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首页> 外文期刊>Journal of Computational Physics >A fast iterative model for discrete velocity calculations on triangular grids
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A fast iterative model for discrete velocity calculations on triangular grids

机译：用于三角网格上离散速度计算的快速迭代模型

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摘要

A fast synthetic type iterative model is proposed to speed up the slow convergence of discrete velocity algorithms for solving linear kinetic equations on triangular lattices. The efficiency of the scheme is verified both theoretically by a discrete Fourier stability analysis and computationally by solving a rarefied gas flow problem. The stability analysis of the discrete kinetic equations yields the spectral radius of the typical and the proposed iterative algorithms and reveal the drastically improved performance of the latter one for any grid resolution. This is the first time that stability analysis of the full discrete kinetic equations related to rarefied gas theory is formulated, providing the detailed dependency of the iteration scheme on the discretization parameters in the phase space. The corresponding characteristics of the model deduced by solving numerically the rarefied gas flow through a duct with triangular cross section are in complete agreement with the theoretical findings. The proposed approach may open a way for fast computation of rarefied gas flows on complex geometries in the whole range of gas rarefaction including the hydrodynamic regime.
机译：提出了一种快速合成类型的迭代模型，以加快离散速度算法的缓慢收敛速度，从而解决三角晶格上的线性动力学方程。该方案的效率在理论上通过离散傅里叶稳定性分析进行了验证，并在计算上通过解决了稀疏气体流动问题得到了验证。离散动力学方程的稳定性分析得出了典型算法和拟议迭代算法的光谱半径，并揭示了在任何网格分辨率下，后者的性能都得到了显着改善。这是首次提出与稀薄气体理论相关的完整离散动力学方程的稳定性分析，从而提供迭代方案对相空间中离散化参数的详细依赖性。通过数值求解稀有气体流经具有三角形横截面的管道得出的模型的相应特征与理论发现完全一致。所提出的方法可能为在包括流体力学状态在内的整个气体稀薄化范围内的复杂几何形状上快速计算稀薄气体流开辟一种途径。

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