caa a22 4500 46316279X CHVBK 20180406164752.0 cr unu---uuuuu 170326e20070801xx s 000 0 eng 10.1007/s11242-006-9090-3 doi (NATIONALLICENCE)springer-10.1007/s11242-006-9090-3 Implementation of Richardson extrapolation in an efficient adaptive time stepping method: applications to reactive transport and unsaturated flow in porous media [Elektronische Daten] [Benjamin Belfort, Jérôme Carrayrou, François Lehmann] Environmental studies are commonly carried out through numerical simulations, which have to be accurate, reliable and efficient. When transient problems are considered, the validity of the solutions requires the calculation and management of the temporal discretization errors. This article describes an adaptive time stepping strategy based on the estimation of the local truncation error via the Richardson extrapolation technique. The time-marching scheme is mathematically based on this a posteriori error estimation that has to be gauged. General optimizations are also suggested making the control of both the temporal error and the evolution of the time step size very efficient. Furthermore, the algorithm connecting these methods is all the more interesting as it could be implemented in many computational codes using different numerical schemes. In the hydrogeochemical domain, this algorithm represents an interesting alternative to a fixed time step as shown by the various numerical tests involving reactive transport and unsaturated flow. Springer Science+Business Media, Inc., 2007 Richardson extrapolation nationallicence Adaptive time stepping nationallicence Reactive transport nationallicence Unsaturated flow nationallicence Belfort Benjamin Institut de Mécanique des Fluides et des Solides, UMR 7507 ULP-CNRS, 2 rue Boussingault, 67000, Strasbourg, France aut Carrayrou Jérôme Institut de Mécanique des Fluides et des Solides, UMR 7507 ULP-CNRS, 2 rue Boussingault, 67000, Strasbourg, France aut Lehmann François Institut de Mécanique des Fluides et des Solides, UMR 7507 ULP-CNRS, 2 rue Boussingault, 67000, Strasbourg, France aut Transport in Porous Media Kluwer Academic Publishers 69/1(2007-08-01), 123-138 0169-3913 69:1<123 2007 69 11242 https://doi.org/10.1007/s11242-006-9090-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11242-006-9090-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Belfort Benjamin Institut de Mécanique des Fluides et des Solides, UMR 7507 ULP-CNRS, 2 rue Boussingault, 67000, Strasbourg, France aut NATIONALLICENCE 700 1- Carrayrou Jérôme Institut de Mécanique des Fluides et des Solides, UMR 7507 ULP-CNRS, 2 rue Boussingault, 67000, Strasbourg, France aut NATIONALLICENCE 700 1- Lehmann François Institut de Mécanique des Fluides et des Solides, UMR 7507 ULP-CNRS, 2 rue Boussingault, 67000, Strasbourg, France aut NATIONALLICENCE 773 0- Transport in Porous Media Kluwer Academic Publishers 69/1(2007-08-01), 123-138 0169-3913 69:1<123 2007 69 11242 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer