Robust and efficient primal-dual Newton-Krylov solvers for viscous-plastic sea-ice models

We present a Newton-Krylov solver for a viscous-plastic sea-ice model. This constitutive relation is commonly used in climate models to describe the material properties of sea ice. Due to the strong nonlinearity introduced by the material law in the momentum equation, the development of fast, robust and scalable solvers is still a substantial challenge. In this paper, we propose a novel primal-dual Newton linearization for the implicitly-in-time discretized momentum equation. Compared to existing methods, it converges faster and more robustly with respect to mesh refinement, and thus enables numerically converged sea-ice simulations at high resolutions. Combined with an algebraic multigrid-preconditioned Krylov method for the linearized systems, which contain strongly varying coefficients, the resulting solver scales well and can be used in parallel. We present experiments for two challenging test problems and study solver performance for problems with up to 8.4 million spatial unknowns.Comment: 18 pages, 7 figure

Magmatic focusing to mid-ocean ridges: the role of grain size variability and non-Newtonian viscosity

Melting beneath mid-ocean ridges occurs over a region that is much broader than the zone of magmatic emplacement to form the oceanic crust. Magma is focused into this zone by lateral transport. This focusing has typically been explained by dynamic pressure gradients associated with corner flow, or by a sub-lithospheric channel sloping upward toward the ridge axis. Here we discuss a novel mechanism for magmatic focusing: lateral transport driven by gradients in compaction pressure within the asthenosphere. These gradients arise from the co-variation of melting rate and compaction viscosity. The compaction viscosity, in previous models, was given as a function of melt fraction and temperature. In contrast, we show that the viscosity variations relevant to melt focusing arise from grain-size variability and non-Newtonian creep. The asthenospheric distribution of melt fraction predicted by our models provides an improved ex- planation of the electrical resistivity structure beneath one location on the East Pacific Rise. More generally, although grain size and non-Newtonian viscosity are properties of the solid phase, we find that in the context of mid-ocean ridges, their effect on melt transport is more profound than their effect on the mantle corner-flow.Comment: 20 pages, 4 figures, 1 tabl

Driving NEMO Towards Exascale: Introduction of a New Software Layer in the NEMO Stack Software

This paper addresses scientific challenges related to high level implementation strategies that leads NEMO to effectively use of the opportunities of exascale systems. We consider two software modules as proof-of-concept: the Sea Surface Height equation solver and the Variational Data Assimilation system, which are components of the NEMO ocean model (OPA). Advantages rising from the introduction of consolidated scientific libraries in NEMO are highlighted: such advantages concern both the "software quality" improvement (see the software quality parameters like robustness, portability, resilence, etc.) and time reduction of software development

Shifted Laplacian multigrid for the elastic Helmholtz equation

The shifted Laplacian multigrid method is a well known approach for preconditioning the indefinite linear system arising from the discretization of the acoustic Helmholtz equation. This equation is used to model wave propagation in the frequency domain. However, in some cases the acoustic equation is not sufficient for modeling the physics of the wave propagation, and one has to consider the elastic Helmholtz equation. Such a case arises in geophysical seismic imaging applications, where the earth's subsurface is the elastic medium. The elastic Helmholtz equation is much harder to solve than its acoustic counterpart, partially because it is three times larger, and partially because it models more complicated physics. Despite this, there are very few solvers available for the elastic equation compared to the array of solvers that are available for the acoustic one. In this work we extend the shifted Laplacian approach to the elastic Helmholtz equation, by combining the complex shift idea with approaches for linear elasticity. We demonstrate the efficiency and properties of our solver using numerical experiments for problems with heterogeneous media in two and three dimensions

Comparison of ice dynamics using full-Stokes and Blatter–Pattyn approximation: application to the Northeast Greenland Ice Stream

Full-Stokes (FS) ice sheet models provide the most sophisticated formulation of ice sheet flow. However, their applicability is often limited due to the high computational demand and numerical challenges. To balance computational demand and accuracy, the so-called Blatter–Pattyn (BP) stress regime is frequently used. Here, we explore the dynamic consequences of using simplified approaches by solving FS and the BP stress regime applied to the Northeast Greenland Ice Stream. To ensure a consistent comparison, we use one single ice sheet model to run the simulations under identical numerical conditions. A sensitivity study to the horizontal grid resolution (from 12.8 to a resolution of 0.1 km) reveals that velocity differences between the FS and BP solution emerge below ∼ 1 km horizontal resolution and continuously increase with resolution. Over the majority of the modelling domain both models reveal similar surface velocity patterns. At the grounding line of the 79∘ North Glacier the simulations show considerable differences whereby the BP model overestimates ice discharge of up to 50 % compared to FS. A sensitivity study to the friction type reveals that differences are stronger for a power-law friction than a linear friction law. Model differences are attributed to topographic variability and the basal drag, in which neglected stress terms in BP become important

FSI-mallien soveltaminen modernien risteilylaivojen kansivarustelurakenteiden tuuliherätteisen värähtelyn ennustamisessa

Recent market trends in the cruise industry aim to provide traditionally land-based attractions on cruise liners. This leads to the integration of special architectural features, such as water parks and amusement rides, in way of the cruise ships’ upper decks. Deck amusements are ideally lightweight structures that comprise of slender beams which aims to reduce the added weight on top decks. To ensure safety it is critical to understand the influence of wind loading introduced by Vortex-Induced Vibration (VIV) on the dynamic structural response. This thesis aims to determine the differences between one- and two-way coupled Fluid-Structure Interaction (FSI) analyses in the context of ship deck outfitting structures subjected to VIV. Accordingly, a large deck amusement structure is idealized as an aluminum portal frame, subject to a constant head wind. Transient one- and two-way coupled FSI simulations, based on Reynolds-Averaged Navier-Stokes (RANS) fluid dynamics model and linear elastic 3D FEA, are conducted using the commercial CFD software STAR-CCM+. Results are assessed and compared against quasi-static and quasi-dynamic beam element idealizations solved by NX Nastran. The investigation carried out reveals that vortex shedding remains at the original shedding frequency in the one-way coupled solution. However, the two-way coupled simulation demonstrates a clear lock-in of the vortex shedding to the portal frame’s natural frequency. Consequently, the dynamic loading experienced by the portal frame is significantly increased and the structure experiences resonant vibration when full two-way FSI coupling is considered. Neither the one-way coupled nor the quasi-dynamic analysis are able to capture these effects.Viimeisimmät suuntaukset risteilymarkkinoilla pyrkivät tuomaan laivoille elämyksiä, jotka ovat aiemmin olleet mahdollisia vain maissa. Tämä on johtanut ennennäkemättömien rakenteiden, kuten vesipuistojen ja huvipuistolaitteiden integroimiseen modernien risteilyalusten yläkansille. Kyseiset rakenteet ovat ideaalisesti mahdollisimman kevyitä sekä koostuvat pitkistä ja suhteellisen ohuista palkeista, minkä tarkoituksena on vähentää ylimääräistä painoa laivan yläkansilla. Riskien minimoimiseksi on äärimmäisen tärkeää ymmärtää, miten jatkuva tuulikuormitus ja siitä johtuva pyörreherätteinen värähtely vaikuttavat rakenteiden dynaamiseen vasteeseen. Tässä diplomityössä selvitetään, kuinka yhteen ja kahteen suuntaan kytketyt neste-rakenne -vuorovaikutusanalyysit eroavat laivan kansivarustelurakenteiden tuuliherätteisen värähtelyn ennustamisessa. Tätä varten suuri huvipuistorakenne on idealisoitu alumiinisena palkkikaarena, joka altistuu vakionopeuksiselle vastatuulelle. Rakenne analysoidaan aikariippuvaisilla yhteen ja kahteen suuntaan kytketyillä neste-rakenne -vuorovaikutussimulaatioilla. Virtausmallinnus perustuu Reynolds-keskiarvoistettuihin Navier-Stokes -yhtälöihin ja rakennemalli lineaariselastiseen 3D-elementtimenetelmään. Simulaatiot lasketaan käyttäen numeerista virtauslaskentaohjelmaa STAR-CCM+. Tuloksia arvioidaan ja verrataan kvasistaattisen ja kvasidynaamisen palkkielementtimallien kanssa. Palkkielementtimallit ratkaistaan käyttäen kaupallista NX Nastran -ratkaisijaa. Diplomityön tulosten perusteella pyörteiden irtoaminen säilyy alkuperäisellä taajuudella laskettaessa yhteen suuntaan kytketyllä analyysilla. Kahteen suuntaan kytketty analyysi osoittaa, että pyörteiden irtoaminen lukkiutuu kaarirakenteen ominaistaajuudelle. Tämän johdosta rakenteen dynaaminen kuormitus kasvaa merkittävästi ja palkkikaari värähtelee resonanssissa. Yhteen suuntaan kytketty laskenta tai arvioidut yksinkertaisemmat menetelmät eivät kykene mallintamaan näitä ilmiöitä

Design of a parallel hybrid direct/iterative solver for CFD problems

We discuss the parallel implementation of a hybrid direct/iterative solver for a special class of saddle point matrices arising from the discretization of the steady Navier-Stokes equations on an Arakawa C-grid, the F-matrices. The two-level method described here has the following properties: (i) it is very robust, even hat comparatively high Reynolds Numbers; (ii) a single parameter controls fill and convergence, making the method straightforward to use; (iii) the convergence rate is independent of the number of unknowns; (iv) it can be implemented on distributed memory machines in a natural way; (v) the matrix on the second level has the same structure and numerical properties as the original problem, so the method can be applied recursively. The implementation focusses on generality, modularity, code reuse and recursiveness. The solver is implemented using building blocks of the Trilinos libraries. We show its performance on a parallel computer for the Navier-Stokes equations