A new efficient Eulerian-Lagrangian localized adjoint method for solving the advection-dispersion equation on unstructured meshes

Advances in Water Resources

Volumn 29, Issue 7, 2006, Pages 1056-1074

  Younes, A ^a   Ackerer, P ^a   Lehmann, F ^a  

^a Faculté de Médecine   (France)

Author keywords

ADE; ELLAM; Quadrature; Strategic integration points; Tracking; Unstructured meshes

Indexed keywords

COMPUTER SIMULATION; FINITE ELEMENT METHOD; INTEGRAL EQUATIONS; INTERPOLATION; NUMERICAL METHODS;

ADVECTION-DISPERSION TRANSPORT EQUATION; EULERIAN-LAGRANGIAN LOCALIZED ADJOINT METHOD; STRATEGIC INTEGRATION POINTS; UNSTRUCTURED MESHES;

LAGRANGE MULTIPLIERS;

COMPUTER SIMULATION; FINITE ELEMENT METHOD; INTEGRAL EQUATIONS; INTERPOLATION; LAGRANGE MULTIPLIERS; NUMERICAL METHODS;

ADVECTION-DIFFUSION EQUATION; FINITE ELEMENT METHOD; INTERPOLATION;

EID: 33744521010     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2005.09.003     Document Type: Article

References (18)

1. Binning P., and Celia M.A. A forward particle tracking Eulerian-Lagrangian localized adjoint method for solution of the contaminant transport equation in three dimensions. Adv Water Resour 25 (2002) 147-157
2. Celia M.A., Russell T.F., Herrera I., and Ewing R.E. An Eulerian-Lagrangian localized adjoint method for the advection-diffusion equation. Adv Water Resour 13 (1990) 187-206
3. Douglas Jr. J., and Russell T.F. Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures. SIAM J Numer Anal 19 (1982) 871-885
4. Healy R.W., and Russell T.F. A finite-volume Eulerian-Lagrangian localized adjoint method for solution of the advection-dispersion equation. Water Resour Res 29 (1993) 2399-2413
5. Healy R.W., and Russell T.F. Solution of the advection-dispersion equation in two dimensions by a finite-volume Eulerian-Lagrangian localized adjoint method. Adv Water Resour 21 (1998) 11-26
6. Leij F.J., and Dane J.H. Analytical solution of the one-dimensional advection equation and two or three-dimensional dispersion equation. Water Resour Res 26 (1990) 1475-1482
7. Morton K.W., Priestley A., and Süli E. Stability of the Lagrange-Galerkin method with non-exact integration. Math Model Numer Anal 22 (1988) 625-653
8. Pollock D.W. Semianalytical computation of path lines for finite-difference models. Groundwater 26 (1988) 743-750
9. Priestley A. Exact projections and the Lagrange-Galerkin method: a realistic alternative to quadrature. J Comput Phys 112 (1994) 316-333
10. Russell T.F., and Binning P. Oh No, not the Wiggles Again!. In: Miller C.T., et al. (Ed). A revisit of an old problem and a new approach, proc computational methods in water resources (2004), Elsevier, Amsterdam 483-494
11. Russell T.F. Numerical dispersion in Eulerian-Lagrangian methods. In: Hassanizadeh S.M., et al. (Ed). Proc computational methods in water resources (2002), Elsevier, Amsterdam 963-970
12. Russell T.F., Heberton C.I., Konikow L.F., and Hornberger G.Z. A finite-volume ELLAM for three-dimensional solute-transport modeling. Groundwater 41 (2003) 258-272
13. Russell T.F., and Celia M.A. An overview of research on Eulerian-Lagrangian localized adjoint methods (ELLAM). Adv Water Resour 25 (2002) 1215-1231
14. Siegel P., Mosé R., Ackerer P., and Jaffré J. Solution of the advection dispersion equation using a combination of discontinuous and mixed finite elements. Int J Numer Methods Fluids 24 (1997) 595-613
15. Wang H., Dahle H.K., Ewing R.E., Espedal M.S., Sharpley R.C., and Man S. An ELLAM scheme for advection diffusion equations in two dimensions. SIAM J Sci Comput 20 (1999) 2160-2194
16. Younes A. An accurate moving grid Eulerian Lagrangian localized adjoint method for solving the one-dimensional variable-coefficient ADE. Int J Numer Methods Fluids 45 (2004) 157-178
17. Younes A., and Ackerer P. Solving the advection-diffusion equation with the Eulerian Lagrangian localized adjoint method on unstructured meshes and non-uniform time stepping. J Comput Phys 208 (2005) 384-402
18. Younes A., Ackerer P., Mosé R., and Chavent G. A new formulation of the mixed finite element method for solving elliptic and parabolic PDE with triangular elements. J Comput Phys 149 (1999) 148-167