RT Journal Article ID 70275fa3501c3ea8 A1 Tambue, Antoine T1 EFFICIENT NUMERICAL SIMULATION OF INCOMPRESSIBLE TWO-PHASE FLOW IN HETEROGENEOUS POROUS MEDIA BASED ON EXPONENTIAL ROSENBROCK−EULER METHOD AND LOWER-ORDER ROSENBROCK-TYPE METHOD JF Journal of Porous Media JO JPM YR 2013 FD 2013-04-29 VO 16 IS 5 SP 381 OP 393 K1 heterogeneous porous media K1 exponential integrators K1 Rosenbrock-type method K1 isothermal incompressible two-phase flow K1 Krylov subspace K1 fast time stepping K1 finite volumes methods AB In this paper, we present the exponential Rosenbrock−Euler method and the lowest-order Rosenbrock-type method combined with the finite volume (two-point or multi-point flux approximations) space discretization to simulate isothermal incompressible two-phase flow in heterogeneous porous media. The exponential Rosenbrock−Euler method (EREM) linearizes the saturation equation at each time step and makes use of a matrix exponential function of the Jacobian, then solves the corresponding stiff linear ordinary differential equations exactly in time up to the given tolerance in the computation of a matrix exponential function of the Jacobian from the space discretization. Using a Krylov subspace technique makes this computation efficient. Besides, this computation can be done using the free-Jacobian technique. The lowest-order Rosenbrock type method, also called linearly implicit method, is deduced from EREM by approximating the exponential function of the Jacobian by the appropriate rational function of the Jacobian. As a result, this scheme is L-stable and only one linear system is normally solved at each time step. All our numerical examples demonstrate that our methods can compete in terms of efficiency and accuracy with the standard time integrators for reservoir simulation in highly anisotropic and heterogeneous porous media. Simulations are performed up to 1.1 million of unknowns with and without capillary pressure. PB Begell House LK https://www.dl.begellhouse.com/journals/49dcde6d4c0809db,38123d330ed01519,70275fa3501c3ea8.html