Optimized Schwarz waveform relaxation for Primitive Equations of the ocean

In this article we are interested in the derivation of efficient domain decomposition methods for the viscous primitive equations of the ocean. We consider the rotating 3d incompressible hydrostatic Navier-Stokes equations with free surface. Performing an asymptotic analysis of the system with respect to the Rossby number, we compute an approximated Dirichlet to Neumann operator and build an optimized Schwarz waveform relaxation algorithm. We establish the well-posedness of this algorithm and present some numerical results to illustrate the method

Optimized Schwarz Waveform Relaxation for Advection Reaction Diffusion Equations in Two Dimensions

Optimized Schwarz Waveform Relaxation methods have been developed over the last decade for the parallel solution of evolution problems. They are based on a decomposition in space and an iteration, where only subproblems in space-time need to be solved. Each subproblem can be simulated using an adapted numerical method, for example with local time stepping, or one can even use a different model in different subdomains, which makes these methods very suitable also from a modeling point of view. For rapid convergence however, it is important to use effective transmission conditions between the space-time subdomains, and for best performance, these transmission conditions need to take the physics of the underlying evolution problem into account. The optimization of these transmission conditions leads to a mathematically hard best approximation problem of homographic type. We study in this paper in detail this problem for the case of linear advection reaction diffusion equations in two spatial dimensions. We prove comprehensively best approximation results for transmission conditions of Robin and Ventcel type. We give for each case closed form asymptotic values for the parameters, which guarantee asymptotically best performance of the iterative methods. We finally show extensive numerical experiments, and we measure performance corresponding to our analysisComment: 42 page

Efficient interface conditions for the coupling of ocean models

International audienceAlthough the two-way nesting is the most usual coupling method in the ocean community, it does not address the correct problem but an approximation, and does not ensure enough regularity through the interface between the two models1. The correct approach consisting in a full coupling is more difficult and expensive than the two-way nesting, since it requires to find and implement an algorithm ensuring that the solutions in each domain satisfy the regularity conditions through the interface. The global-in-time non-overlapping Schwarz algorithm is particularly well suited for such a coupling, and can lead to improved physical results. Our work thus aims at improving the ocean coupling by determining efficient interface conditions for the usual ocean equations (the so-called 3-D primitive equations). These ones are composed of advection-diffusion equations for tracers such as temperature and salinity, and dynamics equations, which can be approximated in the 2-D case by the shallow-water equations

Analysis of ocean-atmosphere coupling algorithms : consistency and stability

International audienceThis paper is focused on the numerical and computational issues associated to ocean-atmosphere coupling. It is shown that usual coupling methods do not provide the solution to the correct problem, but to an approaching one since they are equivalent to performing one single iteration of an iterative coupling method. The stability analysis of these ad-hoc methods is presented, and we motivate and propose the adaptation of a Schwarz domain decomposition method to ocean-atmosphere coupling to obtain a stable and consistent coupling method

Towards Simulation of Complex Ocean Flows: Analysis and Algorithm for Computation of Coupled Partial Differential Equations

The hybrid CFD models which usually consist of 2 sub-models, develop our capability to simulate many emerging problems with multiphysics and multiscale flows, especially for the coastal ocean flows interacted with local phenomena of interest. For most cases, the sub-models are connected with direct interpolation which is easy and workable. It becomes urgently needed to investigate the inner mechanism of such model integration as this simple method does not work well if the two sub-models are different in governing equations, numerical methods, and computational grids. Also, it can not treat complex flow structures as well as the balance in mass or momentum across the interface. Even several different prototypes of interface treatments have been reported but have not been tested on 3D problems or coupling different sets of PDEs. In this thesis, a systemic study about the overlapping domain decomposed problem is presented into the 3 following aspects: 1. Convergence analysis Towards a rigorous mathematical foundation, a study of 1D domain decomposed problem based on advection-diffusion-reaction equation is made. Both Schwarz-Time process and Time-Schwarz process have been analysed with a new but simple method called fully discretization analysis. The convergence ratio formulas of classic and optimized interface treatments have been formed. The expressions for the optimized coefficient pair are found for some cases. 2. Accurate interface algorithm The back and forth error compensation and correction method(BFECC), an accuracy-enhancement method is applied with the interpolation scheme. A fully investigation is made for it, such as supercovnergence, interpolation scheme, node density, mesh ratio, mesh rotation, and mesh with perturbation. Case study on 3D domain decomposed simulation with same sub-model is done, the results generated by different interface treatments show that the calculation benefits from higher order treatment. 3. Different interface treatments The example hybrid CFD model(SIFOM-FVCOM) is studied with the governing equations, grid types, numerical schemes, and calculation flows. The numerical experiments are made by applying different interface treatments on SIFOM-FVCOM. The differences of the results indicate that the interface treatment play a crucial role in success of such simulations. \end{enumerate} This work improves the understanding of the grounded mathematical problem, the effectiveness of optimized interface treatment, the importance of interface treatment\u27s accuracy, and the otherness of applying different interface treatments. In addition, it advances our capability in further developing the interface treatment with better convergence rate as well as higher fidelity

Report on fully coupled data assimilation in simplified systems with implications for Earth system reanalysis

This report describes the Inria contribution to WP2 regarding a study of coupled data assimilation algorithms applied to academic models. This task was twofold: 1. Propose and study new coupled variational data assimilation algorithms. 2. Create a stand-alone coupled single column model (SCM) that mimics the ocean atmosphere behaviour and that can be used to validate the algorithms proposed in 1. Regarding subtask 1, a focus was made on ways to explicitly account for model coupling in the varia-tional optimisation problem, either as a strong contraint or as a weak constraint, or as a combination of both. It is then applied to both linear and non linear coupled problems, and leads to the conclusion that it does bring some noticeable benefit, but at a cost, both in time of development and computing time. The cost-benefit ratio has therefore to be studied for each given application. The coupled SCM has been developed in Fortran and interfaced with the OOPS data assimilation framework. It is documented in this report and a reference test case is given, so that it can be reused by partners of the project and beyond

The Sixth Copper Mountain Conference on Multigrid Methods, part 2

The Sixth Copper Mountain Conference on Multigrid Methods was held on April 4-9, 1993, at Copper Mountain, Colorado. This book is a collection of many of the papers presented at the conference and so represents the conference proceedings. NASA Langley graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The multigrid discipline continues to expand and mature, as is evident from these proceedings. The vibrancy in this field is amply expressed in these important papers, and the collection clearly shows its rapid trend to further diversity and depth

Signals and Images in Sea Technologies

Life below water is the 14th Sustainable Development Goal (SDG) envisaged by the United Nations and is aimed at conserving and sustainably using the oceans, seas, and marine resources for sustainable development. It is not difficult to argue that signals and image technologies may play an essential role in achieving the foreseen targets linked to SDG 14. Besides increasing the general knowledge of ocean health by means of data analysis, methodologies based on signal and image processing can be helpful in environmental monitoring, in protecting and restoring ecosystems, in finding new sensor technologies for green routing and eco-friendly ships, in providing tools for implementing best practices for sustainable fishing, as well as in defining frameworks and intelligent systems for enforcing sea law and making the sea a safer and more secure place. Imaging is also a key element for the exploration of the underwater world for various scopes, ranging from the predictive maintenance of sub-sea pipelines and other infrastructure projects, to the discovery, documentation, and protection of sunken cultural heritage. The scope of this Special Issue encompasses investigations into techniques and ICT approaches and, in particular, the study and application of signal- and image-based methods and, in turn, exploration of the advantages of their application in the previously mentioned areas

Seismic and magnetic constraints on the structure of upper oceanic crust at fast and slow spreading ridges

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 1998The upper ocean crust contains a comprehensive record of the shallow geological processes active along the world's mid-ocean ridge system. This thesis examines the magnetic and seismic structure of the upper crust at two contrasting ridges-the fast spreading East Pacific Rise (EPR) and the slow spreading Mid-Atlantic Ridge (MAR)-to build a more complete understanding about the roles of volcanic emplacement, tectonic disruption and hydrothermal alteration in the near-ridge environment. A technique that inverts potential field measurements. directly from an uneven observation track is developed and applied to near-bottom magnetic data from the spreading segments north of the Kane transform on the MAR. It is concluded that the central anomaly magnetization high marks the locus of focused volcanic emplacement. A cyclic faulting model is proposed to explain the oscillatory magnetization pattern associated with discrete blocks of crust being transported out of the rift valley between intensely altered fault zones. Seismic waveform and amplitude analyses of the magma sill along the EPR reveal it to be a thin (<100 m) body of partial melt. These characteristics have important implications for melt availability and transport within the cycle of eruption and replenishment. A genetic algorithm-based seismic waveform inversion technique is developed and applied to on- and near-axis multichannel data from 17°20'S on the EPR and the spreading segment south of the Oceanographer transform (MAR) to map and compare for the first time the detailed velocity structure of the upper crust at two different spreading rates. Combined with conventionally processed seismic profiles, our results show that, while final extrusive thickness is comparable at all spreading ridges (300-500 m), the style of thickening may vary. While a thin (≤100 m) extrusive carapace quadruples in thickness within 1-4 km of the EPR crest, the extrusive section at the MAR achieves its final thickness within the inner valley. Both show evidence for a narrow zone of volcanic emplacement. Vigorous hydrothermalism at the EPR may produce a more rapid increase in basement velocities relative to the MAR. Rapid modification of the extrusive/dike transition at both ridges indicates that hydrothermalism is enhanced in this interval. Along-axis transport of lavas may thicken the extrusive pile at slow spreading segment ends, strengthening the magnetic highs generated by lava chemistry.ONR graduate fellow. The magnetics portion of this thesis was also supported by NSF grants OCE-9204141, OCE-9200905 (M. A. Tivey & H. Schouten) and NERC GR3/7702 (R. C. Searle). Research for Chapter 4 was partially funded by NSF grant OCE-9402933 (R. S. Detrick). The final two science chapters were supported by NSF grants OCE-9012707, OCE-9300450 (R. S. Detrick), OCE-9401717 (G. M. Kent & R. S. Detrick), OCE-9400623 (M. A. Tivey) and the Education office