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Multistep characteristic method for incompressible flow in porous media. (English) Zbl 1166.76038
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 +(Δt) 2 ), which is in contrast to the convergence of order O(h+Δt) proved for a singlestep characteristic with the same space discretization. Numerical experiments demonstrate the stability and second-order convergence of the scheme.
76M20Finite difference methods (fluid mechanics)
76S05Flows in porous media; filtration; seepage
65M12Stability and convergence of numerical methods (IVP of PDE)
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