Numerical modeling of transient multiphase thermo–mechanical problems: Application to the oceanic lithosphere

[spa] Los modelos numéricos son una herramienta muy útil a la hora de estudiar la geodinámica de gran escala, la interpretación entre litosfera y manto o entre distintas placas tectónicas. En este trabajo se desarrolla una nueva herramienta numérica y se aplica a distintos casos de estudio geofísico. Se detalla todo el proceso de modelado: desde las ecuaciones físicas que gobiernan el problema, las características de las ecuaciones matemáticas, los métodos numéricos usados para aproximarse estas ecuaciones y algunos aspectos de su implementación computacional. El modelo incluye una parte mecánica y una parte térmica acopladas. La recogida utilizada es no-lineal y está basada en los procesos de deformación por difusión y por dislocación del olivino. Las ecuaciones se aproximan usando el método de los Elementos Finitos eXtendido (X-FEM) que es utilizado por primera vez en aplicaciones geofísicas. Este permite trabajar eficientemente con fluidos multiface en un ambiente Euleriano. La herramienta generada se aplica a 3 casos de estudio: i) la estabilidad de la litosfera oceánica, su evolución térmica en el tiempo y las consecuencias de ésta en los observables geofísicos como fotografía, flujo de calor superficial y velocidades sísmicas. Se tiene en cuenta especialmente utilizar parámetros físicos compatibles con los brindados por los estudios de laboratorio. ii) el desprendimiento o detachment de una placa subducida. Se relaciona este proceso con las consecuencias geológicas superficiales que generaría: topografía generada, tiempos en que tarda el proceso, etc. Se estudia también la influencia de los principales procesos que pueden afectar al detachment: calor generado por fisipación viscosa, calor generado por compresión adiabática de los materiales, etc. El tercer caso de estudio relaciona la velocidad de convergencia entre las placas con el ángulo de subducción. Se realizan una serie de experimentos numéricos de forma sistemática para ver la relación entre estos parámetros

Numerical modeling of transient multiphase thermo–mechanical problems: Application to the oceanic lithosphere

Los modelos numéricos son una herramienta muy útil a la hora de estudiar la geodinámica de gran escala, la interpretación entre litosfera y manto o entre distintas placas tectónicas. En este trabajo se desarrolla una nueva herramienta numérica y se aplica a distintos casos de estudio geofísico. Se detalla todo el proceso de modelado: desde las ecuaciones físicas que gobiernan el problema, las características de las ecuaciones matemáticas, los métodos numéricos usados para aproximarse estas ecuaciones y algunos aspectos de su implementación computacional. El modelo incluye una parte mecánica y una parte térmica acopladas. La recogida utilizada es no-lineal y está basada en los procesos de deformación por difusión y por dislocación del olivino. Las ecuaciones se aproximan usando el método de los Elementos Finitos eXtendido (X-FEM) que es utilizado por primera vez en aplicaciones geofísicas. Este permite trabajar eficientemente con fluidos multiface en un ambiente Euleriano. La herramienta generada se aplica a 3 casos de estudio: i) la estabilidad de la litosfera oceánica, su evolución térmica en el tiempo y las consecuencias de ésta en los observables geofísicos como fotografía, flujo de calor superficial y velocidades sísmicas. Se tiene en cuenta especialmente utilizar parámetros físicos compatibles con los brindados por los estudios de laboratorio. ii) el desprendimiento o detachment de una placa subducida. Se relaciona este proceso con las consecuencias geológicas superficiales que generaría: topografía generada, tiempos en que tarda el proceso, etc. Se estudia también la influencia de los principales procesos que pueden afectar al detachment: calor generado por fisipación viscosa, calor generado por compresión adiabática de los materiales, etc. El tercer caso de estudio relaciona la velocidad de convergencia entre las placas con el ángulo de subducción. Se realizan una serie de experimentos numéricos de forma sistemática para ver la relación entre estos parámetros

Coupled mantle dripping and lateral dragging controlling the lithosphere structure of the NW-Moroccan margin and the Atlas Mountains: A numerical experiment

Recent studies integrating gravity, geoid, surface heat flow, elevation and seismic data indicate a prominent lithospheric mantle thickening beneath the NW-Moroccan margin (LAB >200 km-depth) followed by thinning beneath the Atlas Domain (LAB about 80 km-depth). Such unusual configuration has been explained by the combination of mantle underthrusting due to oblique Africa-Eurasia convergence together with viscous dripping fed by asymmetric lateral mantle dragging, requiring a strong crust-mantle decoupling. In the present work we examine the physical conditions under which the proposed asymmetric mantle drip and drag mechanism can reproduce this lithospheric configuration. We also analyse the influence of varying the kinematic boundary conditions as well as the mantle viscosity and the initial lithosphere geometry. Results indicate that the proposed drip-drag mechanism is dynamically feasible and only requires a lateral variation of the lithospheric strength. The further evolution of the gravitational instability can become either in convective removal of the lithospheric mantle, mantle delamination, or subduction initiation. The model reproduces the main trends of the present-day lithospheric geometry across the NW-Moroccan margin and the Atlas Mountains, the characteristic time of the observed vertical movements, the amplitude and rates of uplift in the Atlas Mountains and offers an explanation to the Miocene to Pliocene volcanism. An abnormal constant tectonic subsidence rate in the margin is predicted. (C) 2013 Elsevier B.V. All rights reserved.Peer ReviewedPostprint (author's final draft

Hierarchical x-fem applied to n-phase flow

In this work we proposed an extencion of the level set technique to track any number of free surfaces. This extension is based in a hierarchical ordering of several level set functions. To complete the X–FEM approach, the enrichment via partition of the unity method is also extended. The ridge function, base of the enriched interpolation, is restated to include several level sets and the hierarchy between them

Hierarchical X-FEM for n-phase flow (n > 2)

The eXtended Finite Element Method (X-FEM) has been successfully used in two-phase flow problems involving a moving interface. In order to simulate problems involving more than two phases, the X-FEM has to be further eXtended. The proposed approach is presented in the case of a quasi-static Stokes n-phase flow and it is based on using an ordered collection of level set functions to describe the location of the phases. A level set hierarchy allows describing triple junctions avoiding overlapping or “voids” between materials. Moreover, an enriched solution accounting for several simultaneous phases inside one element is proposed. The interpolation functions corresponding to the enriched degrees of freedom require redefining the associated ridge function accounting for all the level sets. The computational implementation of this scheme involves calculating integrals in elements having several materials inside. An adaptive quadrature accounting for the interfaces locations is proposed to accurately compute these integrals. Examples of the hierarchical X-FEM approach are given for a n-phase Stokes problem in 2 and 3 dimensions.Peer ReviewedPostprint (author’s final draft

Generalized parametric solutions in Stokes flow

The final publication is available at Springer via https://doi.org/10.1016/j.cma.2017.07.016Design optimization and uncertainty quantification, among other applications of industrial interest, require fast or multiple queries of some parametric model. The Proper Generalized Decomposition (PGD) provides a separable solution, a computational vademecum explicitly dependent on the parameters, efficiently computed with a greedy algorithm combined with an alternated directions scheme and compactly stored. This strategy has been successfully employed in many problems in computational mechanics. The application to problems with saddle point structure raises some difficulties requiring further attention. This article proposes a PGD formulation of the Stokes problem. Various possibilities of the separated forms of the PGD solutions are discussed and analyzed, selecting the more viable option. The efficacy of the proposed methodology is demonstrated in numerical examples for both Stokes and Brinkman models.Peer ReviewedPostprint (author's final draft

Proper generalized decomposition for parameterized Helmholtz problems in heterogeneous and unbounded domains: application to harbor agitation

Solving the Helmholtz equation for a large number of input data in an heterogeneous media and unbounded domain still represents a challenge. This is due to the particular nature of the Helmholtz operator and the sensibility of the solution to small variations of the data. Here a reduced order model is used to determine the scattered solution everywhere in the domain for any incoming wave direction and frequency. Moreover, this is applied to a real engineering problem: water agitation inside real harbors for low to mid-high frequencies. The Proper Generalized Decomposition (PGD) model reduction approach is used to obtain a separable representation of the solution at any point and for any incoming wave direction and frequency. Here, its applicability to such a problem is discussed and demonstrated. More precisely, the contributions of the paper include the PGD implementation into a Perfectly Matched Layer framework to model the unbounded domain, and the separability of the operator which is addressed here using an efficient higher-order projection scheme. Then, the performance of the PGD in this framework is discussed and improved using the higher-order projection and a Petrov-Galerkin approach to construct the separated basis. Moreover, the efficiency of the higherorder projection scheme is demonstrated and compared with the higher-order singular value decomposition

An efficient and general approach for implementing thermodynamic phase equilibria information in geophysical and geodynamic studies

We present a flexible, general, and efficient approach for implementing thermodynamic phase equilibria information (in the form of sets of physical parameters) into geophysical and geodynamic studies. The approach is based on Tensor Rank Decomposition methods, which transform the original multidimensional discrete information into a separated representation that contains significantly fewer terms, thus drastically reducing the amount of information to be stored in memory during a numerical simulation or geophysical inversion. Accordingly, the amount and resolution of the thermodynamic information that can be used in a simulation or inversion increases substantially. In addition, the method is independent of the actual software used to obtain the primary thermodynamic information, and therefore, it can be used in conjunction with any thermodynamic modeling program and/or database. Also, the errors associated with the decomposition procedure are readily controlled by the user, depending on her/his actual needs (e.g., preliminary runs versus full resolution runs). We illustrate the benefits, generality, and applicability of our approach with several examples of practical interest for both geodynamic modeling and geophysical inversion/modeling. Our results demonstrate that the proposed method is a competitive and attractive candidate for implementing thermodynamic constraints into a broad range of geophysical and geodynamic studies. MATLAB implementations of the method and examples are provided as supporting information and can be downloaded from the journal's website

Solution of geometrically parametrised problems within a CAD environment via model order reduction

The main objective of this work is to describe a general and original approach for computing an off-line solution for a set of parameters describing the geometry of the domain. That is, a solution able to include information for different geometrical parameter values and also allowing to compute readily the sensitivities. Instead of problem dependent approaches, a general framework is presented for standard engineering environments where the geometry is defined by means of NURBS. The parameters controlling the geometry are now the control points characterising the NURBS curves or surfaces. The approach proposed here, valid for 2D and 3D scenarios, allows a seamless integration with CAD preprocessors. The proper generalised decomposition (PGD), which is applied here to compute explicit geometrically parametrised solutions, circumvents the curse of dimensionality. Moreover, optimal convergence rates are shown for PGD approximations of incompressible flows

Dynamics of double-polarity subduction: application to the Western Mediterranean

The Western Mediterranean tectonic setting and history is studied by means of three-dimensional numerical models. Goals are to understand its dynamics and to test the feasibility of a doublepolarity subduction process that could have a key importance in the complex setup of this area. The physical models, the numerical techniques involved, and some results in two and three dimensions are presented in this work.Peer Reviewe