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This work has been supported by the Spanish Ministerio de Economia y Competitividad grant MTM201789664-P. The co-author Marc Jornet acknowledges the doctorate scholarship granted by Programa de Ayudas de Investigacion y Desarrollo (PAID), Universitat Politecnica de Valencia.
Extending the study on the linear advection equation subject to stochastic velocity field and initial condition
Publicated to:Mathematics And Computers In Simulation. 172 159-174 - 2020-06-01 172(), DOI: 10.1016/j.matcom.2019.12.014
Authors: Calatayud, J; Cortes, J-C; Dorini, F A; Jornet, M
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Abstract
In this paper we extend the study on the linear advection equation with independent stochastic velocity and initial condition performed in Dorini and Cunha (2011). By using both existing and novel results on the stochastic chain rule, we solve the random linear advection equation in the mean square sense. We provide a new expression for the probability density function of the solution stochastic process, which can be computed as accurately as wanted via Monte Carlo simulations, and which does not require the specific probability distribution of the integral of the velocity. This allows us to solve the non-Gaussian velocity case, which was not treated in the aforementioned contribution. Several numerical results illustrate the computations of the probability density function by using our approach. On the other hand, we derive a theoretical partial differential equation for the probability density function of the solution stochastic process. Finally, a shorter and easier derivation of the joint probability density function of the response process at two spatial points is obtained by applying conditional expectations appropriately. (C) 2019 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
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Bibliometric impact. Analysis of the contribution and dissemination channel
The work has been published in the journal Mathematics And Computers In Simulation due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2020, it was in position 45/265, thus managing to position itself as a Q1 (Primer Cuartil), in the category Mathematics, Applied.
From a relative perspective, and based on the normalized impact indicator calculated from the Field Citation Ratio (FCR) of the Dimensions source, it yields a value of: 2.67, which indicates that, compared to works in the same discipline and in the same year of publication, it ranks as a work cited above average. (source consulted: Dimensions Jul 2025)
Specifically, and according to different indexing agencies, this work has accumulated citations as of 2025-07-28, the following number of citations:
- WoS: 5
- Scopus: 5
Impact and social visibility
Leadership analysis of institutional authors
This work has been carried out with international collaboration, specifically with researchers from: Brazil.
There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: First Author (Calatayud Del Valle, Javier) and Last Author (Jornet, M).
the author responsible for correspondence tasks has been Cortés López, Juan Carlos.