Método HDG de orden superior con bases deDubiner para problemas de flujo elípticos

We propose a standard hybridizable discontinuous Galerkin (HDG) method to solve a classic problem in fluids mechanics: Darcy’s law. This model describes the behavior of a fluid trough a porous medium and it is relevant to the flow patterns on the macro scale. Here we present the theoretical results of existence and uniqueness of the weak and discontinuous solution of the second order elliptic equation, as well as the predicted convergence order of the HDG method. We highlight the use and implementation of Dubiner polynomial basis functions that allow us to develop a general and efficient high order numerical approximation. We also show some numerical examples that validate the theoretical results.En este artículo proponemos el uso del método de Galerkin discontinuo híbrido(HDG) para resolver un problema clásico en mecánica de fluidos: la ecuación deDarcy. Este modelo describe el comportamiento de un fluido a través de un medioporoso y es relevante en el estudio de flujo a gran escala. Aquí presentamos algunosresultados teóricos de existencia y unicidad de la solución débil y discontinua de ecuaciones elípticas de segundo orden, así como el orden de convergecia predichopara el método HDG. Destacamos el uso e implementación de bases polinomialesde Dubiner que nos permiten desarrollar aproximaciones numéricas generales yde alto orden. Además mostramos ejemplos numéricos que validan los resultadosteóricos.Palabras clave:Método de Galerkin discontinuo hibridizable; flujo en medioporoso; bases de Dubiner; convergencia de alto orden

A numerical scheme for two-scale phase-field models in porous media

[EN] We consider the flow of two immiscible fluid phases in a porous medium. At the scale of pores, the two fluid phases are separated by interfaces that are transported by the flow. Furthermore, the surface tension at such interfaces depends on the concentration of a surfactant dissolved in one of the fluids. Here we discuss a two-scale model for two-phase porous-media flow, in which concentration-dependent surface tension effects are incorporated. The model is obtained by employing formal homogenization methods and relies on the phase-field approach, in which thin, diffuse interface regions approximate the interfaces. We propose a two-scale numerical scheme and present numerical results revealing the influence of various quantities on the averaged behaviour of the system.This research is supported by the Research Foundation-Flanders (FWO) through the Odysseus programme (Project G0G1316N) and by the German Research Foundation (DFG) through the SFB 1313, Project Number 327154368.Bastidas, M.; Sharmin, S.; Bringedal, C.; Pop, S. (2022). A numerical scheme for two-scale phase-field models in porous media. En Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference. Editorial Universitat Politècnica de València. 364-373. https://doi.org/10.4995/YIC2021.2021.12571OCS36437

Inteligencia de mercados: comportamientos estratégicos sobre precios de oferta en el mercado spot eléctrico Colombiano

El mercado de energía mayorista es uno de los sectores industriales más competitivos de Colombia, y representa uno de los ejes principales en la economía del país. Este mercado ha sido objeto de estudio de varias áreas de conocimiento como la ingeniería eléctrica, economía, finanzas y otros. Aquí se presenta un análisis de los posibles comportamientos estratégicos de los principales agentes de la industria, desde la perspectiva de la inteligencia artificial orientada a la inteligencia de mercados, es decir, un trabajo multidisciplinar centrado en la explicación y emulación de la conducta inteligente y posiblemente estratégica de los agentes involucrados en la actividad de generación de energía en Colombia.The energy market is one of the most competitive Colombian industry sectors, and represents one of the main strategic focus in economy and development of the country. This market has been under study of many knowledge areas such as electric engineering, economy, financial and others. In this work, is presented an analysis of all the possible strategic behaviors of major industry players, from the basis of artificial intelligence oriented to market intelligence, that is, a multidisciplinary work focused on the explanation and emulation of intelligent behavior and possibly strategic of the actors involved in each market activities and in particular the behavior of energy-generating agents in Colombia

Error estimates for the gradient discretisation of degenerate parabolic equation of porous medium type

International audienceThe gradient discretisation method (GDM) is a generic framework for the spatial discretisation of partial differential equations. The goal of this contribution is to establish an error estimate for a class of degenerate parabolic problems, obtained under very mild regularity assumptions on the exact solution. Our study covers well-known models like the porous medium equation and the fast diffusion equations, as well as the strongly degenerate Stefan problem. Several schemes are then compared in a last section devoted to numerical results

Evaluación del rendimiento de tres sistemas de siembra y dos variedades de amaranto (Amaranthus quitensis) y (Amaranthus hypochondriacus)

The cultivation of amaranth in our country has taken great importance due to the existing demand, it is sown underconventional systems existing with a little knowledge about the varieties and the different systems of sowing, in theEcuadorian sierra the one known as Amaranthus has prevailed. quitensis, so the purpose of the research was to evaluatethe yield of two varieties of amaranth (Amaranthus quitensis V1) and (Amaranthus hypochondriacus V2) managing threecontinuous sowing systems (S1), by stroke (S2) and by transplant (S3). Subsequently, it was determined which of thesowing systems reached higher grain yields in kg / plot. Additionally, plant height (m), diameter of the basal stem (cm),number of panicles per plant at 120, 150 and 180 days at harvest was determined. The variety Amaranthus quitensisH.B.H.B.K. or A. hybridus L. (V1), is known in Ecuador as ataco, sangorache, sangoracha, jataco and currently as blackgrain amaranth. In the experiment, an experimental design of divided plots with four repetitions and six treatments wasapplied, analysis of variance was performed; Tukey tests at 5%; and tests of Minimum Significant Difference at 5% forthe factor varieties. The research was carried out in the Experimental Farm Querochaca of the Technical University of Ambato, located in Cevallos, province of Tungurahua-Ecuador. The results stood out in treatment one V1S1, with thefollowing values: the grain yield (GR) was 1.25 g / plot (2480.16 kg / ha); height of the plant (AP) on average 1.56 m;diameter of the basal stem (DDTB) 1.19 cm; number of panicles per plant (NPP) 2.13 and days to harvest (DC) 109.El cultivo de amaranto en nuestro país ha tomado gran importancia debido a la demanda existente, se siembra bajosistemas convencionales existiendo un escaso conocimiento sobre las variedades y los diferentes sistemas de siembra, enla sierra ecuatoriana ha prevalecido la conocida como Amaranthus quitensis, por lo que el objeto de la investigación fueevaluar el rendimientos de dos variedades de amaranto (Amaranthus quitensis V1) y (Amaranthus hypochondriacus V2)manejando tres sistemas de siembra a chorro continuo (S1), por golpe (S2) y mediante trasplante (S3). Posteriormente sedeterminó cuál de los sistemas de siembra alcanzó mayores rendimientos del grano en kg/parcela. Adicionalmente sedeterminó, la altura de planta (m), diámetro del tallo basal (cm), número de panojas por planta a los 120, 150 y 180 días ala cosecha. La variedad Amaranthus quitensis H.B.H.B.K. o A. hybridus L. (V1), es conocido en Ecuador como ataco,sangorache, sangoracha, jataco y actualmente como amaranto de grano negro. En el experimento se aplicó un diseñoexperimental de parcelas divididas con cuatro repeticiones y seis tratamientos, se realizaron análisis de variancia; pruebasde Tukey al 5%; y pruebas de Diferencia Mínima Significativa al 5% para el factor variedades. La investigación seefectuó en la Granja Experimental Docente Querochaca de la Universidad Técnica de Ambato, situada en Cevallos,provincia de Tungurahua-Ecuador. Los resultados sobresalieron en el tratamiento uno V1S1 a los 180 días, con lossiguientes valores: el rendimiento del grano (RG) fue de 1.25 kg/parcela (2480.16 kg/ha); altura de planta (AP) 1,81 m;diámetro del tallo basal (DDTB) 1.49 cm; número de panojas por planta (NPP) 2.79 y días a la cosecha (DC) 109