Finite difference methods for solving the two‐dimensional advection–diffusion equation
- 1 January 1989
- journal article
- research article
- Published by Wiley in International Journal for Numerical Methods in Fluids
- Vol. 9 (1) , 75-98
- https://doi.org/10.1002/fld.1650090107
Abstract
Using weighted discretization with the modified equivalent partial differential equation approach, several accurate finite difference methods are developed to solve the two‐dimensional advection–diffusion equation following the success of its application to the one‐dimensional case. These new methods are compared with the conventional finite difference methods in terms of stability and accuracy. The new methods are more accurate and often more stable than the conventional schemes.Keywords
This publication has 15 references indexed in Scilit:
- A third‐order semi‐implicit finite difference method for solving the one‐dimensional convection‐diffusion equationInternational Journal for Numerical Methods in Engineering, 1988
- Mathematical Models of Dispersion in Rivers and EstuariesAnnual Review of Fluid Mechanics, 1985
- The stability of explicit Euler time‐integration for certain finite difference approximations of the multi‐dimensional advection–diffusion equationInternational Journal for Numerical Methods in Fluids, 1984
- Dispersion analysis in homogeneous lakesInternational Journal for Numerical Methods in Engineering, 1980
- Water Transport in SoilsAnnual Review of Fluid Mechanics, 1980
- An explicit numerical method for solving transient combined heat conduction and convection problemsInternational Journal for Numerical Methods in Engineering, 1979
- Heat transfer to a draining filmInternational Journal of Heat and Mass Transfer, 1973
- Difference schemes for hyperbolic equations with high order of accuracyCommunications on Pure and Applied Mathematics, 1964
- Block diagonally dominant matrices and generalizations of the Gerschgorin circle theoremPacific Journal of Mathematics, 1962
- Dispersion of soluble matter in solvent flowing slowly through a tubeProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1953