空中爆炸问题的高精度数值模拟研究

针对空中爆炸初期强间断和爆炸后期接触间断物理特性，提出了虚拟流体方法（GFM）和真实虚拟流体方法（RGFM）2种界面处理方法相耦合的计算方法。在高密度比、高压力比同时存在的 爆炸初期和压力、密度及速度等物理量相接近的爆炸后期，分别采用RGFM和GFM对物质界面两侧物理量进行处理。采用Local Level Set方法对运动界面进行追踪，并用5阶高精度加权本质非振荡（WENO）格式和3阶TVD Runge-Kutta方法对控制方程进行离散，编制了空中爆炸数值模拟程序，应用该程序对不同高度近地面空中爆炸以及冲击波与挡墙相互作用问题进行数值模拟，模拟结果能够较好地反映空中爆炸中冲击波的产生、传播、反射、绕射及爆炸产物的膨胀等现象，并与经验公式和试验结果吻合较好。证明了该耦合方法能够模拟空中爆炸问题，并且爆炸波在传播过程中具有很好的对称性，为模拟高密度比、高压力比的多物质之间相互作用问题提供了有效的计算方法。

High Resolution Numerical Simulation of Air Explosion

According to the physical characteristics of strong discontinuity at early stage of air explosion and its contact discontinuities at late stage, a new method coupling the ghost fluid method(GFM) with real GFM (RGFM) is proposed to treat the interface. At the initial stage, the situation where high density ratio and pressure ratio co-exist is treated by RGFM, while at the late stage, because explosion pressure, density and velocity, et al. Come close to each other, GFM is used to treat the interface. The moving interface is tracked by Local Level Set method. The governing equations are discredited by high resolution 5th-order weighted essentially non-oscillatory (WENO) scheme and 3rd-order TVD Runge-Kutta scheme. The air explosion is programmed. Using this program, air explosion at different heights and different distances are simulated. The simulation results accord well with the results obtained from empirical formula and experiments, which satisfactorily reflects the shock wave generation, propagation, reflection from the ground, and diffraction of shock wave, and the expansion of explosion products. The result shows that this method can be employed to simulate air explosion, and the explosion wave has good symmetry during propagating. The approach is effective for simulating the interaction of multi-medium flows at high density ratio and pressure ratio.