论文标题
通过基于自适应反卷积的非线性滤波，提高了不可压缩非等温流的LERAY模型的准确性
Improving accuracy in the Leray model for incompressible non-isothermal flows via adaptive deconvolution-based nonlinear filtering
论文作者
论文摘要
本文考虑了不可压缩的，非等热流体流的LERAY正则化模型，该模型根据指示函数使用非线性过滤，并引入了一种有效的数值方法来求解它。所提出的方法使用有限元（Fe）空间离散化的多步，二阶时间离散化，以使所得算法在每个时间级别是线性的，并且将演化方程式从速度滤波器步骤中分解出来。由于在此模型中选择的指标函数是基于近似理论的数学上，因此可以对所提出的数值算法进行稳定分析，即该方法的稳定性和收敛性是可证明的。进行了一系列数值测试以验证理论收敛速率，并将算法与直接数值模拟和流量问题的通常的leray- $α$模型进行比较。
This paper considers a Leray regularization model of incompressible, non-isothermal fluid flows which uses nonlinear filtering based on indicator functions, and introduces an efficient numerical method for solving it. The proposed method uses a multi-step, second-order temporal discretization with a finite element (FE) spatial discretization in such a way that the resulting algorithm is linear at each time level, and decouples the evolution equations from the velocity filter step. Since the indicator function chosen in this model is mathematically based on approximation theory, the proposed numerical algorithm can be analyzed robustly, i.e the stability and convergence of the method is provable. A series of numerical tests are carried out to verify the theoretical convergence rates, and to compare the algorithm with direct numerical simulation and the usual Leray-$α$ model of the flow problem.
