Three-dimensional CFD simulations with large displacement of the geometries using a connectivity-change moving mesh approach

This paper deals with three-dimensional (3D) numerical simulations involving 3D moving geometries with large displacements on unstructured meshes. Such simulations are of great value to industry, but remain very time-consuming. A robust moving mesh algorithm coupling an elasticity-like mesh deformation solution and mesh optimizations was proposed in previous works, which removes the need for global remeshing when performing large displacements. The optimizations, and in particular generalized edge/face swapping, preserve the initial quality of the mesh throughout the simulation. We propose to integrate an Arbitrary Lagrangian Eulerian compressible flow solver into this process to demonstrate its capabilities in a full CFD computation context. This solver relies on a local enforcement of the discrete geometric conservation law to preserve the order of accuracy of the time integration. The displacement of the geometries is either imposed, or driven by fluid–structure interaction (FSI). In the latter case, the six degrees of freedom approach for rigid bodies is considered. Finally, several 3D imposed-motion and FSI examples are given to validate the proposed approach, both in academic and industrial configurations

Towards goal-oriented mesh adaptation for fluid-structure interaction

In order to address fluid-structure interaction, we present an a priori analysis for an ALE compressible flow model. This analysis is the key for an anisotropic metricbased mesh adaptation

Turbulent Output-Based Anisotropic Adaptation

Controlling discretization error is a remaining challenge for computational fluid dynamics simulation. Grid adaptation is applied to reduce estimated discretization error in drag or pressure integral output functions. To enable application to high O(10(exp 7)) Reynolds number turbulent flows, a hybrid approach is utilized that freezes the near-wall boundary layer grids and adapts the grid away from the no slip boundaries. The hybrid approach is not applicable to problems with under resolved initial boundary layer grids, but is a powerful technique for problems with important off-body anisotropic features. Supersonic nozzle plume, turbulent flat plate, and shock-boundary layer interaction examples are presented with comparisons to experimental measurements of pressure and velocity. Adapted grids are produced that resolve off-body features in locations that are not known a priori

Simulation of all-scale atmospheric dynamics on unstructured meshes

The advance of massively parallel computing in the nineteen nineties and beyond encouraged finer grid intervals in numerical weather-prediction models. This has improved resolution of weather systems and enhanced the accuracy of forecasts, while setting the trend for development of unified all-scale atmospheric models. This paper first outlines the historical background to a wide range of numerical methods advanced in the process. Next, the trend is illustrated with a technical review of a versatile nonoscillatory forward-in-time finite-volume (NFTFV) approach, proven effective in simulations of atmospheric flows from small-scale dynamics to global circulations and climate. The outlined approach exploits the synergy of two specific ingredients: the MPDATA methods for the simulation of fluid flows based on the sign-preserving properties of upstream differencing; and the flexible finite-volume median-dual unstructured-mesh discretisation of the spatial differential operators comprising PDEs of atmospheric dynamics. The paper consolidates the concepts leading to a family of generalised nonhydrostatic NFTFV flow solvers that include soundproof PDEs of incompressible Boussinesq, anelastic and pseudo-incompressible systems, common in large-eddy simulation of small- and meso-scale dynamics, as well as all-scale compressible Euler equations. Such a framework naturally extends predictive skills of large-eddy simulation to the global atmosphere, providing a bottom-up alternative to the reverse approach pursued in the weather-prediction models. Theoretical considerations are substantiated by calculations attesting to the versatility and efficacy of the NFTFV approach. Some prospective developments are also discussed

A local anisotropic adaptive algorithm for the solution of low-Mach transient combustion problems

A novel numerical algorithm for the simulation of transient combustion problems at low Mach and moderately high Reynolds numbers is presented. These problems are often characterized by the existence of a large disparity of length and time scales, resulting in the development of directional flow features, such as slender jets, boundary layers, mixing layers, or flame fronts. This makes local anisotropic adaptive techniques quite advantageous computationally. In this work we propose a local anisotropic refinement algorithm using, for the spatial discretization, unstructured triangular elements in a finite element framework. For the time integration, the problem is formulated in the context of semi-Lagrangian schemes, introducing the semi-Lagrange-Galerkin (SLG) technique as a better alternative to the classical semi-Lagrangian (SL) interpolation. The good performance of the numerical algorithm is illustrated by solving a canonical laminar combustion problem: the flame/vortex interaction. First, a premixed methane-air flame/vortex interaction with simplified transport and chemistry description (Test I) is considered. Results are found to be in excellent agreement with those in the literature, proving the superior performance of the SLG scheme when compared with the classical SL technique, and the advantage of using anisotropic adaptation instead of uniform meshes or isotropic mesh refinement. As a more realistic example, we then conduct simulations of non-premixed hydrogenair flame/ vortex interactions (Test II) using a more complex combustion model which involves state-of-the-art transport and chemical kinetics. In addition to the analysis of the numerical features, this second example allows us to perform a satisfactory comparison with experimental visualizations taken from the literature.This research has been partially funded by projects MTM2010-18079 and CSD2010-00011 (CONSOLIDER-INGENIO) of the Spanish "Ministerio de Economía y Competitividad". The authors would like to thank Professors A. Liñán and R. Bermejo their priceless dedication and fruitful discussions, which have tremendously helped in our understanding of the physical phenomena involved in combustion problems, and in the development of the numerical methods suitable for integrating the equations of fluid mechanics

An anisotropic mesh adaptation method for the finite element solution of heterogeneous anisotropic diffusion problems

Heterogeneous anisotropic diffusion problems arise in the various areas of science and engineering including plasma physics, petroleum engineering, and image processing. Standard numerical methods can produce spurious oscillations when they are used to solve those problems. A common approach to avoid this difficulty is to design a proper numerical scheme and/or a proper mesh so that the numerical solution validates the discrete counterpart (DMP) of the maximum principle satisfied by the continuous solution. A well known mesh condition for the DMP satisfaction by the linear finite element solution of isotropic diffusion problems is the non-obtuse angle condition that requires the dihedral angles of mesh elements to be non-obtuse. In this paper, a generalization of the condition, the so-called anisotropic non-obtuse angle condition, is developed for the finite element solution of heterogeneous anisotropic diffusion problems. The new condition is essentially the same as the existing one except that the dihedral angles are now measured in a metric depending on the diffusion matrix of the underlying problem. Several variants of the new condition are obtained. Based on one of them, two metric tensors for use in anisotropic mesh generation are developed to account for DMP satisfaction and the combination of DMP satisfaction and mesh adaptivity. Numerical examples are given to demonstrate the features of the linear finite element method for anisotropic meshes generated with the metric tensors.Comment: 34 page