de Souza, Artur Castiel Reis; de Carvalho, Darlan Karlo Elisiário; dos Santos, José Cícero Araujo; Willmersdorf, Ramiro Brito; Lyra, Paulo Roberto Maciel; Edwards, Michael G. An algebraic multiscale solver for the simulation of two-phase flow in heterogeneous and anisotropic porous media using general unstructured grids (AMS-U). (English) Zbl 1525.76096 Appl. Math. Modelling 103, 792-823 (2022). MSC: 76T06 PDFBibTeX XMLCite \textit{A. C. R. de Souza} et al., Appl. Math. Modelling 103, 792--823 (2022; Zbl 1525.76096) Full Text: DOI
Manzoor, Shahid; Edwards, Michael G.; Dogru, Ali H. Three-dimensional unstructured gridding for complex wells and geological features in subsurface reservoirs, with CVD-MPFA discretization performance. (English) Zbl 1506.74202 Comput. Methods Appl. Mech. Eng. 373, Article ID 113389, 33 p. (2021). MSC: 74L10 65N50 86-08 PDFBibTeX XMLCite \textit{S. Manzoor} et al., Comput. Methods Appl. Mech. Eng. 373, Article ID 113389, 33 p. (2021; Zbl 1506.74202) Full Text: DOI
Manzoor, Shahid; Edwards, Michael G.; Dogru, Ali H.; Al-Shaalan, Tareq M. Interior boundary-aligned unstructured grid generation and cell-centered versus vertex-centered CVD-MPFA performance. (English) Zbl 1405.65160 Comput. Geosci. 22, No. 1, 195-230 (2018); correction ibid. 22, No. 1, 231 (2018). MSC: 65N50 PDFBibTeX XMLCite \textit{S. Manzoor} et al., Comput. Geosci. 22, No. 1, 195--230 (2018; Zbl 1405.65160) Full Text: DOI
Xie, Ya-wei; Edwards, Michael G. Higher resolution total velocity \(Vt\) and \(Va\) finite-volume formulations on cell-centred structured and unstructured grids. (English) Zbl 1396.76064 Comput. Geosci. 21, No. 5-6, 921-936 (2017). MSC: 76M12 65M08 76S05 PDFBibTeX XMLCite \textit{Y.-w. Xie} and \textit{M. G. Edwards}, Comput. Geosci. 21, No. 5--6, 921--936 (2017; Zbl 1396.76064) Full Text: DOI
Ahmed, Raheel; Edwards, Michael G.; Lamine, Sadok; Huisman, Bastiaan A. H.; Pal, Mayur CVD-MPFA full pressure support, coupled unstructured discrete fracture-matrix Darcy-flux approximations. (English) Zbl 1380.76092 J. Comput. Phys. 349, 265-299 (2017). MSC: 76M25 76S05 65M50 PDFBibTeX XMLCite \textit{R. Ahmed} et al., J. Comput. Phys. 349, 265--299 (2017; Zbl 1380.76092) Full Text: DOI Link
Parramore, Elliot; Edwards, Michael G.; Pal, Mayur; Lamine, Sadok Multiscale finite-volume CVD-MPFA formulations on structured and unstructured grids. (English) Zbl 1381.76224 Multiscale Model. Simul. 14, No. 2, 559-594 (2016). MSC: 76M12 65M08 35Q35 35R05 76S05 PDFBibTeX XMLCite \textit{E. Parramore} et al., Multiscale Model. Simul. 14, No. 2, 559--594 (2016; Zbl 1381.76224) Full Text: DOI Link
Lamine, Sadok; Edwards, Michael G. Multidimensional upwind schemes and higher resolution methods for three-component two-phase systems including gravity driven flow in porous media on unstructured grids. (English) Zbl 1423.76301 Comput. Methods Appl. Mech. Eng. 292, 171-194 (2015). MSC: 76M12 65M08 74F10 76S05 PDFBibTeX XMLCite \textit{S. Lamine} and \textit{M. G. Edwards}, Comput. Methods Appl. Mech. Eng. 292, 171--194 (2015; Zbl 1423.76301) Full Text: DOI Link
Ahmed, R.; Edwards, M. G.; Lamine, S.; Huisman, B. A. H.; Pal, M. Control-volume distributed multi-point flux approximation coupled with a lower-dimensional fracture model. (English) Zbl 1351.74073 J. Comput. Phys. 284, 462-489 (2015). MSC: 74R10 65M08 74F10 76S05 PDFBibTeX XMLCite \textit{R. Ahmed} et al., J. Comput. Phys. 284, 462--489 (2015; Zbl 1351.74073) Full Text: DOI Link
Lamine, Sadok; Edwards, Michael G. Higher order cell-based multidimensional upwind schemes for flow in porous media on unstructured grids. (English) Zbl 1286.76149 Comput. Methods Appl. Mech. Eng. 259, 103-122 (2013). MSC: 76S05 76M12 65M08 PDFBibTeX XMLCite \textit{S. Lamine} and \textit{M. G. Edwards}, Comput. Methods Appl. Mech. Eng. 259, 103--122 (2013; Zbl 1286.76149) Full Text: DOI
Pal, Mayur; Edwards, Michael G. A family of multi-point flux approximation schemes for general element types in two and three dimensions with convergence performance. (English) Zbl 1253.76125 Int. J. Numer. Methods Fluids 69, No. 11, 1797-1817 (2012). MSC: 76S05 PDFBibTeX XMLCite \textit{M. Pal} and \textit{M. G. Edwards}, Int. J. Numer. Methods Fluids 69, No. 11, 1797--1817 (2012; Zbl 1253.76125) Full Text: DOI
Pal, Mayur; Edwards, Michael G. The effects of control-volume distributed multi-point flux approximation (CVD-MPFA) on upscaling — a study using the CVD-MPFA schemes. (English) Zbl 1427.76165 Int. J. Numer. Methods Fluids 68, No. 1, 18-35 (2012). MSC: 76M12 76S05 86A05 PDFBibTeX XMLCite \textit{M. Pal} and \textit{M. G. Edwards}, Int. J. Numer. Methods Fluids 68, No. 1, 18--35 (2012; Zbl 1427.76165) Full Text: DOI
Pal, Mayur; Edwards, Michael G. Anisotropy favoring triangulation CVD(MPFA) finite volume approximations. (English) Zbl 1427.76164 Int. J. Numer. Methods Fluids 67, No. 10, 1247-1263 (2011). MSC: 76M12 PDFBibTeX XMLCite \textit{M. Pal} and \textit{M. G. Edwards}, Int. J. Numer. Methods Fluids 67, No. 10, 1247--1263 (2011; Zbl 1427.76164) Full Text: DOI
Edwards, Michael G.; Zheng, Hongwen; Lamine, Sadok; Pal, Mayur Continuous elliptic and multi-dimensional hyperbolic Darcy-flux finite-volume methods. (English) Zbl 1272.76177 Comput. Fluids 46, No. 1, 12-22 (2011). MSC: 76M12 76S05 65N08 PDFBibTeX XMLCite \textit{M. G. Edwards} et al., Comput. Fluids 46, No. 1, 12--22 (2011; Zbl 1272.76177) Full Text: DOI
Pal, Mayur; Edwards, Michael G. Non-linear flux-splitting schemes with imposed discrete maximum principle for elliptic equations with highly anisotropic coefficients. (English) Zbl 1301.86002 Int. J. Numer. Methods Fluids 66, No. 3, 299-323 (2011). MSC: 86-08 86A20 65N08 76M12 PDFBibTeX XMLCite \textit{M. Pal} and \textit{M. G. Edwards}, Int. J. Numer. Methods Fluids 66, No. 3, 299--323 (2011; Zbl 1301.86002) Full Text: DOI
Friis, Helmer A.; Edwards, Michael G. A family of MPFA finite-volume schemes with full pressure support for the general tensor pressure equation on cell-centered triangular grids. (English) Zbl 1427.76161 J. Comput. Phys. 230, No. 1, 205-231 (2011). MSC: 76M12 76S05 PDFBibTeX XMLCite \textit{H. A. Friis} and \textit{M. G. Edwards}, J. Comput. Phys. 230, No. 1, 205--231 (2011; Zbl 1427.76161) Full Text: DOI
Pal, Mayur; Edwards, Michael G. q-families of CVD(MPFA) schemes on general elements: numerical convergence and the maximum principle. (English) Zbl 1269.76075 Arch. Comput. Methods Eng. 17, No. 2, 137-189 (2010). MSC: 76M12 76S05 76T30 76-02 PDFBibTeX XMLCite \textit{M. Pal} and \textit{M. G. Edwards}, Arch. Comput. Methods Eng. 17, No. 2, 137--189 (2010; Zbl 1269.76075) Full Text: DOI
Edwards, Michael G.; Zheng, Hongwen Quasi-positive continuous Darcy-flux finite-volume methods. (English) Zbl 1308.76184 Fitt, Alistair D. (ed.) et al., Progress in industrial mathematics at ECMI 2008. Proceedings of the 15th European conference on mathematics for industry, London, UK, June 30 - July 4, 2008. Berlin: Springer (ISBN 978-3-642-12109-8/hbk; 978-3-642-12110-4/ebook). Mathematics in Industry 15, 819-824 (2010). MSC: 76M12 PDFBibTeX XMLCite \textit{M. G. Edwards} and \textit{H. Zheng}, Math. Ind. 15, 819--824 (2010; Zbl 1308.76184) Full Text: DOI
Edwards, Michael G.; Zheng, Hongwen Quasi-positive families of continuous Darcy-flux finite volume schemes on structured and unstructured grids. (English) Zbl 1402.76078 J. Comput. Appl. Math. 234, No. 7, 2152-2161 (2010). MSC: 76M12 65N08 76S05 PDFBibTeX XMLCite \textit{M. G. Edwards} and \textit{H. Zheng}, J. Comput. Appl. Math. 234, No. 7, 2152--2161 (2010; Zbl 1402.76078) Full Text: DOI
Lamine, Sadok; Edwards, Michael G. Multidimensional upwind convection schemes for flow in porous media on structured and unstructured quadrilateral grids. (English) Zbl 1402.76081 J. Comput. Appl. Math. 234, No. 7, 2106-2117 (2010). MSC: 76M12 76S05 65M08 PDFBibTeX XMLCite \textit{S. Lamine} and \textit{M. G. Edwards}, J. Comput. Appl. Math. 234, No. 7, 2106--2117 (2010; Zbl 1402.76081) Full Text: DOI
Edwards, Michael G.; Zheng, Hongwen Double-families of quasi-positive Darcy-flux approximations with highly anisotropic tensors on structured and unstructured grids. (English) Zbl 1253.76091 J. Comput. Phys. 229, No. 3, 594-625 (2010). MSC: 76M25 76S05 65N08 PDFBibTeX XMLCite \textit{M. G. Edwards} and \textit{H. Zheng}, J. Comput. Phys. 229, No. 3, 594--625 (2010; Zbl 1253.76091) Full Text: DOI
Lamine, Sadok; Edwards, Michael G. Higher-resolution convection schemes for flow in porous media on highly distorted unstructured grids. (English) Zbl 1195.76266 Int. J. Numer. Methods Eng. 76, No. 8, 1139-1158 (2008). MSC: 76M12 76S05 PDFBibTeX XMLCite \textit{S. Lamine} and \textit{M. G. Edwards}, Int. J. Numer. Methods Eng. 76, No. 8, 1139--1158 (2008; Zbl 1195.76266) Full Text: DOI
Edwards, Michael G.; Zheng, Hongwen A quasi-positive family of continuous Darcy-flux finite-volume schemes with full pressure support. (English) Zbl 1231.76178 J. Comput. Phys. 227, No. 22, 9333-9364 (2008). MSC: 76M12 76S05 65N06 PDFBibTeX XMLCite \textit{M. G. Edwards} and \textit{H. Zheng}, J. Comput. Phys. 227, No. 22, 9333--9364 (2008; Zbl 1231.76178) Full Text: DOI
Edwards, Michael G.; Pal, Mayur Positive-definite \(q\)-families of continuous subcell Darcy-flux CVD(MPFA) finite-volume schemes and the mixed finite element method. (English) Zbl 1236.76035 Int. J. Numer. Methods Fluids 57, No. 4, 355-387 (2008). MSC: 76M12 76M10 76S05 PDFBibTeX XMLCite \textit{M. G. Edwards} and \textit{M. Pal}, Int. J. Numer. Methods Fluids 57, No. 4, 355--387 (2008; Zbl 1236.76035) Full Text: DOI
Pal, Mayur; Edwards, Michael G.; Lamb, Anthony R. Convergence study of a family of flux-continuous, finite volume schemes for the general tensor pressure equation. (English) Zbl 1108.76046 Int. J. Numer. Methods Fluids 51, No. 9-10, 1177 - 1203 (2006). MSC: 76M12 76S05 65N12 PDFBibTeX XMLCite \textit{M. Pal} et al., Int. J. Numer. Methods Fluids 51, No. 9--10, 1177--1203 (2006; Zbl 1108.76046) Full Text: DOI
Edwards, Michael G. M-matrix flux splitting for general full tensor discretization operators on structured and unstructured grids. (English) Zbl 0983.76055 J. Comput. Phys. 160, No. 1, 1-28 (2000). MSC: 76M12 76T99 76S05 86A05 PDFBibTeX XMLCite \textit{M. G. Edwards}, J. Comput. Phys. 160, No. 1, 1--28 (2000; Zbl 0983.76055) Full Text: DOI