论文标题
快速方法和分数磁流体动力耦合流和传热模型的融合分析的广义二年级流体
Fast method and convergence analysis of fractional magnetohydrodynamic coupled flow and heat transfer model for generalized second-grade fluid
论文作者
论文摘要
在本文中，我们首先为广义二年级流体建立了新的分数磁流失动力学（MHD）耦合流量和传热模型。该耦合模型由分数动量方程和具有广义形式的傅立叶定律形式的热传导方程组成。二阶分数向后差公式应用于时间离散化，Legendre光谱方法用于空间离散化。事实证明，完全离散的方案是稳定和收敛的，精度为$ O（τ^2+n^{ - r}）$，其中$τ$是时间步长，$ n $是多项式学位。为了降低记忆要求和计算成本，开发了一种快速方法，该方法基于真实线上积分的梯形规则的全球均匀近似。并且证明了使用这种快速方法的数值方案的严格收敛性。我们介绍了几个数值实验的结果，以验证所提出方法的有效性。最后，我们通过多孔培养基模拟不稳定的分数MHD流量和广义二年级流体的热传递。相关参数对速度和温度的影响进行了详细介绍和分析。
In this paper, we first establish a new fractional magnetohydrodynamic (MHD) coupled flow and heat transfer model for a generalized second-grade fluid. This coupled model consists of a fractional momentum equation and a heat conduction equation with a generalized form of Fourier law. The second-order fractional backward difference formula is applied to the temporal discretization and the Legendre spectral method is used for the spatial discretization. The fully discrete scheme is proved to be stable and convergent with an accuracy of $O(τ^2+N^{-r})$, where $τ$ is the time step size and $N$ is the polynomial degree. To reduce the memory requirements and computational cost, a fast method is developed, which is based on a globally uniform approximation of the trapezoidal rule for integrals on the real line. And the strict convergence of the numerical scheme with this fast method is proved. We present the results of several numerical experiments to verify the effectiveness of the proposed method. Finally, we simulate the unsteady fractional MHD flow and heat transfer of the generalized second-grade fluid through a porous medium. The effects of the relevant parameters on the velocity and temperature are presented and analyzed in detail.
