Publications

Journal Articles

  1. Ahmed, R., Xie, Y., Edwards, M. A Cell-Centred CVD-MPFA Finite Volume Method for Two-Phase Fluid Flow Problems with Capillary Heterogeneity and Discontinuity Transport in Porous Media
  2. Manzoor, S., Edwards, M., Dogru, A., Al-Shaalan, T. Interior boundary-aligned unstructured grid generation and cell-centered versus vertex-centered CVD-MPFA performance Computational Geosciences
  3. Ahmed, R., Edwards, M., Lamine, S., Huisman, B., Pal, M. CVD-MPFA full pressure support, coupled unstructured discrete fracture–matrix Darcy-flux approximations Journal of Computational Physics 349 265 299
  4. Xie, Y., Edwards, M. Higher resolution total velocity Vt and Va finite-volume formulations on cell-centred structured and unstructured grids Computational Geosciences
  5. Parramore, E., Edwards, M., Pal, M., Lamine, S. Multiscale Finite-Volume CVD-MPFA Formulations on Structured and Unstructured Grids Multiscale Modeling & Simulation 14 2 559 594
  6. Ahmed, R., Edwards, M., Lamine, S., Huisman, B., Pal, M. Three-dimensional control-volume distributed multi-point flux approximation coupled with a lower-dimensional surface fracture model Journal of Computational Physics 303 470 497
  7. Lamine, S., Edwards, M. Multidimensional upwind schemes and higher resolution methods for three-component two-phase systems including gravity driven flow in porous media on unstructured grids Computer Methods in Applied Mechanics and Engineering 292 171 194
  8. Ahmed, R., Edwards, M., Lamine, S., Huisman, B., Pal, M., Edwards, M. Control-volume distributed multi-point flux approximation coupled with a lower-dimensional fracture model Journal of Computational Physics 284 462 489
  9. Lamine, S., Edwards, M. Higher order cell-based multidimensional upwind schemes for flow in porous media on unstructured grids Computer Methods in Applied Mechanics and Engineering 259 103 122
  10. Pal, M., Edwards, M. The effects of control-volume distributed multi-point flux approximation (CVD-MPFA) on upscaling-A study using the CVD-MPFA schemes International Journal for Numerical Methods in Fluids 68 1 18 35
  11. Pal, M., Edwards, M., Edwards, M. A family of multi-point flux approximation schemes for general element types in two and three dimensions with convergence performance International Journal for Numerical Methods in Fluids 69 11 1797 1817
  12. Pal, M., Edwards, M. Non-linear flux-splitting schemes with imposed discrete maximum principle for elliptic equations with highly anisotropic coefficients International Journal for Numerical Methods in Fluids 66 3 299 323
  13. Edwards, M. Multi-dimensional wave-oriented upwind schemes with reduced cross-wind diffusion for flow in porous media International Journal for Numerical Methods in Fluids
  14. Pal, M., Edwards, M. Anisotropy favoring triangulation CVD(MPFA) finite-volume approximations International Journal for Numerical Methods in Fluids 67 10 1247 1263
  15. Edwards, M., Zheng, H. Quasi M-Matrix Multifamily Continuous Darcy-Flux Approximations with Full Pressure Support on Structured and Unstructured Grids in Three Dimensions SIAM Journal on Scientific Computing 33 2 455 487
  16. Friis, H., Edwards, M. A family of MPFA finite-volume schemes with full pressure support for the general tensor pressure equation on cell-centered triangular grids Journal of Computational Physics 230 1 205
  17. Edwards, M., Zheng, H., Lamine, S., Pal, M. Continuous elliptic and multi-dimensional hyperbolic Darcy-flux finite-volume methods Computers & Fluids 46 1 12
  18. Edwards, M. Global and local central non-upwind finite volume schemes for hyperbolic conservation laws in porous media International Journal for Numerical Methods in Fluids
  19. Pal, M., Edwards, M. q-Families of CVD(MPFA) Schemes on General Elements: Numerical Convergence and the Maximum Principle Archives of Computational Methods in Engineering 17 2 137 189
  20. Lamine, S., Edwards, M. Multidimensional upwind convection schemes for flow in porous media on structured and unstructured quadrilateral grids Journal of Computational and Applied Mathematics 234 7 2106 2117
  21. Edwards, M., Zheng, H. Quasi-positive families of continuous Darcy-flux finite volume schemes on structured and unstructured grids Journal of Computational and Applied Mathematics 234 7 2152 2161
  22. Lamine, S., Edwards, M. Higher Order Multidimensional Upwind Convection Schemes for Flow in Porous Media on Structured and Unstructured Quadrilateral Grids SIAM Journal on Scientific Computing 32 3 1119 1139
  23. Edwards, M., Zheng, H. Double-families of quasi-positive Darcy-flux approximations with highly anisotropic tensors on structured and unstructured grids Journal of Computational Physics 229 3 594 625
  24. Friis, H., Edwards, M., Mykkeltveit, J. Symmetric Positive Definite Flux-Continuous Full-Tensor Finite-Volume Schemes on Unstructured Cell-Centered Triangular Grids SIAM Journal on Scientific Computing 31 2 1192 1220
  25. Edwards, M., Pal, M. Positive-definiteq-families of continuous subcell Darcy-flux CVD(MPFA) finite-volume schemes and the mixed finite element method International Journal for Numerical Methods in Fluids 57 4 355 387
  26. Lamine, S., Edwards, M. Higher-resolution convection schemes for flow in porous media on highly distorted unstructured grids International Journal for Numerical Methods in Engineering 76 8 1139 1158
  27. Edwards, M., Zheng, H. A quasi-positive family of continuous Darcy-flux finite-volume schemes with full pressure support Journal of Computational Physics 227 22 9333 9364
  28. Edwards, M. Higher-Resolution Hyperbolic - Coupled - Elliptic Flux-Continuous CVD Schemes on Structured and Unstructured Grids in 3-D 1079 1095
  29. Edwards, M. The Dominant Wave-Capturing Flux: A Finite-Volume Scheme without Decomposition for Systems of Hyperbolic Conservation Laws 275 294
  30. Pal, M., Edwards, M., Lamb, A. Convergence study of a family of flux-continuous finite-volume schemes for the general tensor pressure equation 1177 1203
  31. Edwards, M. Higher-resolution hyperbolic-coupled-elliptic flux-continuous CVD schemes on structured and unstructured grids in 2-D International Journal for Numerical Methods in Fluids 51 9-10 1059 1077
  32. Edwards, M., Edwards, M. Split full tensor discretization operators for general hexahedral grids SPE Journal 9
  33. Wen, X., Durlofsky, L., Edwards, M., Edwards, M. Upscaling of channel systems in two dimensions using flow-based grids Transport in Porous Media 51 3 343 366
  34. Wen, X., Durlofsky, L., Edwards, M., Edwards, M. Use of Border Regions for Improved Permeability Upscaling Mathematical Geology 35 5 521 547
  35. Edwards, M. Unstructured, Control-Volume Distributed, Full-Tensor Finite Volume Schemes With Flow Based Grids 433 452
  36. He, C., Edwards, M., Durlofsky, L., Edwards, M. Numerical calculation of equivalent cell permeability tensors for general quadrilateral control volumes Computational Geosciences 6 1 29 47
  37. Edwards, M., Edwards, M. M-Matrix Flux Splitting for General Full Tensor Discretization Operators on Structured and Unstructured Grids Journal of Computational Physics 160 1 1 28
  38. Edwards, M., Rogers, C., Edwards, M. Finite volume discretization with imposed flux continuity for the general tensor pressure equation Computational Geosciences 2 4 259 290

Conference Contributions

  1. Manzoor, S., Edwards, M., Dogru, A., Al-Shaalan, T., Edwards, M. 3D Geological Feature Honored Cell-centered and Vertex-centered Unstructured Grid Generation, and CVD-MPFA Performance