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Its numerical fluxes are derived by computing the radial derivatives of \u201cbubbles\u201d which are deduced from available discrete data by exploiting the stationary Dirichlet--Green function of the convection-diffusion operator. These fluxes are reminiscent of Scharfetter and Gummel's in the sense that they contain modified Bessel functions which allow one to pass smoothly from diffusive to drift-dominating regimes. For certain flows, monotonicity properties are established in the vanishing viscosity limit (``asymptotic monotony'') along with second-order accuracy when the grid is refined. Practical benchmarks are displayed to assess the feasibility of the scheme, including the \u201cwestern currents\u201d with a Navier--Stokes--Coriolis model of ocean circulation.<\/jats:p>","DOI":"10.1137\/17m1151353","type":"journal-article","created":{"date-parts":[[2018,9,18]],"date-time":"2018-09-18T11:49:10Z","timestamp":1537271350000},"page":"2845-2870","source":"Crossref","is-referenced-by-count":12,"title":["A Truly Two-Dimensional Discretization of Drift-Diffusion Equations on Cartesian Grids"],"prefix":"10.1137","volume":"56","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9612-6748","authenticated-orcid":true,"given":"Roberta","family":"Bianchini","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7482-254X","authenticated-orcid":true,"given":"Laurent","family":"Gosse","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,9,18]]},"reference":[{"key":"atypb1","volume-title":"Handbook of Mathematical Functions","author":"Abramowitz M.","year":"1972"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/s006070170035"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2011.16.687"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-08-02161-3"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1137\/0720034"},{"key":"atypb6","first-page":"1","volume":"4","author":"Bouchut F.","year":"2018","journal-title":"J. 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