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Long description:

Microsoft --- Office --- Excel --- Tabellenkalkulation --- Funktionen --- Formeln --- Analysen --- Office 365 --- Solver --- 2019 --- 2016 --- Verweise

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Phase change materials (PCMs) are of high interest in thermal storage and thermal management applications for the earth and for space environments. Nevertheless, their functionality is intrinsically attached to phase change processes, which, from experience, it is known that they are computationally challenging. The present project arises with the intention to give a numerical solution to this problematic.

A solver based on the enthalpy-porosity technique, capable to deal with diffusive-convective phase change has been adapted for OpenFOAM 4.1. For the implementation of the enthalpy technique, the work of Voller Mushy has been closely followed, and a detailed explanation of the equations employed and the assumptions that support them is given. Furthermore, the numerical approach is also specified, with a close attention to the discretization process based on the Finite Volume Method (FVM). The solver algorithm is provided with a deep explanation of its implementation in OpenFOAM. Furthermore, an analysis of the convergence of the numerical solution is provided.

Moreover, the works of several authors, have been employed to help in some aspects of the implementation and validation of the solver. As part of this validation, the controversial case of the melting of pure Gallium in a rectangular cavity is computed with the OpenFOAM solver. The author gives some discussion about the results obtained and compares them with the existing literature in order to assess the accuracy of the mathematical model employed.

The last part of the project employs the customize solver to analyze the thermal behaviour of a PCM during melting. Three different cases are proposed and tested for two different geometries: one under gravity conditions, where natural convection is part of the heat transfer process, and another two independent of gravity or proper of micro-gravity environments: a pure conductive case and a case with Bénard-Marangoni convection.

Enthalpy-porosity technique --- OpenFOAM solver --- Finite Volume Method --- PCMs --- Marangoni Convection --- Melting of Gallium --- Ingénierie, informatique & technologie > Ingénierie aérospatiale

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In the framework of the completion of EMShip (Erasmus Mundus Double Master in Ship Design and Offshore Structures) Program, this master thesis was undertaken at LHEEA (Laboratory in Hydrodynamics, Energetics and Atmospheric Environment), a CNRS/Ecole Centrale Nantes research laboratory.

The purpose of this thesis is the estimation of the non-linearities associated with sea-keeping computation encountered in highly cambered waves. Linear methods like NEMOH developed for small displacements computations do not give good result. To estimate nonlinearity the weakly-nonlinear seakeeping code known as CN-WSC (Weak-Scatterer) was developed. 

To quantify the non-linearities associated with highly cambered waves, a vertical cylinder was taken and it's motion response are calculated with CN-WSC (Weak-Scatterer) and similar calculations are done with linear code NEMOH. The motions calculated with both methods are compared and differences in the motion for highly cambered waves are illustrated as non-linearities were studied.

Nonlinear potential flow solver --- Weakly Scatterer --- Seakeeping of Ships and Offshore structures --- benchmarking --- CN_WSC --- fluid mechanics --- Ingénierie, informatique & technologie > Ingénierie mécanique

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The recent implementation of wear models in the nonlinear solver LS-Dyna allows its use in the numerical simulation of Rotor-Stator Interaction for the very first time. The new capabilities of the solver are studied and are compared to the ones of nonlinear solver Metafor, already capable of simulating Rotor-Stator Interaction. Specifically, the feasibility of such simulations is studied, the best suited contact algorithms are selected, and the performance is assessed. To that end, two LS-Dyna models are developed: a basic ONERA test bench whose purpose is to select the most adequate contact models, and a compressor blade rub test whose purpose is to ensure the correct application of wear on the finite elements model. The choice of contact model is constrained by the limited support of wear in the solver. Penalty methods for contact were considered, double-pass algorithms were rejected due to high variation of contact loads, leaving single-pass algorithms. The penalty computation was selected to ensure the least dependence on the mesh. Soft constraint formulation is not fully independent of the mesh, but offers nodal mass normalization. The specificity of wear computation in LS-Dyna is its application in post-processing only, preventing wear affecting the compressor blade dynamics. The simulation of Rotor-Stator Interaction in LS-Dyna thus necessitates extensive use of computation stops and restarts. A fully functional method to compute Rotor-Stator Interaction was successfully developed for LS-Dyna, with performance similar to Metafor.

metafor --- ls-dyna --- dyna --- interaction --- rotor --- stator --- compressor --- wear --- contact --- divergence --- vibration --- safran --- aero --- boosters --- booster --- engine --- low --- pressure --- onera --- model --- finite --- elements --- nonlinear --- explicit --- implicit --- time --- integration --- solver --- gap --- close --- open --- abradable --- material --- Ingénierie, informatique & technologie > Ingénierie aérospatiale

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Numerical methods are a specific form of mathematics that involve creating and use of algorithms to map out the mathematical core of a practical problem. Numerical methods naturally find application in all fields of engineering, physical sciences, life sciences, social sciences, medicine, business, and even arts. The common uses of numerical methods include approximation, simulation, and estimation, and there is almost no scientific field in which numerical methods do not find a use. Results communicated here include topics ranging from statistics (Detecting Extreme Values with Order Statistics in Samples from Continuous Distributions) and Statistical software packages (dCATCH—A Numerical Package for d-Variate near G-Optimal Tchakaloff Regression via Fast NNLS) to new approaches for numerical solutions (Exact Solutions to the Maxmin Problem max‖Ax‖ Subject to ‖Bx‖≤1; On q-Quasi-Newton’s Method for Unconstrained Multiobjective Optimization Problems; Convergence Analysis and Complex Geometry of an Efficient Derivative-Free Iterative Method; On Derivative Free Multiple-Root Finders with Optimal Fourth Order Convergence; Finite Integration Method with Shifted Chebyshev Polynomials for Solving Time-Fractional Burgers’ Equations) to the use of wavelets (Orhonormal Wavelet Bases on The 3D Ball Via Volume Preserving Map from the Regular Octahedron) and methods for visualization (A Simple Method for Network Visualization).

Research & information: general --- Mathematics & science --- Clenshaw–Curtis–Filon --- high oscillation --- singular integral equations --- boundary singularities --- local convergence --- nonlinear equations --- Banach space --- Fréchet-derivative --- finite integration method --- shifted Chebyshev polynomial --- Caputo fractional derivative --- Burgers’ equation --- coupled Burgers’ equation --- maxmin --- supporting vector --- matrix norm --- TMS coil --- optimal geolocation --- probability computing --- Monte Carlo simulation --- order statistics --- extreme values --- outliers --- multiobjective programming --- methods of quasi-Newton type --- Pareto optimality --- q-calculus --- rate of convergence --- wavelets on 3D ball --- uniform 3D grid --- volume preserving map --- Network --- graph drawing --- planar visualizations --- multiple root solvers --- composite method --- weight-function --- derivative-free method --- optimal convergence --- multivariate polynomial regression designs --- G-optimality --- D-optimality --- multiplicative algorithms --- G-efficiency --- Caratheodory-Tchakaloff discrete measure compression --- Non-Negative Least Squares --- accelerated Lawson-Hanson solver --- Clenshaw–Curtis–Filon --- high oscillation --- singular integral equations --- boundary singularities --- local convergence --- nonlinear equations --- Banach space --- Fréchet-derivative --- finite integration method --- shifted Chebyshev polynomial --- Caputo fractional derivative --- Burgers’ equation --- coupled Burgers’ equation --- maxmin --- supporting vector --- matrix norm --- TMS coil --- optimal geolocation --- probability computing --- Monte Carlo simulation --- order statistics --- extreme values --- outliers --- multiobjective programming --- methods of quasi-Newton type --- Pareto optimality --- q-calculus --- rate of convergence --- wavelets on 3D ball --- uniform 3D grid --- volume preserving map --- Network --- graph drawing --- planar visualizations --- multiple root solvers --- composite method --- weight-function --- derivative-free method --- optimal convergence --- multivariate polynomial regression designs --- G-optimality --- D-optimality --- multiplicative algorithms --- G-efficiency --- Caratheodory-Tchakaloff discrete measure compression --- Non-Negative Least Squares --- accelerated Lawson-Hanson solver