Special Issue "Modeling and Numerical Analysis of Energy and Environment"

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: 20 August 2020.

Special Issue Editor

Prof. Arturo Hidalgo
Guest Editor
Departamento de Ingeniería Geológica y Minera, ETS de Ingenieros de Minas y Energía, Universidad Politécnica de Madrid (UPM), C/Alenza 4, 28003 Madrid, Spain
Interests: numerical simulation; finite volume methods; environmental applications; computational fluid dynamics

Special Issue Information

Dear Colleagues,

Mathematical modelling and numerical simulation are fundamental tools in the description of a wide variety of physical and technical phenomena. The capability of mathematical models to represent real situations and therefore, to make predictions on the behaviour of these systems makes their use essential when dealing with real-world applications.

This Special Issue mainly focuses on new research related to the mathematical modelling of energy and environmental processes and its numerical analysis. Some applications of interest may include the mathematical modelling of heat transfer in architecture so as to get efficient heating and cooling in buildings. Moreover, in the context of both energy and the environment, research on mathematical models for the study of non-conventional energy sources, such as solar energy (both photovoltaic and thermosolar), wind turbines or mathematical modelling for biomass formation can be relevant. In addition, Magnetohydrodynamics modelling for fusion plasmas and its influence on nuclear fusion may represent relevant research for this Special Issue. Other applications to be considered are based on shallow water models in the context of environmental hydrodynamics, with applications to different hydrodynamic situations which may include, for instance, dam breaks involving shock propagation and wet-dry fonts. In addition, environmental flows based on multi-phase flow model and flow in porous media can be part of this Special Issue.

A very relevant feature of this Special Issue is the numerical resolution of the mathematical models under study, based on a wide variety of numerical schemes such as finite volumes, finite elements, finite differences or Discontinuous Galerkin, to name a few. Relevant research may include new and very efficient numerical methods which represent a step forward in the numerical resolution of mathematical models in the context of energy and environment applications.

Rigorous analytical theory of the mathematical models under study is also very relevant for this Special Issue.

To sum up, this Special Issue intends to gather new research on mathematical models mainly focused on energy and environmental applications. Particular emphasis will be placed on the numerical resolution of the models, using very efficient numerical schemes, and also on a rigorous theoretical analysis of the models under study.

Prof. Arturo Hidalgo
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1200 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.


  • Mathematical modelling in Energy and Environment
  • Efficient numerical schemes
  • Heat transfer in industry and buildings
  • Aerodynamics
  • Fluid dynamics
  • Shallow water models, dam-break
  • Multiphase flows, flow in porous media

Published Papers (1 paper)

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Open AccessFeature PaperArticle
A Second-Order Well-Balanced Finite Volume Scheme for the Multilayer Shallow Water Model with Variable Density
Mathematics 2020, 8(5), 848; https://doi.org/10.3390/math8050848 - 23 May 2020
In this work, we consider a multilayer shallow water model with variable density. It consists of a system of hyperbolic equations with non-conservative products that takes into account the pressure variations due to density fluctuations in a stratified fluid. A second-order finite volume [...] Read more.
In this work, we consider a multilayer shallow water model with variable density. It consists of a system of hyperbolic equations with non-conservative products that takes into account the pressure variations due to density fluctuations in a stratified fluid. A second-order finite volume method that combines a hydrostatic reconstruction technique with a MUSCL second order reconstruction operator is developed. The scheme is well-balanced for the lake-at-rest steady state solutions. Additionally, hints on how to preserve a general class of stationary solutions corresponding to a stratified density profile are also provided. Some numerical results are presented, including validation with laboratory data that show the efficiency and accuracy of the approach introduced here. Finally, a comparison between two different parallelization strategies on GPU is presented. Full article
(This article belongs to the Special Issue Modeling and Numerical Analysis of Energy and Environment)
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