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Zbl 1166.76038
Long, Xiaohan; Yuan, Yirang
Multistep characteristic method for incompressible flow in porous media. (English)
[J] Appl. Math. Comput. 214, No. 1, 259-270 (2009). ISSN 0096-3003

Summary: We present a multistep difference scheme for the problem of miscible displacement of incompressible fluid flow in porous media. The discretization involves a three-level time scheme based on the characteristic method, and a five-point finite difference scheme for space discretization. We prove that the convergence is of order $O(h^{2}+(\Delta t)^{2})$, which is in contrast to the convergence of order $O(h+\Delta t)$ proved for a singlestep characteristic with the same space discretization. Numerical experiments demonstrate the stability and second-order convergence of the scheme.

MSC 2000:: *76M20 Finite difference methods
76S05 Flows in porous media
65M12 Stability and convergence of numerical methods (IVP of PDE)

Keywords: five-point finite difference scheme; second-order convergence

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