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首页> 外文期刊>Advances in computational mathematics >Linear second order in time energy stable schemes for hydrodynamic models of binary mixtures based on a spatially pseudospectral approximation
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Linear second order in time energy stable schemes for hydrodynamic models of binary mixtures based on a spatially pseudospectral approximation

机译：基于空间伪谱逼近的二元混合物的流体动力学模型的时间能量稳定方案的线性二阶。基于空间伪谱逼近

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摘要

We develop two linear, second order energy stable schemes for solving the governing system of partial differential equations of a hydrodynamic phase field model of binary fluid mixtures. We first apply the Fourier pseudo-spectral approximation to the partial differential equations in space to obtain a semi-discrete, time-dependent, ordinary differential and algebraic equation (DAE) system, which preserves the energy dissipation law at the semi-discrete level. Then, we discretize the DAE system by the Crank-Nicolson (CN) and the second-order backward differentiation/extrapolation (BDF/EP) method in time, respectively, to obtain two fully discrete systems. We show that the CN method preserves the energy dissipation law while the BDF/EP method does not preserve it exactly but respects the energy dissipation property of the hydrodynamic model. The two new fully discrete schemes are linear, unconditional stable, second order accurate in time and high order in space, and uniquely solvable as linear systems. Numerical examples are presented to show the convergence property as well as the efficiency and accuracy of the new schemes in simulating mixing dynamics of binary polymeric solutions.
机译：我们开发了两个线性的二阶能量稳定方案，用于解决二元流体混合物流体相色谱局域模型的部分微分方程的控制系统。我们首先将傅里叶伪光谱近似应用于空间中的部分微分方程，以获得半离散，时间依赖性，常差分和代数（DAE）系统，其在半离散水平处保留能量耗散量。然后，我们分别通过曲柄-Nicolson（CN）和第二阶的向后分化/外推（BDF / EP）方法离散DAE系统，以获得两个完全分立的系统。我们表明CN方法保留了能量耗散规律，而BDF / EP方法不完全保留它，而是尊重流体动力学模型的能量耗散特性。这两个新的完全离散方案是线性，无条件稳定的，第二顺序在空间中以时间和高阶准确，并且作为线性系统唯一可溶解。提出了数值例子以显示收敛性，以及模拟二元聚合物溶液的混合动态的新方案的效率和准确性。

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