On efficient implicit upwind schemes

ECMOR 2008 - 11th European Conference on the Mathematics of Oil Recovery

Volumn , Issue , 2008, Pages

  Natvig, J R ^a   Lie, K A ^a  

^a SINTEF ICT   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

EFFICIENCY; GALERKIN METHODS; INCOMPRESSIBLE FLOW; NONLINEAR SYSTEMS; RESERVOIR MANAGEMENT;

COMMERCIAL SIMULATORS; DISCONTINUOUS GALERKIN; DISCRETIZATIONS; HYPERBOLIC TRANSPORTS; ORDERS OF MAGNITUDE; RESERVOIR MODELS; RESERVOIR SIMULATION; SYSTEM OF NONLINEAR EQUATIONS;

NONLINEAR EQUATIONS;

EID: 85086615203     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.3997/2214-4609.20146356     Document Type: Conference Paper

References (11)

1. Davis, T.A. and Duff, I.S. [1997] UMFPACK: An unsymmetric-pattern multifrontal method for sparse LU factorization. SIAM J. Matrix Anal. Appl, 18(1), 140-158.
2. Dennis, Jr., J.E., Martínez, J.M., and Zhang, X. [1994] Triangular decomposition methods for solving reducible nonlinear systems of equations. SIAM J. Optim., 4(2), 358-382.
3. Duff, I.S. and Reid, J.K. [1978] An implementation of Tarjan's algorithm for the block triangu-larization of a matrix. ACM Trans. Math. Software, 4(2), 137-147.
4. Gmelig Meyling, R.H.J. [1991] Numerical methods for solving the nonlinear hyperbolic equations of porous media flow. In: Third International Conference on Hyperbolic Problems, Vol. I, II (Uppsala, 1990). Studentlitteratur, Lund, 503-517.
5. Kwok, F. [2007] Scalable linear and nonlinear algorithms for multiphase flow in porous media.
6. Natvig, J.R. and Lie, K.A. [2008] Fast computation of multiphase flow in porous medis by implicit discontinuous Galerkin schemes with optimal ordering of elements. J. Comput. Phys.
7. Natvig, J.R., Lie, K.A., Eikemo, B., and Berre, I. [2007] A discontinuous Galerkin method for computing single-phase flow in porous media. Adv. Water Resour, 30(12), 2424-2438.
8. Press, W.H., Teukolsky, S.A., Vetterling, W.T., and Flannery, B.P. [1992] Numerical recipes in C. Cambridge University Press, Cambridge, second edition. The art of scientific computing.
9. Reed, W.H. and Hill, T.R. [1973] Triangular mesh methods for the neutron transport equation. (LA-UR-73-479).
10. Tarjan, R. [1972] Depth-first search and linear graph algorithms. SIAM J. Comput., 1(2), 146-160.
11. Wang, F and Xu, J. [1999] A crosswind block iterative method for convection-dominated problems. SIAMJ. Sci. Comput., 21(2), 620-645.