs to a discontinuous

problem combining shock wave and interface.In this paper, a new third-order

common weight WENO scheme and GPU parallel program are developed to

simulate the two-dimensional detonation wave diffraction and circular scattered

detonation wave interaction of condensed insensitive explosives PBX-9502

and LX-17. The numerical results show that the method and program used in

this paper can simulate the initiation and propagation of detonation wave without

oscillation, and can accurately simulate the physical phenomena

such as detonation wave propagation, interaction and diffraction. It shows

that the scheme developed in this paper has the properties of highefficiency

and high precision in simulating complex detonation phenomena.