A large time step Godunov scheme for free-surface shallow water equations

An algorithm for simulating free surface flows is presented using large time step based on the wave-propagation method proposed by LeVeque, and an exact Riemann solver is used. A multiple wave approximation approach was suggested for eliminating the discontinuities found in the rarefaction fans of dam-breaking flows. In addition, we use the random choice method to reduce non-physical oscillations. Applications demonstrate that the algorithm proposed in this paper can considerably increase the CFL number up to 25 when modeling dam-break flows, while retaining satisfactory accuracy and efficiency. This suggests that our algorithm has the potential to be applied to modeling free surface flows.     

室内热羽流特性小波分析及数值模拟方法比较

通过室内热羽流实验和计算流体力学数值模拟研究，比较了不同热羽流强度下的轴心速度和不同湍流模型对计算结果的影响。实验中高频采样的热羽流速度数据采用小波变换进行处理，处理后体现平均速度变化的低频信息和体现湍流脉动的高频信息直观反映了热羽流流动的特征。实验结果表明，热羽流具有非稳态准周期的波动特性。物体表面温度越高，产生的热羽流平均速度和湍流脉动幅度越大。数值模拟结果表明，非定常雷诺时均法的模拟结果最终趋于稳定而无法反映热羽流的波动特性，大涡模拟方法能够较好地反映热羽流流动的非稳态特征。此外，隐式格式时间步长的选择可以借鉴CFL (Courant-Friedrichs-Lewy)条件进行设置，得到较为准确的模拟结果。