1,721,011 research outputs found
Implicit tracking for multi-fluid simulations
No full textIn this work, we introduce a new method for tracking the interfaces among several immiscible fluids. To advance the solution in time, we use a MUSCL-type scheme which couples a partial volume representation with a level set one to build the numerical fluxes. In particular we show the positiveness and conservation properties of this method. Some numerical tests are given to demonstrate the conservativeness and the performances of our method. © 2010 Elsevier Inc
A control problem approach to Coulomb’s friction
Full text linkIn this work we present a formulation of Coulomb's friction in a fractured elastic body as a PDE control problem where the observed quantity is the tangential stress across an internal interface, while the control parameter is the slip i.e. the displacement jump across the interface. The cost function aims at minimizing the norm of a non-linear and not everywhere differentiable complementarity function, written in terms of the tangential stress and the slip. The interesting point of this method is that gives rise to an iterative procedure where at each iteration we solve a problem with given slip at the interface, without resorting to the use of Lagrange multipliers. We carry out a formal derivation of the method, with some preliminary results, and a numerical experiment to verify the efficacy of the technique
Analysis of a model for precipitation and dissolution coupled with a Darcy flux
No full textIn this paper we deal with the numerical analysis of an upscaled model of a reactive flow in a porous medium, which describes the transport of solutes undergoing precipitation and dissolution, leading to the formation/degradation of crystals inside the porous matrix. The model is defined at the Darcy scale, and it is coupled to a Darcy flow characterized by a permeability field that changes in space and time according to the precipitated crystal concentration. The model involves a non-linear multi-valued reaction term, which is treated exactly by solving an inclusion problem for the solutes and the crystals dynamics. We consider a weak formulation for the coupled system of equations expressed in a dual mixed form for the Darcy field and in a primal form for the solutes and the precipitate, and show its well posedness without resorting to regularization of the reaction term. Convergence to the weak solution is proved for its finite element approximation. We perform numerical experiments to study the behavior of the system and to assess the effectiveness of the proposed discretization strategy. In particular we show that a method that captures the discontinuity yields sharper dissolution fronts with respect to methods that regularize the discontinuous term
Simulations of large scale three-dimensional sedimentary basin dynamics through domain decomposition techniques
No full textDerivation and analysis of a fluid-dynamical model in thin and long elastic vessels
No full textStarting from the three-dimensional Newtonian and incompress- ible Navier-Stokes equations in a compliant straight vessel, we derive a reduced one-dimensional model by an averaging procedure which takes into considera- tion the elastic properties of the wall structure. In particular, we neglect terms of the first order with respect to the ratio between the vessel radius and length. Furthermore, we consider that the viscous effects are negligible with respect to the propagative phenomena. The result is a one-dimensional nonlinear hy- perbolic system of two equations in one space dimension, which describes the mean longitudinal velocity of the flow and the radial wall displacement. The modelling technique here applied to straight cylindrical vessels may be gener- alized to account for curvature and torsion. An analysis of well posedness is presented which demonstrates, under reasonable hypotheses, the global in time existence of regular solutions
Numerical simulation of geochemical compaction with discontinuous reactions
No full textThe present work deals with the numerical simulation of porous media subject to the coupled effects of mechanical compaction and reactive flows that can significantly alter the porosity due to dissolution, precipitation or transformation of the solid matrix. These chemical processes can be effectively modelled as ODEs with discontinuous right hand side, where the discontinuity depends on time and on the solution itself. Filippov theory can be applied to prove existence and to determine the solution behaviour at the discontinuities. From the numerical point of view, tailored numerical schemes are needed to guarantee positivity, mass conservation and accuracy. In particular, we rely on an event-driven approach such that, if the trajectory crosses a discontinuity, the transition point is localized exactly and integration is restarted accordingly
A mixed-dimensional model for direct current simulations in the presence of a thin high-resistivity liner
Full text linkIn this work, we present a mixed-dimensional mathematical model to obtain the electric potential and current density in direct current simulations when a thin liner is included in the modelled domain. The liner is used in landfill management to prevent leakage of leachate from the waste body into the underground and is made of a highly-impermeable high-resistivity plastic material. The electrodes and the liner have diameters and thickness, respectively, that are much smaller than their other dimensions, thus their numerical simulation might be too costly in an equi-dimensional setting. Our approach is to approximate them as objects of lower dimension and derive the corresponding equations. The obtained mixed-dimensional model is validated against laboratory experiments of increasing complexity to show the reliability of the proposed mathematical model. Our tests also show that configurations with current and voltage electrodes on either sides of the liner confining the landfill may be effective in detecting damages of the membrane
Modeling fracture propagation in poro-elastic media combining phase-field and discrete fracture models
No full textWe present a novel model for fluid-driven fracture propagation in poro-elastic media. Our approach combines ideas from dimensionally reduced discrete fracture models with diffuse phase-field models. The main advantage of this combined approach is that the fracture geometry is always represented explicitly, while the propagation remains geometrically flexible. We prove that our model is thermodynamically consistent. In order to solve our model numerically, we propose a mixed-dimensional discontinuous Galerkin scheme with a computational grid fully conforming to the fractures. As the fracture propagates, the diffuse phase-field acts as indicator to identify new fracture facets to be added to the discrete fracture network. Numerical experiments demonstrate that our approach reproduces classical scenarios for fracturing porous media
A numerical procedure for geochemical compaction in the presence of discontinuous reactions
No full textThe process by which rocks are formed from the burial of a fresh sediment involves the coupled effects of mechanical compaction and geochemical reactions. Both of them affect the porosity and permeability of the rock and, in particular, geochemical reactions can significantly alter them, since dissolution and precipitation processes may cause a structural transformation of the solid matrix. Often, the differential problems that arise from the modeling of these chemical reactions may present a discontinuous right hand side, where the discontinuity depends on the solution itself. In this work we have developed a numerical model to simulate this complex multi-physics problem by treating the discontinuous right hand side with a specially tailored event-driven numerical scheme. We show the performance of this strategy in terms of positivity and mass conservation, also in comparison with a more traditional approach that relies on a regularization of the discontinuous terms
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