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The modelling of transport phenomena in fluid mechanics and heat transfer presents numerical problems in the simulation of both steady and time-dependent problems with dominant advection. The nature of these problems is different in stationary and evolutionary situations. In this paper, some of the most recent finite element methods for solving the time-dependent advection equation are introduced. The accuracy and stability of the proposed schemes are discussed, and interconnections between them established using the theory of characteristics. The solutions of both linear and non-linear advection equations are considered, using methods based on the Taylor series in time and least squares methods, as well as methods making explicit use of the characteristic curves.

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Authors: DONEA J, JRC Ispra (IT);QUARTAPELLE L, Istituto di Fisica del Politecnico di Milano (IT)
Bibliographic Reference: Article: Computer Methods in Applied Mechanics and Engineering, Vol. 95 (1992) pp. 169-203
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