| 黄懿,于海东,尤天庆.密度基两相流求解方法的显式大时间步格式研究[J].计算力学学报,2024,41(6):1087~1096 |
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| 密度基两相流求解方法的显式大时间步格式研究 |
| An investigation on the explicit large-time step scheme in the density-based two-phase flow solver |
| 投稿时间：2023-05-21 修订日期：2023-08-07 |
| DOI：10.7511/jslx20230521002 |
| 中文关键词: 两相流 显式大时间步格式 非守恒型方程 松弛方法 叠波法 |
| 英文关键词:two-phase flow large time step non-conservative equations relaxation method wave adding method |
| 基金项目:自然基金联合基金项目(U20B2004)资助. |
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| 摘要点击次数: 41 |
| 全文下载次数: 28 |
| 中文摘要: |
| 两相流的六方程模型是双曲非守恒型系统,并具有非平衡源项。基于密度的方程求解方法则包含了齐次的双曲型方程求解以及非平衡源项的松弛过程。在齐次方程的求解中,Godunov型格式下的时间步长受到CFL数小于1的限制,计算效率不高。显式大时间步(LTS)格式是双曲守恒型方程的求解中突破CFL数限制的重要方法之一。在线性波的假设下,本文将通量差分裂(FDS)形式的LTS格式推广到了非守恒型的两相流六方程模型的求解中,提出了基于HLLC型Riemann求解器的LTS格式(LTS-HLLC)。研究表明,在两相明显分离的区域,LTS-HLLC格式下增大CFL数可以减小数值粘性,提升了对激波等间断的分辨率也更易产生振荡,这与双曲守恒型方程中LTS格式的效果相同。但是在两相混合的区域,增大CFL数会加大松弛过程的耗散,使得对间断的分辨率反而降低。采用LTS-HLLC格式提高CFL数可以有效降低计算消耗的CPU时间,提高计算效率。 |
| 英文摘要: |
| The two-phase flow six-equation model is a hyperbolic non-conservative system,with non-equilibrium source terms.The density-based numerical method contains the solution of the homogeneous hyperbolic equations and relaxation of the non-equilibrium source terms.In the solution of homogeneous equations,the time step with Godunov’s scheme is limited by the CFL number less than 1,which leads to low computation efficiency.The large time step scheme is one of the important methods to break the limit in hyperbolic conservative equations.Under the linear wave assumption,this research extends the flux-difference splitting type of LTS scheme to solving the non-conservative two-phase six-equation model and proposes the LTS scheme (LTS-HLLC) based on HLLC type Riemann solver.It is found that increasing the CFL number with the LTS-HLLC scheme can reduce the numerical viscosity in two-phase regions with obvious interfaces,improve the resolution of the discontinuity,like shocks,and produce oscillations easily,which is the same as those in the hyperbolic conservative equations with the LTS scheme.However,in two-phase mixture regions,increasing CFL number can enhance the diffusion of the relaxation process,reducing the resolution of the discontinuity.Increasing the CFL number with LTS-HLLC scheme can effectively reduce the CPU time and improve the computation efficiency. |
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