The Buckley-Leverett equation with spatially stochastic flux function

SIAM Journal on Applied Mathematics

Volumn 57, Issue 5, 1997, Pages 1443-1454

  Holden, Lars ^a  

^a NORWEGIAN COMPUTING CENTER   (Norway)

Author keywords

Buckley Leverett equation; Scalar conservation law; Stochastic partial differential equations

Indexed keywords

COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; MATHEMATICAL MODELS; RANDOM PROCESSES; THEOREM PROVING;

BUCKLEY LEVERETT EQUATION; SCALAR CONSERVATION LAW; STOCHASTIC FLUX FUNCTION;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0031259147     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139994273077     Document Type: Article

References (17)

1. C. DAFERMOS, Polygonal approximations of solutions of the initial value problem for a conservation law, J. Math. Anal. Appl., 38 (1972), pp. 33-41.
2. S. EKRANN AND M. DALE, Averaging of relative permeability in heterogeneous reservoirs, in The Mathematics of Oil Recovery, P. King, ed., Oxford University Press, Oxford, UK, 1992, pp. 173-199.
3. T. GIMSE AND N. H. RISEBRO, Riemann problems with a discontinuous flux function, in Proc. Third Internat. Conf. Hyp. Prob., B. Engquist and B. Gustavsen, eds., Studentlitteratur, Chartwell-Bratt, Uppsala, Sweden, June 1990, pp. 488-502.
4. J. GLIMM, Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math., 18 (1965), pp. 109-209.
5. H. H. HALDORSEN AND E. DAMSLETH, Stochastic modeling, J. Petr. Techn., (1990), pp. 404-412.
6. H. HOLDEN AND L. HOLDEN, On scalar conservation laws in one dimension, in Ideas and Methods in Mathematical Analysis, Stochastics and Applications, S. Albeverio, J. E. Fenstad, H. Holden, and T. Lindstrøm, eds., Cambridge University Press, Cambridge, UK, 1992, pp. 480-509.
7. H. HOLDEN AND N. H. RISEBRO, Stochastic properties of the Buckley-Leverett equation, SIAM J. Appl. Math., 51 (1991), pp. 1472-1488.
8. L. HOLDEN AND R. HØEGH-KROHN, A class of n nonlinear hyperbolic conservation laws, J. Differential Equations, 84 (1990), pp. 73-99.
9. L. HOLDEN, H. OMRE, AND H. TJELMELAND, Integrated reservoir description, SPE 24275, in European Petroleum Computer Conference, Stavanger, Norway, May 1992, Society of Petroleum Engineers, Dallas, TX.
10. P. R. KING, The use of renormalization for calculating effective permeability, Transport in Porous Media, 4 (1989), pp. 37-58.
11. H. P. LANGTANGEN, Deterministic and stochastic sensitivity analysis of a mathematical model for polymer flooding, Geophysical Prospecting, 36 (1988), pp. 223-243.
12. H. P. LANGTANGEN, A. TVEITO, AND R. WINTHER, Instability of Buckley-Leverett flow in a heterogeneous medium, Transport in Porous Media, 9 (1992), pp. 165-185.
13. O. A. OLEINIK, Discontinuous solutions of non-linear differential equations, Trans. Amer. Math. Soc., 26 (1963), pp. 95-172.
14. H. OMRE, H. TJELMELAND, Y. QI, AND L. HINDERAKER, Assessment of Uncertainty in the Production Characteristics of a Sand Stone Reservoir, NIPER 3RC-86, presented at the Third International "Reservoir Characterization" Technical Conference, Tulsa, OK, Nov. 1991.
15. D. W. PEACEMAN, Fundamentals of Numerical Reservoir Simulation, Elsevier, Amsterdam, Oxford, New York, 1977.
16. C. B. TJØLSEN, E. DAMSLETH, AND T. BU, Stochastic relative permeabilities usually have neglectable effect on reservoir performance, SPE 26473, in 68th Annual Technical Conference and Exhibition, Houston, TX, Oct. 1993, Society of Petroleum Engineers, Dallas, TX.
17. B. ØKSENDAL, Stochastic Differential Equations: An Introduction with Applications, 3rd ed., Universitext, Springer-Verlag, Berlin, 1992.