Modified class of explicit and enhanced stability region schemes: Application to mixed convection flow in a square cavity with a convective wall,International Journal for Numerical Methods in Fluids

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Modified class of explicit and enhanced stability region schemes: Application to mixed convection flow in a square cavity with a convective wall
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2020-12-11 , DOI: 10.1002/fld.4951
Yasir Nawaz ₁ , Muhammad Shoaib Arif ₁

Affiliation

A modification of Adams–Bashforth methods is given to construct time discretization schemes for partial differential equations. The second‐order modified method is shown to have a larger stability region than second‐order standard Adams–Bashforth for the two‐dimensional heat equation. Later the scheme is applied on considered flow problem in a square cavity. The flow problem is a modified mathematical model of the heat and mass transfer of mixed convection flow in a square cavity with effects of the inclined magnetic field and thermal radiations. In addition to this, another feature of the present contribution is to apply the coupling approach for employing a mixture of stable and unstable schemes. This coupling approach is based upon the difference quotient that has been used in the literature to construct flux limiters for reducing oscillations in the discontinuous solutions of hyperbolic conservation laws. Since proposed scheme produces oscillation in the beginning and then diverges for the chosen diffusion number that falls in the unstable region, so these oscillations, due to instability, is reduced by coupling it with the scheme that can produce the convergent solution. The convergence of the proposed scheme for the considered modified nondimensional mathematical model of mixed convection flow is also given. The improvement is shown in graphs when proposed second order in time scheme is compared with the standard second order in time Adams–Bashforth method. Also, the mixture of first‐order and unconditionally unstable Richardson's schemes is applied, and the solution is obtained, and some plots are provided.

中文翻译：

明确和增强的稳定区域方案的修改类：在具有对流壁的方腔中的混合对流流动中的应用

修改了Adams–Bashforth方法，以构造偏微分方程的时间离散方案。对于二维热方程，二阶改进方法的稳定性区域要比二阶标准Adams–Bashforth大。后来，该方案被应用于方腔中考虑的流动问题。流动问题是在倾斜磁场和热辐射的作用下，对流在方形空腔中的传热和传质的改进数学模型。除此之外，本发明的另一个特征是将耦合方法应用于采用稳定方案和不稳定方案的混合。这种耦合方法基于差分商，该差分商已在文献中用于构建磁通限制器，以减少双曲线守恒律的不连续解中的振荡。由于建议的方案在开始时产生振荡，然后针对落入不稳定区域的所选扩散数发散，因此，由于不稳定而导致的振荡，可以通过将其与可以产生收敛解的方案耦合来减少。还给出了所考虑的混合对流的改进的无量纲数学模型的拟议方案的收敛性。当将建议的时间顺序二阶与标准时间二阶Adams–Bashforth方法进行比较时，图表中会显示出改进。同样，一阶和无条件不稳定的理查森的混合

更新日期：2020-12-11

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