Convergence of implicit monotone schemes with applications in multiphase flow in porous media. (English) Zbl 1207.35022
The authors study convergence of implicit monotone schemes for multiphase flow in porous media. In particular to stabilise the approximation the so-called phase-based upwinding is used. It is shown that the nonlinear Gauss-Seidel or Jacobi algorithms converge for a scheme with implicit time-stepping. In particular they obtained an alternative proof that for one-dimensional problems the scheme converges to the entropy solution of the conservation laws for arbitrary CFL numbers. At the end of paper the accuracy of phase-based upstream scheme is studied.
Reviewer: Mária Lukáčová (Hamburg)
MSC:
35A35 | Theoretical approximation in context of PDEs |
35L65 | Hyperbolic conservation laws |
65H10 | Numerical computation of solutions to systems of equations |
65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |