Riv.Mat.Univ.Parma (6) 4 (2001)


The adjoint advection-diffusion equation in stationary and time dependent problems: a reciprocity relation

dedicated to the memory of Giulio Di Cola

Pages: 9-19
Received: 23 October 2000    Revised: 28 June 2001
Mathematics Subject Classification (2000): 76R99

Abstract: Both stationary and time dependent adjoint problems associated to advection-diffusion problems are formulated. The adjoint problem is then interpreted as a model for an advection-diffusion process of a tracer called the "adjoint tracer". The construction of such a model is a sine qua non condition for the integration of the adjoint advection-diffusion equation by means of probabilistic methods. A reciprocity relation relating direct and adjoint transition probability density functions is derived. Strategies to solving advection-diffusion problems by means of Monte Carlo methods are illustrated.

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