Time-stepping and Krylov methods for large-scale instability problems

With the ever increasing computational power available and the development of high-performances computing, investigating the properties of realistic very large-scale nonlinear dynamical systems has been become reachable. It must be noted however that the memory capabilities of computers increase at a slower rate than their computational capabilities. Consequently, the traditional matrix-forming approaches wherein the Jacobian matrix of the system considered is explicitly assembled become rapidly intractable. Over the past two decades, so-called matrix-free approaches have emerged as an efficient alternative. The aim of this chapter is thus to provide an overview of well-grounded matrix-free methods for fixed points computations and linear stability analyses of very large-scale nonlinear dynamical systems.Comment: To appear in "Computational Modeling of Bifurcations and Instabilities in Fluid Mechanics", eds. A. Gelfgat, Springe

Closed-loop optimal control for shear flows using reinforcement learning

International audienc

Machine Learning model for gas-liquid interface reconstruction in CFD numerical simulations

The volume of fluid (VoF) method is widely used in multi-phase flow simulations to track and locate the interface between two immiscible fluids. A major bottleneck of the VoF method is the interface reconstruction step due to its high computational cost and low accuracy on unstructured grids. We propose a machine learning enhanced VoF method based on Graph Neural Networks (GNN) to accelerate the interface reconstruction on general unstructured meshes. We first develop a methodology to generate a synthetic dataset based on paraboloid surfaces discretized on unstructured meshes. We then train a GNN based model and perform generalization tests. Our results demonstrate the efficiency of a GNN based approach for interface reconstruction in multi-phase flow simulations in the industrial context.Comment: 12 pages, fullpaper of ECCOMAS202

Alice in "Bio-land": engineering challenges in the world of Life-Sciences

Alice is an engineer who ventures into the research world of life sciences. To her eyes, life sciences researchers work backwards compared to what happens in her world. It appears that their research methodology has a number of issues that may limit its potential. Nevertheless, she also becomes aware that a different set of problems arises if her own traditional top-down engineering approach is applied to life sciences. This article discusses how the authors see the role of systems and computational biology as a fundamental methodological "middle-ground" between these two (apparently) distant worlds. This article is part of a special issue on life sciences computing

Global stability analysis of 3D micro-combustion model

We report on the linear stability of micro-combustion in pipe, where two instabilities manifest at high and low flow-rates. The combustion of a stoichiometric methane/air premixed mixture has been numerically investigated within a 3D reduced model. This model reproduces decently the flame dynamics in the range of speed between 5–100 cm/s. The flame position, the stability thresholds of the Flame with Repetitive Extinction and Ignition (FREI) and the flame shape are in accordance with the experiments. Furthermore, an analysis of the integral values of all mechanisms involved in the flame evolution has been carried out near the two stability thresholds. The phase shift between the reaction term and the radial diffusion has been identified as the source of instability in both cases. The global behavior has been then investigated with a linear stability analysis. The 2D and 3D temperature and concentration perturbations have been found by solving the eigenvalue problem obtained by linearizing the model around the basic state. Only one unstable axisymmetric mode has been found. This is in agreement with the direct numerical simulation of the model

DS-GPS : A Deep Statistical Graph Poisson Solver (for faster CFD simulations)

This paper proposes a novel Machine Learning-based approach to solve a Poisson problem with mixed boundary conditions. Leveraging Graph Neural Networks, we develop a model able to process unstructured grids with the advantage of enforcing boundary conditions by design. By directly minimizing the residual of the Poisson equation, the model attempts to learn the physics of the problem without the need for exact solutions, in contrast to most previous data-driven processes where the distance with the available solutions is minimized

Complementary Deep - Reduced Order Model

International audienc

A synthetic forcing to trigger laminar-turbulent transition in parallel wall bounded flows via receptivity

Research on laminar-turbulent transition of wall-bounded parallel flows has usually focused on controlled scenarios where transition is triggered by perturbations having simple shapes and spectra. These disturbances strongly differ from the environmental noise usually present in experimental setups or industrial applications, where uncontrolled transition is usually observed. In this paper a new method is proposed to trigger uncontrolled transition to turbulence in wall-bounded parallel flows exploiting the receptivity of the flow to a volume forcing. Using some concepts provided by linear stability and sensitivity analysis, such as the resolvent, we propose a method for constructing a volume forcing capable of inducing stochastic velocity perturbations with a prescribed energy level, eventually leading to laminar-turbulent transition as a response of the system to external noise. The method has been tested in a channel flow configuration, using direct numerical simulations of the fully nonlinear Navier-Stokes equations in the presence of the volume forcing constructed on the basis of optimal forcing functions. Subcritical transition to turbulence induced by the prescribed forcing has been investigated and compared to other transition scenarios, where deterministic perturbations are imposed for obtaining a turbulent flow. Finally, the fully developed turbulent flows induced by the proposed method has been analysed, showing that low-order statistics and energy balance equations are practically unaffected by the continuous synthetic forcing

Time-Stepping and Krylov Method for large scale instability problems

With the ever increasing computational power available and the development of high-performances computing, investigating the properties of realistic very large-scale nonlinear dynamical systems has become reachable. It must be noted however that the memory capabilities of computers increase at a slower rate than their computational capabilities. Consequently, the traditional matrix-forming approaches wherein the Jacobian matrix of the system considered is explicitly assembled become rapidly intractable. Over the past two decades, so-called matrix-free approaches have emerged as an efficient alternative. The aim of this chapter is thus to provide an overview of well-grounded matrix-free methods for fixed points computations and linear stability analyses of very large-scale nonlinear dynamical systems