Krylov隐式积分因子法在火焰加速数值模拟中的应用
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摘要
基于描述可燃气体火焰加速及爆燃转爆轰的Navier-Stokes方程组,针对非刚性的对流扩散项及刚性的反应项之间的不同时间尺度,从而导致了直接数值模拟十分困难的问题,构造了Krylov隐式积分因子法(IIF)进行直接数值模拟,对刚性的反应项采用隐格式,非刚性的对流扩散项采用显格式,从而减少了计算步数,提高了计算效率,对于由隐格式带来的方程组,采用Krylov子空间映射来降低方程组的阶数使得计算量减小,数值模拟结果与实验结果相吻合.研究结果表明,IIF方法可以较好地应用于NS方程组的数值模拟中.
In order to solve the problem in direct numerical simulation based on Navier-Stokes equations to describe flame acceleration and deflagration to detonation transition of combustible gas,a Krylov implicit integration factor(IIF)method was proposed to overcome the difficulty due to the different time scale caused by the non-stiff advection-diffusion terms and stiff reaction terms in Navier-Stokes equations.Explicit scheme was used to discretize the non-stiff terms and implicit scheme to discretize the stiff reaction terms.The equations with implicit scheme make large time step size computations possible.And the large sparse matrix is projected to the Krylov subspace,and the dimension of the Krylov subspace is much smaller than the dimension of the large sparse matrix at lower computational cost.The results of numerical simulation are identical with experimental results.The results show that IIF method could apply in the simulation for NS equations well.
In order to solve the problem in direct numerical simulation based on Navier-Stokes equations to describe flame acceleration and deflagration to detonation transition of combustible gas,a Krylov implicit integration factor(IIF)method was proposed to overcome the difficulty due to the different time scale caused by the non-stiff advection-diffusion terms and stiff reaction terms in Navier-Stokes equations.Explicit scheme was used to discretize the non-stiff terms and implicit scheme to discretize the stiff reaction terms.The equations with implicit scheme make large time step size computations possible.And the large sparse matrix is projected to the Krylov subspace,and the dimension of the Krylov subspace is much smaller than the dimension of the large sparse matrix at lower computational cost.The results of numerical simulation are identical with experimental results.The results show that IIF method could apply in the simulation for NS equations well.
引文
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[2]Nie Qing,Zhang Yongtao,Zhao Rui.Efficient semi-implicit schemes for stiff systems[J].Journal of Computational Physics,2006,214:521-537.
[3]Chen Shanqin,Zhang Yongtao.Krylov implicit integration factor methods for spatial discretization on high dimensional unstructured meshes:application to discontinuous Galerkin methods[J].Journal of Computational Physics,2011,230:4336-4352.
[4]Liu Xinfeng,Nie Qing.Compact integration factor methods for complex domains and adaptive mesh refinement[J].Journal of Computational Physics,2010,229:5692-5706.
[5]Jiang Tian,Zhang Yongtao.Krylov implicit integration factor WENO methods for semilinear and fully nonlinear advection-diffusion-reaction equations[J].Journal of Computational Physics,2013,253:368-388.
[6]王成,宋清官.基于Additive Runge-Kutta方法的激波聚焦起爆高精度数值模拟[J].北京理工大学学报,2016,36(2):137-143.Wang Cheng,Song Qingguan.Numerical application of additive Runge-Kutta methods on detonation initiation with convergence of shock waves[J].Transactions of Beijing Institute of Technology,2016,36(2):137-143.(in Chinese)
[7]赵慧,李健,郝莉.不同曲率弯管对气相爆轰波传播特性的影响[J].北京理工大学学报,2014,34(增刊1):176-180.Zhao Hui,Li Jian,Hao Li.The influence of different bend curvature on gaseous detonation wave propagation[J].Transactions of Beijing Institute of Technology,2014,34(suppl 1):176-180.(in Chinese)
[8]蔺伟,宋清官,王成,等.浓度梯度对瓦斯爆炸影响的数值模拟[J].北京理工大学学报,2015,35(4):336-340.Lin Wei,Song Qingguan,Wang Cheng,et al.Numerical investigation about the effect of concentration gradient on methane explosion[J].Transactions of Beijing Institute of Technology,2015,35(4):336-340.(in Chinese)
[9]Moler C,Van L C.Nineteen dubious ways to compute the exponential of a matrix,twenty-five years later[J].SIAM Review,2003,45:3-49.
[10]Bychkov V,Petchenko A,Akkerman V,et al.Theory and modeling of accelerating flames in tubes[J].Physical Review E,2005,72:04630701-04630710.