caa a22 4500 469064935 CHVBK 20180323132905.0 cr unu---uuuuu 170328e19920701xx s 000 0 eng 10.1007/BF00890532 doi (NATIONALLICENCE)springer-10.1007/BF00890532 A technique to test finite difference schemes to model some geophysical processes in a geological structure [Elektronische Daten] [Giansilvio Ponzini, Nicola Tosi] A preliminary problem to solve in the set-up of a mathematical model simulating a geophysical process is the choice of a suitable discrete scheme to approximate the governing differential equations. This paper presents a simple technique to test finite difference schemes used in the modeling of geophysical processes occurring in a geological structure. This technique consists in generating analytical solutions similar to the ones characterizing a geophysical process, given general information on some relevant parameters. Useful information for the choice of the discrete scheme to employ in the mathematical model simulating the original geophysical process can be obtained from the comparison between the analytical solution and the approximated numerical solutions generated by means of different discrete schemes. Two classes of numerical examples approximating the differential equation that governs the steady state earth's heat flow have been treated using three different finite differences schemes. The first class of examples deals with media whose phenomenological parameters vary as continuous space functions; the second class, instead, deals with media whose phenomenological parameters vary as discontinuous space functions. The finite difference schemes that have been utilized are: Centered Finite Difference Scheme (CDS), Arithmetic Mean Scheme (AMS), and Harmonic Mean Scheme (HMS). The numerical simulations showed that: the CDS may yield physically inconsistent solutions if the lattice internodal distance is too large, but in case of phenomenological parameters varying as a continuous function, this pitfall can be avoided increasing the lattice node refinement. In case of phenomenological parameters varying as a discontinuous function, instead, the CDS may yield physically inconsistent solutions for any lattice-node refinement. The HMS produced good results for both classes of examples showing to be a scheme suitable to model situations like these. International Association for Mathematical Geology, 1992 earth's heat flow nationallicence geological modeling nationallicence finite difference schemes nationallicence model validation nationallicence Ponzini Giansilvio Dipartimento di Scienze della Terra, Geofisica, Università di Milano, Via Cicognara 7, 20129, Milano, Italy aut Tosi Nicola Dipartimento di Scienze della Terra, Geofisica, Università di Milano, Via Cicognara 7, 20129, Milano, Italy aut Mathematical Geology Kluwer Academic Publishers-Plenum Publishers 24/5(1992-07-01), 499-537 0882-8121 24:5<499 1992 24 11004 https://doi.org/10.1007/BF00890532 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00890532 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ponzini Giansilvio Dipartimento di Scienze della Terra, Geofisica, Università di Milano, Via Cicognara 7, 20129, Milano, Italy aut NATIONALLICENCE 700 1- Tosi Nicola Dipartimento di Scienze della Terra, Geofisica, Università di Milano, Via Cicognara 7, 20129, Milano, Italy aut NATIONALLICENCE 773 0- Mathematical Geology Kluwer Academic Publishers-Plenum Publishers 24/5(1992-07-01), 499-537 0882-8121 24:5<499 1992 24 11004 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer