Mining has been embedded in the public consciousness as a dirty, non-innovative, outdated and env... more Mining has been embedded in the public consciousness as a dirty, non-innovative, outdated and environmentally harmful industry. Proper education, especially the academic one, becomes crucial to successfully change this image. This article depicts the initial assumptions of the international project Master in Entrepreneurship, Innovation and Technology Integration in Mining (MEITIM), co-financed by EIT Raw Materials, that aims to diagnose the current state of Polish higher education in the field of mining at, among others, the Wroclaw University of Science and Technology (WUST), concerning the experience of the Technical University of Madrid (UPM) and Lappeenranta University of Technology (LUT). The MEITIM project allowed identifying the directions of necessary changes in the didactic process as an indispensable set of skills and knowledge for a future mining graduate. Such activities are dictated by many guidelines and arrangements, among others, at the level of the European Commiss...
Communications on Applied Mathematics and Computation
Two-phase flow in porous media is a very active field of research, due to its important applicati... more Two-phase flow in porous media is a very active field of research, due to its important applications in groundwater pollution, $${\text {CO}}_2$$ CO 2 sequestration, or oil and gas production from petroleum reservoirs, just to name a few of them. Fractional flow equations, which make use of Darcy’s law, for describing the movement of two immiscible fluids in a porous medium, are among the most relevant mathematical models in reservoir simulation. This work aims to solve a fractional flow model formed by an elliptic equation, representing the spatial distribution of the pressure, and a hyperbolic equation describing the space-time evolution of water saturation. The numerical solution of the elliptic part is obtained using a finite-element (FE) scheme, while the hyperbolic equation is solved by means of two different numerical approaches, both in the finite-volume (FV) framework. One is based on a monotonic upstream-centered scheme for conservation laws (MUSCL)-Hancock scheme, whereas...
In this work, we propose a mathematical model representing the thermal interaction between vegeta... more In this work, we propose a mathematical model representing the thermal interaction between vegetation cover and the soil underneath it. This model consists of a one-dimensional reaction–diffusion equation describing the evolution of the temperature in the vegetation cover coupled with a two-dimensional reaction–diffusion equation to represent the evolution of the temperature in the soil. The thermal interaction between the vegetation cover and the soil is studied and the distribution of temperatures in the soil with depth is also obtained. The vegetation cover acts in this model as a dynamic and diffusive boundary condition for the soil. The developed model takes into account the latent heat of fusion, which appears when the transformation of ice into liquid water or vice versa occurs inside the soil. The numerical approach for the solution of the mathematical model conducted in this work is based on the finite volume method with Weighted Essentially Non-Oscillatory technique for sp...
Preface P.D. Lax Foreword E.F. Toro Scientific committee Sponsors Thanks! I Invited lectures Sant... more Preface P.D. Lax Foreword E.F. Toro Scientific committee Sponsors Thanks! I Invited lectures Santiago and the Jacobean pilgrimage at the height of the Middle Ages: Mentality and culture F. Singul Recent developments on the Lagrangian and remapping methods for compressible fluid flows J. Cheng & C.-W. Shu Coupling of nonlinear hyperbolic systems: A journey from mathematical to numerical issues F. Coquel Stochastic convergence and the software tool W* R. Kaufman, T. Kaman, Y. Yu & J. Glimm Numerical relativistic magnetohydrodynamics in dynamical spacetimes J.M*. Ibanez Initiation of reactive blast waves by external energy sources A. Linan, V. Kurdyumov & A.L. Sanchez Numerical performance of discontinuous and stabilized continuous Galerkin methods for convection-diffusion problems P.F. Antonietti & A. Quarteroni The Riemann problem in computational science E.F. Toro II Recent advances in the numerical computation of environmental conservation laws with source terms Finite volume discr...
The aim of this work is to introduce a mathematical model representing the evolution of the tempe... more The aim of this work is to introduce a mathematical model representing the evolution of the temperature in a vegetation cover and the ground underneath it. Vegetation, and its interaction with soil, plays a very important role in the protection of soil surface from the action of sun and precipitations. A reduction in the vegetated mass increase the risk of desertification, soil erosion or surface runoffs which which can give rise to soil loss and sediment retention. These processes can favour climate change and global warming, which are major concerns nowadays. The mathematical model presented takes into account the main processes involved in vegetation cover and the interaction with the soil, among which, we can mention the Leaf Area Index, which is a dimensionless quantity defined as the one-sided green leaf area per unit ground surface area, or albedo and co-albedo which are clearly influenced by the vegetation. It is also considered a nonlinear heat capacity in the soil which in...
We consider a coupled model surface-deep ocean effect, where an Energy Balance Model (EBM) is use... more We consider a coupled model surface-deep ocean effect, where an Energy Balance Model (EBM) is used for modelling the surface temperature and a two-dimensional heat equation represents the evolution of the temperature of the deep ocean. Although the model under study is based on that proposed by Watts & Morantine (1990), here we consider a modified model that incorporates other processes, such as the nonlinear diffusion and the action of coalbedo, depending on the temperature. The stationary states of the model under study, taking the solar constant as the parameter, are numerically attained. The results of the simulation are depicted in a {(Q,u)} plot where u is the temperature in the surface and Q is the solar constant. The numerical solution is achieved by means of a finite volume scheme with Weighted Essentially Non-Oscillatory (WENO) reconstruction in space and third order Runge-Kutta scheme, which verifies the Total Variation Diminishing (TVD) property, for time integration. Th...
The river floods happening in populated areas are serious natural risks that give rise to human a... more The river floods happening in populated areas are serious natural risks that give rise to human and economic losses. In order to predict the consequences of river floods and to implement preventive and corrective measures, the mathematical modelling and numerical simulation play, nowadays, a very important role. Among the wide variety of software available for the numerical simulation in fluvial dynamics we have used, in this work, the hydrodynamic model IBER, which is free access simulation software for solving 2D shallow water models. In this paper we focus our attention in floods happening in the vicinity of the confluence of two rivers where there are also crops, with economic importance for the inhabitants of the area that may be affected by the inundation. As an example of this type of geographical region we have used data obtained from the region Las Omañas in NW Spain where, although there is the confluence of rivers Luna and Omaña, the confluence region does not belong to the study area, since we pay our attention to the inundations happening in the village Las Omañas, which is due to the action of one of both rivers, namely the river Omaña.
International Journal of Oil, Gas and Coal Technology, 2019
In underground mining, gas accumulation or gas content anomaly caused by geological structures of... more In underground mining, gas accumulation or gas content anomaly caused by geological structures often results in catastrophic coal and gas outburst accidents, this kind of outburst has already been reported for decades and caused thousands of casualties. However, so far there have been very few studies about how to conduct risk assessment for this kind of geological-structure-related outburst. In this study, our aim is to develop an approach to evaluate the risk of fault-related outburst. The approach developed in this study is a stress-based approach and it considers the associated factors including the gas pressure, the fault attitude and the tectonic stresses. The fault-related outburst index proposed in this work not only can be used for evaluating the fault sealing capability but also can be used for quantitatively assessing the risk degree of fault-related outburst. It is a practical approach and can be recommended to apply in more underground engineering. [
CENTRAL EUROPEAN SYMPOSIUM ON THERMOPHYSICS 2019 (CEST), 2019
We are concerned with a global climate model with deep ocean effect. The model includes a dynamic... more We are concerned with a global climate model with deep ocean effect. The model includes a dynamic and diffusive boundary condition arising from an energy balance on the Earth surface. The scales of time and space are relatively large. One of the characteristics of climate energy balance models is the sensitivity to the variations of a Solar parameter Q. Analytically, it was proved that there exists a range of Q with at least three stationary solutions. In this work we analyze numerically the existence of more than three stationary solutions according to that positive parameter Q.
Fault activation caused by construction, earthquakes, or mining can produce disastrous water-inru... more Fault activation caused by construction, earthquakes, or mining can produce disastrous water-inrush episodes in underground mines. Fault activation is generally caused by stress concentration at the fault tip, so in this study, a computational model of a typical underground stope with a hidden fault was established to quantitatively assess the magnitude of the stress concentration of the stress fields of the fault-tip. Numerical simulation was performed using the extended finite element method and fracture mechanics. Stress intensity factors, which represent the magnitude of the stress concentration, were obtained using the interaction integral method to quantitatively evaluate the tip fields and assess the possibility of fault activation. The mining depth, fluid pressure, fault dip, and fault length were analyzed and the advance of a working face was simulated to determine whether underground mining would cause fault activation.
International Journal of Mining, Reclamation and Environment, 2017
In this study, a new approach is proposed and developed for evaluating the comprehensive outburst... more In this study, a new approach is proposed and developed for evaluating the comprehensive outburst index (range between Oand 100), which is a quantitative assessment approach and will enable us to better understand the risk degree of coal and gas outburst in coal mines. By selecting some typical risk-free and high-risk outburst mines from China as the evaluation targets, we assessed their comprehensive outburst indexes with the developed approach. The assessment results are fully consistent with the actual situations, which indicates that our new developed approach is reliable and can be recommended for applying in more coal mines.
Sudden water inrush has been a deadly killer in underground engineering for decades. Currently, e... more Sudden water inrush has been a deadly killer in underground engineering for decades. Currently, especially in developing countries, frequent water inrush accidents still kill a large number of miners every year. In this study, an approach for predicting the probability of fault-induced water inrush in underground engineering using the adaptive neuro-fuzzy inference system (ANFIS) was developed. Six parameters related to the aquifer, the water-resisting properties of the aquifuge and the mining-induced stresses were extracted as the major parameters to construct the ANFIS model. The constructed ANFIS was trained with twenty reported real fault-induced water inrush cases, and another five new cases were used to test the prediction performance of the trained ANFIS. The final results showed that the prediction results of the five cases were completely consistent with the actual situations. This indicates that the ANFIS is highly accurate in the prediction of fault-induced water inrush and suggests that quantitative assessment of fault-induced water inrush using the ANFIS is possible.
A high order one-step ADER-WENO finite volume scheme with Adaptive Mesh Refinement (AMR) in multi... more A high order one-step ADER-WENO finite volume scheme with Adaptive Mesh Refinement (AMR) in multiple space dimensions is presented. A high order one-step time discretization is achieved using a local space-time discontinuous Galerkin predictor method, while a high order spatial accuracy is obtained through a WENO reconstruction. Thanks to the one-step nature of the underlying scheme, the resulting algorithm can be efficiently imported within an AMR framework on space-time adaptive meshes. We provide convincing evidence that the presented high order AMR scheme behaves better than traditional second order AMR methods. Tests are shown of the new scheme for nonlinear systems of hyperbolic conservation laws, including the classical Euler equations and the equations of ideal magnetohydrodynamics. The proposed scheme is likely to become a useful tool in several astrophysical scenarios.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2014
We study a climatologically important interaction of two of the main components of the geophysica... more We study a climatologically important interaction of two of the main components of the geophysical system by adding an energy balance model for the averaged atmospheric temperature as dynamic boundary condition to a diagnostic ocean model having an additional spatial dimension. In this work, we give deeper insight than previous papers in the literature, mainly with respect to the 1990 pioneering model by Watts and Morantine. We are taking into consideration the latent heat for the two phase ocean as well as a possible delayed term. Non-uniqueness for the initial boundary value problem, uniqueness under a non-degeneracy condition and the existence of multiple stationary solutions are proved here. These multiplicity results suggest that an S-shaped bifurcation diagram should be expected to occur in this class of models generalizing previous energy balance models. The numerical method applied to the model is based on a finite volume scheme with nonlinear weighted essentially non-oscill...
In this work it is studied the numerical solution of a global climate model. The model is based o... more In this work it is studied the numerical solution of a global climate model. The model is based on the one proposed by Watts and Morantine in (4) but here it is considered a temperature-dependent co-albedo. The main difficulty is the dynamic and diffusive boundary condition whichrepresents the coupling between the deep ocean and the atmospheric surface. Results for the continuous model can be found in (1) and (2) where existence of solutiones is proved via fix point iteration. We shall use a finite volume scheme to solve both the 1D model and the 2D model using high order reconstruction in time and space.
In this article we extend the high order ADER finite volume schemes introduced for stiff hyperbol... more In this article we extend the high order ADER finite volume schemes introduced for stiff hyperbolic balance laws by Dumbser, Enaux and Toro (J. Comput. Phys. 227:3971-4001, 2008) to nonlinear systems of advection-diffusion-reaction equations with stiff algebraic source terms. We derive a new efficient formulation of the local space-time discontinuous Galerkin predictor using a nodal approach whose interpolation points are tensorproducts of Gauss-Legendre quadrature points. Furthermore, we propose a new simple and efficient strategy to compute the initial guess of the locally implicit space-time DG scheme: the Gauss-Legendre points are initialized sequentially in time by a second order accurate MUSCL-type approach for the flux term combined with a Crank-Nicholson method for the stiff source terms. We provide numerical evidence that when starting with this initial guess, the final iterative scheme for the solution of the nonlinear algebraic equations of the local space-time DG predictor method becomes more efficient. We apply our new numerical method to some systems of advection-diffusion-reaction equations with particular emphasis on the asymptotic preserving property for linear model systems and the compressible Navier-Stokes equations with chemical reactions.
We study a reaction-diffusion mathematical model for the evolution of atherosclerosis as an infia... more We study a reaction-diffusion mathematical model for the evolution of atherosclerosis as an infiammation process by combining analytical tools with computer-intensive numerical calculations. The computational work involved the calculation of more than sixty thousand solutions of the full reaction-diffusion system and lead to the complete characterisation of the w-limit for every initial condition. Qualitative properties of the solution are rigorously proved, sorne of them hinted at by the numerical study.
This article appeared in a journal published by Elsevier. The attached copy is furnished to the a... more This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: http://www.elsevier.com/copyright
Mining has been embedded in the public consciousness as a dirty, non-innovative, outdated and env... more Mining has been embedded in the public consciousness as a dirty, non-innovative, outdated and environmentally harmful industry. Proper education, especially the academic one, becomes crucial to successfully change this image. This article depicts the initial assumptions of the international project Master in Entrepreneurship, Innovation and Technology Integration in Mining (MEITIM), co-financed by EIT Raw Materials, that aims to diagnose the current state of Polish higher education in the field of mining at, among others, the Wroclaw University of Science and Technology (WUST), concerning the experience of the Technical University of Madrid (UPM) and Lappeenranta University of Technology (LUT). The MEITIM project allowed identifying the directions of necessary changes in the didactic process as an indispensable set of skills and knowledge for a future mining graduate. Such activities are dictated by many guidelines and arrangements, among others, at the level of the European Commiss...
Communications on Applied Mathematics and Computation
Two-phase flow in porous media is a very active field of research, due to its important applicati... more Two-phase flow in porous media is a very active field of research, due to its important applications in groundwater pollution, $${\text {CO}}_2$$ CO 2 sequestration, or oil and gas production from petroleum reservoirs, just to name a few of them. Fractional flow equations, which make use of Darcy’s law, for describing the movement of two immiscible fluids in a porous medium, are among the most relevant mathematical models in reservoir simulation. This work aims to solve a fractional flow model formed by an elliptic equation, representing the spatial distribution of the pressure, and a hyperbolic equation describing the space-time evolution of water saturation. The numerical solution of the elliptic part is obtained using a finite-element (FE) scheme, while the hyperbolic equation is solved by means of two different numerical approaches, both in the finite-volume (FV) framework. One is based on a monotonic upstream-centered scheme for conservation laws (MUSCL)-Hancock scheme, whereas...
In this work, we propose a mathematical model representing the thermal interaction between vegeta... more In this work, we propose a mathematical model representing the thermal interaction between vegetation cover and the soil underneath it. This model consists of a one-dimensional reaction–diffusion equation describing the evolution of the temperature in the vegetation cover coupled with a two-dimensional reaction–diffusion equation to represent the evolution of the temperature in the soil. The thermal interaction between the vegetation cover and the soil is studied and the distribution of temperatures in the soil with depth is also obtained. The vegetation cover acts in this model as a dynamic and diffusive boundary condition for the soil. The developed model takes into account the latent heat of fusion, which appears when the transformation of ice into liquid water or vice versa occurs inside the soil. The numerical approach for the solution of the mathematical model conducted in this work is based on the finite volume method with Weighted Essentially Non-Oscillatory technique for sp...
Preface P.D. Lax Foreword E.F. Toro Scientific committee Sponsors Thanks! I Invited lectures Sant... more Preface P.D. Lax Foreword E.F. Toro Scientific committee Sponsors Thanks! I Invited lectures Santiago and the Jacobean pilgrimage at the height of the Middle Ages: Mentality and culture F. Singul Recent developments on the Lagrangian and remapping methods for compressible fluid flows J. Cheng & C.-W. Shu Coupling of nonlinear hyperbolic systems: A journey from mathematical to numerical issues F. Coquel Stochastic convergence and the software tool W* R. Kaufman, T. Kaman, Y. Yu & J. Glimm Numerical relativistic magnetohydrodynamics in dynamical spacetimes J.M*. Ibanez Initiation of reactive blast waves by external energy sources A. Linan, V. Kurdyumov & A.L. Sanchez Numerical performance of discontinuous and stabilized continuous Galerkin methods for convection-diffusion problems P.F. Antonietti & A. Quarteroni The Riemann problem in computational science E.F. Toro II Recent advances in the numerical computation of environmental conservation laws with source terms Finite volume discr...
The aim of this work is to introduce a mathematical model representing the evolution of the tempe... more The aim of this work is to introduce a mathematical model representing the evolution of the temperature in a vegetation cover and the ground underneath it. Vegetation, and its interaction with soil, plays a very important role in the protection of soil surface from the action of sun and precipitations. A reduction in the vegetated mass increase the risk of desertification, soil erosion or surface runoffs which which can give rise to soil loss and sediment retention. These processes can favour climate change and global warming, which are major concerns nowadays. The mathematical model presented takes into account the main processes involved in vegetation cover and the interaction with the soil, among which, we can mention the Leaf Area Index, which is a dimensionless quantity defined as the one-sided green leaf area per unit ground surface area, or albedo and co-albedo which are clearly influenced by the vegetation. It is also considered a nonlinear heat capacity in the soil which in...
We consider a coupled model surface-deep ocean effect, where an Energy Balance Model (EBM) is use... more We consider a coupled model surface-deep ocean effect, where an Energy Balance Model (EBM) is used for modelling the surface temperature and a two-dimensional heat equation represents the evolution of the temperature of the deep ocean. Although the model under study is based on that proposed by Watts & Morantine (1990), here we consider a modified model that incorporates other processes, such as the nonlinear diffusion and the action of coalbedo, depending on the temperature. The stationary states of the model under study, taking the solar constant as the parameter, are numerically attained. The results of the simulation are depicted in a {(Q,u)} plot where u is the temperature in the surface and Q is the solar constant. The numerical solution is achieved by means of a finite volume scheme with Weighted Essentially Non-Oscillatory (WENO) reconstruction in space and third order Runge-Kutta scheme, which verifies the Total Variation Diminishing (TVD) property, for time integration. Th...
The river floods happening in populated areas are serious natural risks that give rise to human a... more The river floods happening in populated areas are serious natural risks that give rise to human and economic losses. In order to predict the consequences of river floods and to implement preventive and corrective measures, the mathematical modelling and numerical simulation play, nowadays, a very important role. Among the wide variety of software available for the numerical simulation in fluvial dynamics we have used, in this work, the hydrodynamic model IBER, which is free access simulation software for solving 2D shallow water models. In this paper we focus our attention in floods happening in the vicinity of the confluence of two rivers where there are also crops, with economic importance for the inhabitants of the area that may be affected by the inundation. As an example of this type of geographical region we have used data obtained from the region Las Omañas in NW Spain where, although there is the confluence of rivers Luna and Omaña, the confluence region does not belong to the study area, since we pay our attention to the inundations happening in the village Las Omañas, which is due to the action of one of both rivers, namely the river Omaña.
International Journal of Oil, Gas and Coal Technology, 2019
In underground mining, gas accumulation or gas content anomaly caused by geological structures of... more In underground mining, gas accumulation or gas content anomaly caused by geological structures often results in catastrophic coal and gas outburst accidents, this kind of outburst has already been reported for decades and caused thousands of casualties. However, so far there have been very few studies about how to conduct risk assessment for this kind of geological-structure-related outburst. In this study, our aim is to develop an approach to evaluate the risk of fault-related outburst. The approach developed in this study is a stress-based approach and it considers the associated factors including the gas pressure, the fault attitude and the tectonic stresses. The fault-related outburst index proposed in this work not only can be used for evaluating the fault sealing capability but also can be used for quantitatively assessing the risk degree of fault-related outburst. It is a practical approach and can be recommended to apply in more underground engineering. [
CENTRAL EUROPEAN SYMPOSIUM ON THERMOPHYSICS 2019 (CEST), 2019
We are concerned with a global climate model with deep ocean effect. The model includes a dynamic... more We are concerned with a global climate model with deep ocean effect. The model includes a dynamic and diffusive boundary condition arising from an energy balance on the Earth surface. The scales of time and space are relatively large. One of the characteristics of climate energy balance models is the sensitivity to the variations of a Solar parameter Q. Analytically, it was proved that there exists a range of Q with at least three stationary solutions. In this work we analyze numerically the existence of more than three stationary solutions according to that positive parameter Q.
Fault activation caused by construction, earthquakes, or mining can produce disastrous water-inru... more Fault activation caused by construction, earthquakes, or mining can produce disastrous water-inrush episodes in underground mines. Fault activation is generally caused by stress concentration at the fault tip, so in this study, a computational model of a typical underground stope with a hidden fault was established to quantitatively assess the magnitude of the stress concentration of the stress fields of the fault-tip. Numerical simulation was performed using the extended finite element method and fracture mechanics. Stress intensity factors, which represent the magnitude of the stress concentration, were obtained using the interaction integral method to quantitatively evaluate the tip fields and assess the possibility of fault activation. The mining depth, fluid pressure, fault dip, and fault length were analyzed and the advance of a working face was simulated to determine whether underground mining would cause fault activation.
International Journal of Mining, Reclamation and Environment, 2017
In this study, a new approach is proposed and developed for evaluating the comprehensive outburst... more In this study, a new approach is proposed and developed for evaluating the comprehensive outburst index (range between Oand 100), which is a quantitative assessment approach and will enable us to better understand the risk degree of coal and gas outburst in coal mines. By selecting some typical risk-free and high-risk outburst mines from China as the evaluation targets, we assessed their comprehensive outburst indexes with the developed approach. The assessment results are fully consistent with the actual situations, which indicates that our new developed approach is reliable and can be recommended for applying in more coal mines.
Sudden water inrush has been a deadly killer in underground engineering for decades. Currently, e... more Sudden water inrush has been a deadly killer in underground engineering for decades. Currently, especially in developing countries, frequent water inrush accidents still kill a large number of miners every year. In this study, an approach for predicting the probability of fault-induced water inrush in underground engineering using the adaptive neuro-fuzzy inference system (ANFIS) was developed. Six parameters related to the aquifer, the water-resisting properties of the aquifuge and the mining-induced stresses were extracted as the major parameters to construct the ANFIS model. The constructed ANFIS was trained with twenty reported real fault-induced water inrush cases, and another five new cases were used to test the prediction performance of the trained ANFIS. The final results showed that the prediction results of the five cases were completely consistent with the actual situations. This indicates that the ANFIS is highly accurate in the prediction of fault-induced water inrush and suggests that quantitative assessment of fault-induced water inrush using the ANFIS is possible.
A high order one-step ADER-WENO finite volume scheme with Adaptive Mesh Refinement (AMR) in multi... more A high order one-step ADER-WENO finite volume scheme with Adaptive Mesh Refinement (AMR) in multiple space dimensions is presented. A high order one-step time discretization is achieved using a local space-time discontinuous Galerkin predictor method, while a high order spatial accuracy is obtained through a WENO reconstruction. Thanks to the one-step nature of the underlying scheme, the resulting algorithm can be efficiently imported within an AMR framework on space-time adaptive meshes. We provide convincing evidence that the presented high order AMR scheme behaves better than traditional second order AMR methods. Tests are shown of the new scheme for nonlinear systems of hyperbolic conservation laws, including the classical Euler equations and the equations of ideal magnetohydrodynamics. The proposed scheme is likely to become a useful tool in several astrophysical scenarios.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2014
We study a climatologically important interaction of two of the main components of the geophysica... more We study a climatologically important interaction of two of the main components of the geophysical system by adding an energy balance model for the averaged atmospheric temperature as dynamic boundary condition to a diagnostic ocean model having an additional spatial dimension. In this work, we give deeper insight than previous papers in the literature, mainly with respect to the 1990 pioneering model by Watts and Morantine. We are taking into consideration the latent heat for the two phase ocean as well as a possible delayed term. Non-uniqueness for the initial boundary value problem, uniqueness under a non-degeneracy condition and the existence of multiple stationary solutions are proved here. These multiplicity results suggest that an S-shaped bifurcation diagram should be expected to occur in this class of models generalizing previous energy balance models. The numerical method applied to the model is based on a finite volume scheme with nonlinear weighted essentially non-oscill...
In this work it is studied the numerical solution of a global climate model. The model is based o... more In this work it is studied the numerical solution of a global climate model. The model is based on the one proposed by Watts and Morantine in (4) but here it is considered a temperature-dependent co-albedo. The main difficulty is the dynamic and diffusive boundary condition whichrepresents the coupling between the deep ocean and the atmospheric surface. Results for the continuous model can be found in (1) and (2) where existence of solutiones is proved via fix point iteration. We shall use a finite volume scheme to solve both the 1D model and the 2D model using high order reconstruction in time and space.
In this article we extend the high order ADER finite volume schemes introduced for stiff hyperbol... more In this article we extend the high order ADER finite volume schemes introduced for stiff hyperbolic balance laws by Dumbser, Enaux and Toro (J. Comput. Phys. 227:3971-4001, 2008) to nonlinear systems of advection-diffusion-reaction equations with stiff algebraic source terms. We derive a new efficient formulation of the local space-time discontinuous Galerkin predictor using a nodal approach whose interpolation points are tensorproducts of Gauss-Legendre quadrature points. Furthermore, we propose a new simple and efficient strategy to compute the initial guess of the locally implicit space-time DG scheme: the Gauss-Legendre points are initialized sequentially in time by a second order accurate MUSCL-type approach for the flux term combined with a Crank-Nicholson method for the stiff source terms. We provide numerical evidence that when starting with this initial guess, the final iterative scheme for the solution of the nonlinear algebraic equations of the local space-time DG predictor method becomes more efficient. We apply our new numerical method to some systems of advection-diffusion-reaction equations with particular emphasis on the asymptotic preserving property for linear model systems and the compressible Navier-Stokes equations with chemical reactions.
We study a reaction-diffusion mathematical model for the evolution of atherosclerosis as an infia... more We study a reaction-diffusion mathematical model for the evolution of atherosclerosis as an infiammation process by combining analytical tools with computer-intensive numerical calculations. The computational work involved the calculation of more than sixty thousand solutions of the full reaction-diffusion system and lead to the complete characterisation of the w-limit for every initial condition. Qualitative properties of the solution are rigorously proved, sorne of them hinted at by the numerical study.
This article appeared in a journal published by Elsevier. The attached copy is furnished to the a... more This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: http://www.elsevier.com/copyright
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