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首页> 外文期刊>International journal of numerical methods for heat & fluid flow >Unconditionally stable numerical scheme for natural convection problems
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Unconditionally stable numerical scheme for natural convection problems

机译：自然对流问题的无条件稳定数值格式

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Purpose - Both the importance of the natural convection in science and engineering and the shortage of publications in the field of numerical features of time-stepping schemes for the simulation of coupled heat and fluid flow problems motivate the present work. The paper aims to discuss these issues. Design/methodology/approach - The paper presents the unconditionally stable time-stepping scheme for simulation of coupled problems of mass and heat transport. The paper is divided into two parts. The first part concerns the mathematical formulation of the scheme and discusses its implementation. The second part focuses on the numerical simulation and its results. A detailed investigation of the temporal order of the scheme with respect to the L2-norms of the errors of the pressure, velocity, temperature and divergence of velocity fields has also been given. Findings - The work shows that it is possible to formulate a numerical scheme which is unconditionally stable with respect to the time step size. Moreover, application of the spectral element method for the spatial discretization results in a high order of approximation in space and very good overall accuracy. Furthermore, the investigation of the numerical features of the scheme showed that the formal temporal order of the scheme (formally second order) has been deferred very slightly and the order of 1.8-1.9 is achieved for all unknown fields. Originality/value - The paper presents a new unconditionally stable scheme for simulation of unsteady flows with bidirectional coupling of heat transfer and the fluid flow. It also carefully investigates the numerical behaviour of the method.
机译：目的-自然对流在科学和工程中的重要性以及时间步长方案的数值特征领域中用于模拟热力和流体流动耦合问题的出版物的缺乏，都推动了这项工作。本文旨在讨论这些问题。设计/方法/方法-本文提出了无条件稳定的时间步长方案，用于模拟传质和传热的耦合问题。本文分为两部分。第一部分涉及该方案的数学公式，并讨论了其实施。第二部分着重于数值模拟及其结果。还给出了关于压力，速度，温度和速度场散度的误差的L2-范数的该方案的时间顺序的详细研究。结果-这项工作表明，有可能制定一种相对于时间步长大小无条件稳定的数值方案。此外，光谱元素方法在空间离散化中的应用导致空间近似的高阶和非常好的总体精度。此外，对该方案的数值特征的研究表明，该方案的形式时间顺序（正式为二阶）已被稍微推迟了，并且在所有未知字段中均达到了1.8-1.9的顺序。原创性/价值-本文提出了一种新的无条件稳定方案，用于模拟具有传热和流体流动的双向耦合的非稳定流动。它还仔细研究了该方法的数值行为。

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