水下爆炸柱形高压气泡膨胀过程的RGFM和高精度格式数值模拟

为了对柱形装药水下爆炸高压气泡膨胀过程进行三维数值模拟，用level set方法追踪气水界面，详细描述了精确对柱形气泡进行level set建模；对于流场，使用Euler方程描述，并用高精度格式(五阶WENO和四阶R-K法)离散空间项和时间项；对于level set方程，使用五阶HJ-WENO离散；用RGFM处理气水界面附近网格节点。给出了水下流场不同时刻的压力云图、柱形高压气泡的形状演变以及流场中几个指定点的压力峰值。通过三维建模和计算验证，用RGFM结合高精度格式可以很好地对柱形高压气泡膨胀问题进行三维数值模拟，同时也可以较精确地追踪高密度比、高压力比的三维气水界面。计算结果表明，柱形高压气泡在膨胀过程中，形状逐渐向椭球形变化；位于固壁附近的柱形高压气泡受固壁反射波的影响，在固壁法线方向上的膨胀会受到抑制；双圆柱形高压气泡膨胀产生的冲击波，可以彼此抑制对方的膨胀。

Simulation of expanding process of high pressure cylindrical bubblesin underwater explosion using RGFM and high accuracy schemes

This paper presents a 3D numerical simulation of expanding process of high pressure cylindrical bubbles in underwater explosion. Level set method was used to track gas-water interface. The detail on precise definition of initial level set values of cylindrical bubble was also provided. The flow field was solved by Euler equation with fifth-order WENO spatial discretization and fourth-order R-K (Runge-Kutta) time discretization. HJ-WENO was employed to discretized level set equation. The flow states at grid nodes just next to gas-water interface were updated by RGFM algorithm. Pressure cloud pictures at different times, the shape changes of high pressure bubbles and pressure peak at given points were offered. Some interesting conclusions are concluded, as that high pressure cylindrical bubble becomes ellipsoidal gradually during expanding process, the expansion of bubbles nearby the wall is restricted in the normal by reflected wave, and expansion of double cylindrical bubbles is restricted by shock wave from each other. The numerical results also show excellent performance of RGFM and high accuracy scheme when applied to simulation of high pressure cylindrical bubbles expanding.