An efficient discontinuous Galerkin method for advective transport in porous media

We consider a discontinuous Galerkin scheme for computing transport in heterogeneous media. An efficient solution of the resulting linear system of equations is possible by taking advantage of a priori knowledge of the direction of flow. By arranging the elements in a suitable sequence, one does not need to assemble the full system and may compute the solution in an element-by-element fashion. We demonstrate this procedure on boundary-value problems for tracer transport and time-of-flight.

[1]  Juhani Pitkäranta,et al.  An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation , 1986 .

[2]  G. T. Eigestad,et al.  Improved streamlines and time-of-flight for streamline simulation on irregular grids , 2007 .

[3]  Akhil Datta-Gupta,et al.  A semianalytic approach to tracer flow modeling in heterogeneous permeable media , 1996 .

[4]  Chi-Wang Shu,et al.  The Runge-Kutta local projection $P^1$-discontinuous-Galerkin finite element method for scalar conservation laws , 1988, ESAIM: Mathematical Modelling and Numerical Analysis.

[5]  Knut-Andreas Lie,et al.  A Method To Improve the Mass Balance in Streamline Methods , 2007, All Days.

[6]  John K. Reid,et al.  An Implementation of Tarjan's Algorithm for the Block Triangularization of a Matrix , 1978, TOMS.

[7]  Hussein Hoteit,et al.  Multicomponent fluid flow by discontinuous Galerkin and mixed methods in unfractured and fractured media , 2005 .

[8]  D. W. Pollock.  Semianalytical Computation of Path Lines for Finite‐Difference Models , 1988 .

[9]  José Mario Martínez,et al.  Triangular Decomposition Methods for Solving Reducible Nonlinear Systems of Equations , 1994, SIAM J. Optim..

[10]  Qun Lin,et al.  CONVERGENCE OF THE DISCONTINUOUS GALERKIN METHOD FOR A SCALAR HYPERBOLIC EQUATION , 1993 .

[11]  W. H. Reed,et al.  Triangular mesh methods for the neutron transport equation , 1973 .

[12]  Knut-Andreas Lie,et al.  Fast computation of arrival times in heterogeneous media , 2006 .

[13]  Knut-Andreas Lie,et al.  A DISCONTINUOUS GALERKIN METHOD FOR COMPUTING TIME-OF-FLIGHT IN DISCRETE-FRACTURE MODELS , 2006 .

[14]  Jostein R. Natvig,et al.  Fast computation of multiphase flow in porous media by implicit discontinuous Galerkin schemes with optimal ordering of elements , 2008, J. Comput. Phys..

[15]  P. Raviart,et al.  On a Finite Element Method for Solving the Neutron Transport Equation , 1974 .

[16]  Michael Andrew Christie,et al.  Tenth SPE Comparative Solution Project: a comparison of upscaling techniques , 2001 .

[17]  Chi-Wang Shu,et al.  TVB Runge-Kutta local projection discontinuous galerkin finite element method for conservation laws. II: General framework , 1989 .

[18]  Robert Sedgewick,et al.  Algorithms in C , 1990 .