节点中心型DG方法耦合RGFM的研究

Node-Centered DG Method Coupled with Real-Ghost Fluid Method

  • 摘要: 针对二维可压缩流体的复杂多介质界面问题提出了一种新的数值模拟方法,该方法结合了间断Galerkin (DG) 方法和真实虚拟流体方法(real-ghost fluid method,RGFM),构建了一种新的数值求解器. 求解器采用节点中心型DG方法对Euler方程进行空间离散,并利用加权本质无振荡 (WENO) 重构限制器抑制非物理振荡,确保数值格式的稳定性. Level-set方法和RGFM则被用于精确捕捉和处理多介质界面. 为了验证该DG-RGFM求解器的有效性,计算了多个数值算例,包括等熵旋涡、Noh问题、Sedov问题、水中强冲击波与空气泡相互作用以及激波与氦气泡相互作用等典型算例. 数值结果表明,所提出的DG-RGFM求解器能够有效地模拟复杂的多介质界面问题,并展现出良好的保真性和鲁棒性,为相关问题的数值模拟提供了一种有潜在应用价值的方案.

     

    Abstract: A new numerical simulation method was proposed for the complex multi-media interface problem of two-dimensional compressible fluids, which combined the discontinuous Galerkin (DG) method and the real-ghost fluid method (RGFM) to construct a new numerical solver. The solver employed a node-centered DG method for spatial discretization of the Euler equation and a weighted essentially no-oscillation (WENO) reconstruction limiter to suppress unphysical oscillations and to ensure the stability of the numerical format, while the Level-set method and the RGFM were used to accurately capture and process the multimedium interface. In order to verify the effectiveness of this DG-RGFM solver, several numerical examples were computed in this paper, including typical examples of isentropic vortices, the Noh problem, the Sedov problem, the interaction of a strong shock wave in water with an air bubble, and the interaction of a surge wave with a helium bubble. The numerical results show that the proposed DG-RGFM solver is able to effectively simulate complex multimedium interface problems and exhibits good fidelity and robustness, which provides a potentially applicable scheme for the numerical simulation of related problems.

     

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