On convergence of a discrete problem describing transport processes in the pressing section of a paper machine including dynamic capillary effects: One-dimensional case

详细信息	查看全文 | 推荐本文 |

• 作者：G. Printsypar^a ; ^b ; ^{galina.printsypar@itwm.fraunhofer.de} ; ^{galina.printsypar@gmail.com} ; R. 膶iegis^c ; ^{raimondas.ciegis@vgtu.lt}
• 关键词：Saturated and unsaturated fluid flow in porous media ; Richards&rsquo ; approach ; Dynamic capillary pressure ; Finite volume methods ; Convergence of approximate solution
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2012
• 期刊代码：72_03770427
• 类别：cp
• 出版时间：August, 2012
• 卷：236
• 期：14
• 页码：3409-3425
• 文件大小：520 K

摘要

This work presents a proof of convergence of a discrete solution to a continuous one. At first, the continuous problem is stated as a system of equations which describe the filtration process in the pressing section of a paper machine. Two flow regimes appear in the modeling of this problem. The model for the saturated flow is presented by the Darcy鈥檚 law and the mass conservation. The second regime is described by the Richards鈥?approach together with a dynamic capillary pressure model. The finite volume method is used to approximate the system of PDEs. Then, the existence of a discrete solution to the proposed finite difference scheme is proven. Compactness of the set of all discrete solutions for different mesh sizes is proven. The main theorem shows that the discrete solution converges to the solution of the continuous problem. At the end we present numerical studies for the rate of convergence.