Ghina Jannoun

Adaptive time-step with anisotropic meshing for incompressible flows

This paper presents a method of combining anisotropic mesh adaptation and adaptive time-stepping for Computational Fluid Dynamics (CFD). First, we recall important features of the anisotropic meshing approach using a posteriori estimates relying on the length distribution tensor approach and the associated edge based error analysis. Then we extend the proposed technique to contain adaptive time advancing based on a newly developed time error estimator. The objective of this paper is to show that the combination of time and space anisotropic adaptations with highly stretched elements can be used to compute high Reynolds number flows within reasonable computational and storage costs. In particular, it will be shown that boundary layers, flow detachments and all vortices are well captured automatically by the mesh. The time-step is controlled by the interpolation error and preserves the accuracy of the mesh adapted solution. A Variational MultiScale (VMS) method is employed for the discretization of the Navier-Stokes equations. Numerical solutions of some benchmark problems demonstrate the applicability of the proposed space-time error estimator. An important feature of the proposed method is its conceptual and computational simplicity as it only requires from the user a number of nodes according to which the mesh and the time-steps are automatically adapted.

On the stabilized finite element method for steady convection-dominated problems with anisotropic mesh adaptation

In this work, we combine the use of the Streamline Upwind Petrov-Galerkin (SUPG) method with anisotropic mesh adaptation to obtain accurate solutions for steady convection-dominated problems. The anisotropic mesh adaptation framework is introduced in the context of a local mesh generation method based on a mesh topology modification and a minimal volume principle. A new route to get a metric field directly at the node of the mesh is highlighted using the length distribution tensor and an edge based error analysis. An a posteriori error estimation is applied to the stabilized finite element solution detecting automatically all sharp gradients, inner and boundary layers. The numerical examples show that the use of the anisotropic mesh adaptation algorithm allows the recovery of the global convergence order of the numerical schemes while producing accurate and oscillation free numerical solutions.

Modeling of heat transfer and turbulent flows inside industrial furnaces

Abstract In this work, we present a three-dimensional computational fluid-dynamics model for simulating complex industrial furnaces. The focus in set on the mathematical modeling of heated solids inside the furnace. A stabilized finite element method is used to numerically solve time-dependent, three-dimensional, conjugate heat transfer and turbulent fluid flows. In order to simulate the fluid–solid interaction, we propose the immersed volume method combined with a direct anisotropic mesh adaptation process enhancing the interface representation. The method demonstrates the capability of the model to simulate an unsteady heat transfer flow of natural convection, conduction and radiation in a complex 3D industrial furnace with the presence of six conducting steel solids.

Immersed NURBS for CFD Applications

We present a new immersed method for Computational Fluid Dynamics applications. It is based on the use of Non Uniform Rational B-Splines (NURBS). The distance function to an immersed solid is computed directly from its Computer Aided Design (CAD) description. This allows to bypass the generation of surface meshes and to obtain accurate levelset functions for complex geometries. Combined with a metric based anisotropic mesh adaptation and stabilized Finite Elements Method (FEM), it allows a novel, efficient and flexible approach to deal with a wide range of fluid structure interaction problems. The metric field is computed directly at the node of the mesh using the length distribution tensor and an edge based error analysis. Several 2D and 3D numerical examples will demonstrate the applicability of the proposed method.

Edge-Based Anisotropic Mesh Adaptation for CFD Applications

This paper presents an anisotropic mesh adaptation technique relying on the length distribution tensor approach and an edge based error estimator. It enables to calculate a stretching factor providing a new edge length distribution, its associated tensor and the corresponding metric. The optimal stretching factor field is obtained by solving an optimization problem under the constraint of a fixed number of nodes. It accounts for different component fields in a single metric. With such features, the method proves to be simple and efficient and can be easily applied to a large panel of challenging CFD applications.