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首页> 外文期刊>Journal of Computational Physics >Two new upwind difference schemes for a coupled system of convection-diffusion equations arising from the steady MHD duct flow problems
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Two new upwind difference schemes for a coupled system of convection-diffusion equations arising from the steady MHD duct flow problems

机译：对流扩散方程耦合系统产生的两个新的迎风差分方案，源于稳定的MHD管道流动问题

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摘要

In this paper, we develop two new upwind difference schemes for solving a coupled system of convection-diffusion equations arising from the steady incompressible MHD duct flow problem with a transverse magnetic field at high Hartmann numbers. Such an MHD duct flow is convection-dominated and its solution may exhibit localized phenomena such as boundary layers, namely, narrow boundary regions where the solution changes rapidly. Most conventional numerical schemes cannot efficiently solve the layer problems because they are lacking in either stability or accuracy. In contrast, the newly proposed upwind difference schemes can achieve a reasonable accuracy with a high stability, and they are capable of resolving high gradients near the layer regions without refining the grid. The accuracy of the first new upwind scheme is O(h+k) and the second one improves the accuracy to O(ε~2(h+k)+ε(h~2+k~2)+(h~3+k~3)), where 0<ε:=1/M?1 and M is the high Hartmann number. Numerical examples are provided to illustrate the performance of the newly proposed upwind difference schemes.
机译：在本文中，我们开发了两个新的迎风差分方案，用于求解由高Hartmann数下的横向磁场产生的稳态不可压缩MHD管道流动问题引起的对流扩散方程的耦合系统。这种MHD管道流是对流为主的，其解可能会显示局部现象，例如边界层，即溶液迅速变化的狭窄边界区域。大多数常规数值方案都缺乏稳定性或准确性，因此无法有效解决层问题。相反，新提出的迎风差异方案可以以较高的稳定性实现合理的精度，并且能够在不细化网格的情况下解决层区域附近的高梯度。第一个新的迎风方案的精度为O（h + k），第二个新方案将精度提高为O（ε〜2（h + k）+ε（h〜2 + k〜2）+（h〜3 + k〜3）），其中0 <ε：= 1 / M？1，M是高哈特曼数。提供了数值示例，以说明新提出的迎风差异方案的性能。

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