The Experts below are selected from a list of 64344 Experts worldwide ranked by ideXlab platform
Andrea Manzoni - One of the best experts on this subject based on the ideXlab platform.
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an efficient computational framework for reduced basis approximation and a posteriori Error estimation of parametrized navier stokes flows
Mathematical Modelling and Numerical Analysis, 2014Co-Authors: Andrea ManzoniAbstract:We present the current Reduced Basis framework for the efficient numerical approximation of parametrized steady Navier-Stokes equations. We have extended the existing setting developed in the last decade (see e.g. [S. Deparis, SIAM J. Numer. Anal. 46 (2008) 2039-2067; A. Quarteroni and G. Rozza, Numer. Methods Partial Differ. Equ. 23 (2007) 923-948; K. Veroy and A.T. Patera, Int. J. Numer. Methods Fluids 47 (2005) 773-788]) to more general affine and nonaffine parametrizations (such as volume-based techniques), to a simultaneous velocity-Pressure Error estimates and to a fully decoupled Offline/Online procedure in order to speedup the solution of the reduced-order problem. This is particularly suitable for real-time and many-query contexts, which are both part of our final goal. Furthermore, we present an efficient numerical implementation for treating nonlinear advection terms in a convenient way. A residual-based a posteriori Error estimation with respect to a truth, full-order Finite Element approximation is provided for joint Pressure/velocity Errors, according to the Brezzi-Rappaz-Raviart stability theory. To do this, we take advantage of an extension of the Successive Constraint Method for the estimation of stability factors and of a suitable fixed-point algorithm for the approximation of Sobolev embedding constants. Finally, we present some numerical test cases, in order to show both the approximation properties and the computational efficiency of the derived framework. © 2014 EDP Sciences, SMAI .
Erik Burman - One of the best experts on this subject based on the ideXlab platform.
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well posedness and h div conforming finite element approximation of a linearised model for inviscid incompressible flow
arXiv: Numerical Analysis, 2019Co-Authors: Gabriel R Barrenechea, Erik Burman, Johnny GuzmanAbstract:We consider a linearised model of incompressible inviscid flow. Using a regularisation based on the Hodge Laplacian we prove existence and uniqueness of weak solutions for smooth domains. The model problem is then discretised using H(div)-conforming finite element methods, for which we prove Error estimates for the velocity approximation in the $L^2$-norm of order $O(h^{k+\frac12})$. We also prove Error estimates for the Pressure Error in the $L^2$-norm.
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Fractional-step methods and finite elements with symmetric stabilization for the transient Oseen problem
ESAIM: Mathematical Modelling and Numerical Analysis, 2017Co-Authors: Erik Burman, Alexandre Ern, Miguel Angel FernándezAbstract:This paper deals with the spatial and time discretization of the transient Oseen equations. Finite elements with symmetric stabilization in space are combined with several time-stepping schemes (monolithic and fractional-step). Quasi-optimal (in space) and optimal (in time) Error estimates are established for smooth solutions in all flow regimes. We first analyze monolithic time discretizations using the Backward Differentation Formulas of order 1 and 2 (BDF1 and BDF2). We derive a new estimate on the time-average of the Pressure Error featuring the same robustness with respect to the Reynolds number as the velocity estimate. Then, we analyze fractional-step Pressure-projection methods using BDF1. The stabilization of velocities and Pressures can be treated either implicitly or explicitly. Numerical results illustrate the main theoretical findings.
Joh M Toole - One of the best experts on this subject based on the ideXlab platform.
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implementation of a titanium strain gauge Pressure transducer for ctd applications
Deep Sea Research Part I: Oceanographic Research Papers, 1993Co-Authors: Robe C Millard, Gary Ond, Joh M TooleAbstract:Abstract The installation and operational characteristics of a titanium element strain gauge Pressure sensor in conductivity-temperature-depth (CTD) instruments is described. The behavior of the sensor is examined in both steady state and transient conditions, the latter consisting of thermal shocks achieved in laboratory plunge tests. The titanium Pressure sensor has superior linearity and reduced hysteresis as compared with strain gauges which utilize a stainless steel lement. However, significant transient Pressure Errors are noted for certain gauge installations. A model of the Pressure sensor's transient is developed from heat transfer theory, which is solved for an idealization of the Mark III CTD configuration. This, in turn, motivates a numerical procedure for reducing the thermally-induced static and transient Pressure Error in the titanium strain gauge Pressure sensor data, and an installation procedure that thermally isolates the gauge. Residual Pressure Error in calibrated data from the titanium strain gauge is an acceptably fraction of a decibar.
J G M Kuerten - One of the best experts on this subject based on the ideXlab platform.
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analysis of the numerical dissipation rate of different runge kutta and velocity interpolation methods in an unstructured collocated finite volume method in openfoam
Computer Physics Communications, 2020Co-Authors: E M J Komen, E M A Frederix, T H J Coppen, Valerio Dalessandro, J G M KuertenAbstract:Abstract The approach used for computation of the convecting face fluxes and the cell face velocities results in different underlying numerical algorithms in finite volume collocated grid solvers for the incompressible Navier–Stokes equations. In this study, the effect of the following five numerical algorithms on the numerical dissipation rate and on the temporal consistency of a selection of Runge–Kutta schemes is analysed: (1) the original algorithm of Rhie and Chow (1983), (2) the standard OpenFOAM method, (3) the algorithm used by Vuorinen et al. (2014), (4) the Kazemi-Kamyab et al. (2015) method, and (5) the D’Alessandro et al. (2018) approach. The last three algorithms refer to recent implementations of low dissipative numerical methods in OpenFOAM®. No new computational methods are presented in this paper. Instead, the main scientific contributions of this paper are: (1) the systematic assessment of the effect of the considered five numerical approaches on the numerical dissipation rate and on the temporal consistency of the selected Runge–Kutta schemes within one unified framework which we have implemented in OpenFOAM, and (2) the application of the method of Komen et al. (2017) in order to quantify the numerical dissipation rate introduced by three of the five numerical methods in quasi-DNS and under-resolved DNS of fully-developed turbulent channel flow. In addition, we explain the effects of the introduced numerical dissipation on the observed trends in the corresponding numerical results. As one of the major conclusions, we found that the Pressure Error, which is introduced due to the application of a compact stencil in the Pressure Poisson equation , causes a reduction of the order of accuracy of the temporal schemes for the test cases in this study. Consequently, application of higher order temporal schemes is not useful from an accuracy point of view, and the application of a second order temporal scheme appears to be sufficient.
Michael T Vaughan - One of the best experts on this subject based on the ideXlab platform.
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deviatoric stress measurements at high Pressure and temperature
High‐pressure science and technology, 2008Co-Authors: Donald J Weidner, Yanbin Wang, Yue Meng, Michael T VaughanAbstract:X‐ray diffraction of samples at high Pressure and temperature provide information not only on the unit cell dimensions, but also on the deviatoric stress in the sample. Macroscopic stress is defined by the relative strains inferred from the different diffraction lines in an elastically anisotropic sample. Cubic materials are particularly useful for determining the macroscopic stress since, under hydrostatic stress, all diffraction lines will display the same strain. Measurements on samples with a superconducting wiggler synchrotron source in a large volume high Pressure apparatus (SAM85), capable of generating 15 GPa Pressure and 1500 °C temperature have been inverted for deviatoric stress as a function of Pressure and temperature for NaCl and gold. Deviatoric stress determinations provide information on the yield strength of the sample. In addition, the presence of deviatoric stress will significantly affect the Pressure calibration based on a diffraction standard. Measurements in a diamond anvil cell at room temperature with a neon Pressure medium demonstrate that a systematic Pressure Error of up to 2 GPa occurs at about 30 GPa using gold as the Pressure standard. This Error is significantly reduced by heating to only 100 °C. Microscopic deviatoric stress is inferred from peak broadening. Strength measurements have been made on diamond at temperatures up to 1500 °C at 10 GPa in SAM85 from this type of data.
