Viscous Shock Capturing in a Time-Explicit Discontinuous Galerkin Method

We present a novel, cell-local shock detector for use with discontinuous Galerkin (DG) methods. The output of this detector is a reliably scaled, element-wise smoothness estimate which is suited as a control input to a shock capture mechanism. Using an artificial viscosity in the latter role, we obtain a DG scheme for the numerical solution of nonlinear systems of conservation laws. Building on work by Persson and Peraire, we thoroughly justify the detector's design and analyze its performance on a number of benchmark problems. We further explain the scaling and smoothing steps necessary to turn the output of the detector into a local, artificial viscosity. We close by providing an extensive array of numerical tests of the detector in use.Comment: 26 pages, 21 figure

HDG-NEFEM with Degree Adaptivity for Stokes Flows

This paper presents the first degree adaptive procedure able to directly use the geometry given by a CAD model. The technique uses a hybridisable discontinuous Galerkin discretisation combined with a NURBS-enhanced rationale, completely removing the uncertainty induced by a polynomial approximation of curved boundaries that is common within an isoparametric approach. The technique is compared against two strategies to perform degree adaptivity currently in use. This paper demonstrates, for the first time, that the most extended technique for degree adaptivity can easily lead to a non-reliable error estimator if no communication with CAD software is introduced whereas if the communication with the CAD is done, it results in a substantial computing time. The proposed technique encapsulates the CAD model in the simulation and is able to produce reliable error estimators irrespectively of the initial mesh used to start the adaptive process. Several numerical examples confirm the findings and demonstrate the superiority of the proposed technique. The paper also proposes a novel idea to test the implementation of high-order solvers where different degrees of approximation are used in different elements

Workshop on numerical and physical modelling in multiphase flowsa cross-fertilization approach

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CFD simulations of large-scale reorganizations in PWR rod bundle flows

International audienceA coolant flow is used in Pressurized-Water Reactors (PWR) cores to extract the heat generated by nuclear reactions. Its temperature must be as homogeneous as possible in order to avoid a localized boiling, which would deteriorate the behaviour of the reactor. This flow is injected in the interstices of rod bundles, which namely are arrays of cylinders held together by support grids. While the initial velocity flow field is mostly aligned with the cylinder axes, mixing vanes are placed on the support grids in order to vastly increase inter-channel velocities and thus improve the overall thermal mixing. As depicted inthe sketch in figure 1, large-scale structures are generated in cross-section planes orthogonal to the rod axes in the wake of the mixing grid, and their layout as well as their evolution downstream of the grids have a large impact on the flow boiling margin. A thorough investigation of these coolant flow large-scale structures thus constitutes a key element of PWR safetyanalyses.Both experiments and Computational Fluid Dynamics (CFD) simulations have been used regularly in the last decades to investigate these large-scale flow structures. Notable experiments include the AGATE facility operated at the CEA Grenoble [3] as well as the OECD/NEA-KAERI benchmark test [2]. An example of a large-scale cross-flow pattern observed in the 5x5 rod bundle flow of the AGATE facility is shown in figure 2. Interestingly, this pattern spontaneously reorganized itself in thefar wake of the mixing grid so as to rotate from a mostly 45 and#9702; angle to a 135 and#9702; one. This phenomenon can be related to earlier observations of a pattern change in the wake of a mixing grid by Shen et al. [4], therein dubbed as a velocity inversion. In addition to the results obtained by Bieder et al. [1], CFD simulations of rod bundle flows based on a Large-Eddy Simulation (LES) sub-grid scale model have been performed, both in a reduced 3x3 rod bundle and in a 5x5 one, with the aim of reproducing such experimental large-scale reorganizations of the cross-section flow.Furthermore, a method of coupling between the 3D axial coordinate and the time variable through the Taylor frozen turbulence hypothesis is being used to advance a physical explanation to the large-scale reorganization phenomena. 2DDirect Numerical Simulations (DNS) have thus been performed in rod bundle cross-section geometries from an initial condition based on a 2D slice of the 3D flow in the immediate wake of the grid in LES simulations. A comparison between the evolution over time of the 2D simulated flow in a cross-section geometry and the axial evolution of a steady 3D flow cross-section is then carried out, revealing interesting parallels

Minimum enstrophy states and bifurcations in 2D Euler flows within an annular domain

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Minimum enstrophy states and bifurcations in 2D Euler flows around a central obstacle

International audienceRod bundle flows inside nuclear cores of pressurized water reactors (PWR) are mainly aligned with the direction parallel to the rods. In the planes orthonormal to this direction, some secondary flows occur and play an important role in the thermal mixing characteristics. These flows exhibit spontaneous reorganisations that seem comparable to the phase transitions observed between meta-stable states of the Northern Hemisphere atmosphere (Corvellec [5]). In order to put forward an explanation of this phenomenon, equilibrium states of the 2D Euler equations are computed from a variational problem consisting in minimizing the total enstrophy function (related to entropy) while conserving kinetic energy and circulation inside the domain. This method can be related to MRS theory ([7, 9]). We obtain the most probable equilibrium states depending on control parameters and geometry here restricted to the representative configuration of a ring-shaped domain. We have solved numerically this problem and obtained the different caloric curves and phase diagrams. A bifurcation between 1-eddy solution (’zonal’) and 2-eddy solution (’blocked’) has been identified confirming the existence of meta-stable states in flows containing a central obstacle

Minimum enstrophy principle for two-dimensional inviscid flows around obstacles

International audienceLarge-scale coherent structures emerging in two-dimensional flows can be predicted from statistical physics inspired methods consisting in minimizing the global enstrophy while conserving the total energy and circulation in the Euler equations. In many situations, solid obstacles inside the domain may also constrain the flow and have to be accounted for via a minimum enstrophy principle. In this work, we detail this extended variational formulation and its numerical resolution. It is shown from applications to complex geometries containing multiple circular obstacles that the number of solutions is enhanced, allowing many possibilities of bifurcations for the large-scale structures. These phase change phenomena can explain the downstream recombinations of the flow in rod-bundle experiments and simulations