An upwind center difference parallel method and numerical analysis for the displacement problem with moving boundary. Issue 5 (6th March 2019)

• Record Type: Journal Article
• Authors: Li, Changfeng; Yuan, Yirang
• Is Part Of: Numerical methods for partial differential equations. Volume 35:Issue 5(2019)
• Page Start: 1654
• Page End: 1675
• Publication Date: 2019-03-06
• Subjects: convergence analysis -- domain decomposition -- moving boundary -- seepage displacement -- upwind center finite difference; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22369
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract : A nonlinear coupled mathematical system of two‐phase seepage flow displacement is discussed in this paper including an elliptic equation for the pressure and a convection‐dominated diffusion equation for the saturation. In fact, the boundary of an underground region where the fluid flows through is nonstationary. So a moving boundary should be considered. The saturation equation is convection‐dominated, therefore the method of upwind finite difference is introduced for the accurate computation. The upwind approximation could eliminate numerical oscillation and strong stability is shown. Since the computational work of saturation is larger than the pressure, the authors apply a parallel method, decomposing the whole domain into several nonoverlapping subdomains, to simplify the computation. A domain decomposition method coupled with upwind differences is presented for the saturation. The pressure equation is discretized by a five‐point center finite difference method. By using a transformation and defining new inner products and norms, error estimates in l 2 norm is discussed. Finally, two experimental tests are given to illustrate the efficiency and accuracy of the parallel algorithm.