An unconditionally energy-stable scheme for the convective heat transfer equation
An unconditionally energy-stable scheme for the convective heat transfer equation
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DOI：
10.1108/hff-08-2022-0477
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发表时间：
2023-05
期刊：
影响因子：
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通讯作者：
Xiaoyu Liu;S. Dong;Zhiyong Xie
中科院分区：
文献类型：
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作者：
Xiaoyu Liu;S. Dong;Zhiyong Xie
目的提出一种近似对流换热方程的无条件能量稳定格式。该方案源于广义正辅助变量（gPAV）思想，并对对流项进行了特殊处理。原始对流项被其线性近似加上校正项所取代，校正项在辅助变量的控制下。该方案需要在每个时间步长内计算两个温度场，并且由离散化得到的线性代数系统包含一个定期更新的系数矩阵。这个辅助变量由一个定义良好的显式公式给出，该公式保证了其计算值的正性。与未处理对流项的半隐式方案和基于gpav的方案相比，当前方案可以提供更大的精度范围，并在大（或相当大）的时间步长下实现更精确的模拟。大量的数值实验证明了该方案的准确性和稳定性。独创性/价值本研究证明了当前方案的无条件离散能量稳定性，与时间步长无关。
Purpose This paper aims to present an unconditionally energy-stable scheme for approximating the convective heat transfer equation. Design/methodology/approach The scheme stems from the generalized positive auxiliary variable (gPAV) idea and exploits a special treatment for the convection term. The original convection term is replaced by its linear approximation plus a correction term, which is under the control of an auxiliary variable. The scheme entails the computation of two temperature fields within each time step, and the linear algebraic system resulting from the discretization involves a coefficient matrix that is updated periodically. This auxiliary variable is given by a well-defined explicit formula that guarantees the positivity of its computed value. Findings Compared with the semi-implicit scheme and the gPAV-based scheme without the treatment on the convection term, the current scheme can provide an expanded accuracy range and achieve more accurate simulations at large (or fairly large) time step sizes. Extensive numerical experiments have been presented to demonstrate the accuracy and stability performance of the scheme developed herein. Originality/value This study shows the unconditional discrete energy stability property of the current scheme, irrespective of the time step sizes.