Multi-Dimensional, Compressible Viscous Flow on a Moving Voronoi Mesh

Numerous formulations of finite volume schemes for the Euler and Navier-Stokes equations exist, but in the majority of cases they have been developed for structured and stationary meshes. In many applications, more flexible mesh geometries that can dynamically adjust to the problem at hand and move with the flow in a (quasi) Lagrangian fashion would, however, be highly desirable, as this can allow a significant reduction of advection errors and an accurate realization of curved and moving boundary conditions. Here we describe a novel formulation of viscous continuum hydrodynamics that solves the equations of motion on a Voronoi mesh created by a set of mesh-generating points. The points can move in an arbitrary manner, but the most natural motion is that given by the fluid velocity itself, such that the mesh dynamically adjusts to the flow. Owing to the mathematical properties of the Voronoi tessellation, pathological mesh-twisting effects are avoided. Our implementation considers the full Navier-Stokes equations and has been realized in the AREPO code both in 2D and 3D. We propose a new approach to compute accurate viscous fluxes for a dynamic Voronoi mesh, and use this to formulate a finite volume solver of the Navier-Stokes equations. Through a number of test problems, including circular Couette flow and flow past a cylindrical obstacle, we show that our new scheme combines good accuracy with geometric flexibility, and hence promises to be competitive with other highly refined Eulerian methods. This will in particular allow astrophysical applications of the AREPO code where physical viscosity is important, such as in the hot plasma in galaxy clusters, or for viscous accretion disk models.Comment: 26 pages, 21 figures. Submitted to MNRA

A Nitsche-based cut finite element method for a fluid--structure interaction problem

We present a new composite mesh finite element method for fluid--structure interaction problems. The method is based on surrounding the structure by a boundary-fitted fluid mesh which is embedded into a fixed background fluid mesh. The embedding allows for an arbitrary overlap of the fluid meshes. The coupling between the embedded and background fluid meshes is enforced using a stabilized Nitsche formulation which allows us to establish stability and optimal order \emph{a priori} error estimates, see~\cite{MassingLarsonLoggEtAl2013}. We consider here a steady state fluid--structure interaction problem where a hyperelastic structure interacts with a viscous fluid modeled by the Stokes equations. We evaluate an iterative solution procedure based on splitting and present three-dimensional numerical examples.Comment: Revised version, 18 pages, 7 figures. Accepted for publication in CAMCo

Computational Engineering

The focus of this Computational Engineering Workshop was on the mathematical foundation of state-of-the-art and emerging finite element methods in engineering analysis. The 52 participants included mathematicians and engineers with shared interest on discontinuous Galerkin or Petrov-Galerkin methods and other generalized nonconforming or mixed finite element methods

Hybridisable Discontinuous Galerkin Formulation of Compressible Flows

This work presents a review of high-order hybridisable discontinuous Galerkin (HDG) methods in the context of compressible flows. Moreover, an original unified framework for the derivation of Riemann solvers in hybridised formulations is proposed. This framework includes, for the first time in an HDG context, the HLL and HLLEM Riemann solvers as well as the traditional Lax-Friedrichs and Roe solvers. HLL-type Riemann solvers demonstrate their superiority with respect to Roe in supersonic cases due to their positivity preserving properties. In addition, HLLEM specifically outstands in the approximation of boundary layers because of its shear preservation, which confers it an increased accuracy with respect to HLL and Lax-Friedrichs. A comprehensive set of relevant numerical benchmarks of viscous and inviscid compressible flows is presented. The test cases are used to evaluate the competitiveness of the resulting high-order HDG scheme with the aforementioned Riemann solvers and equipped with a shock treatment technique based on artificial viscosity.Comment: 60 pages, 31 figures. arXiv admin note: substantial text overlap with arXiv:1912.0004

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

Developing A Physics-informed Deep Learning Paradigm for Traffic State Estimation

The traffic delay due to congestion cost the U.S. economy $ 81 billion in 2022, and on average, each worker lost 97 hours each year during commute due to longer wait time. Traffic management and control strategies that serve as a potent solution to the congestion problem require accurate information on prevailing traffic conditions. However, due to the cost of sensor installation and maintenance, associated sensor noise, and outages, the key traffic metrics are often observed partially, making the task of estimating traffic states (TSE) critical. The challenge of TSE lies in the sparsity of observed traffic data and the noise present in the measurements. The central research premise of this dissertation is whether and how the fundamental principles of traffic flow theory could be harnessed to augment machine learning in estimating traffic conditions. This dissertation develops a physics-informed deep learning (PIDL) paradigm for traffic state estimation. The developed PIDL framework equips a deep learning neural network with the strength of the governing physical laws of the traffic flow to better estimate traffic conditions based on partial and limited sensing measurements. First, this research develops a PIDL framework for TSE with the continuity equation Lighthill-Whitham-Richards (LWR) conservation law - a partial differential equation (PDE). The developed PIDL framework is illustrated with multiple fundamental diagrams capturing the relationship between traffic state variables. The framework is expanded to incorporate a more practical, discretized traffic flow model - the cell transmission model (CTM). Case studies are performed to validate the proposed PIDL paradigm by reconstructing the velocity and density fields using both synthetic and realistic traffic datasets, such as the next-generation simulation (NGSIM). The case studies mimic a multitude of application scenarios with pragmatic considerations such as sensor placement, coverage area, data loss, and the penetration rate of connected autonomous vehicles (CAVs). The study results indicate that the proposed PIDL approach brings exceedingly superior performance in state estimation tasks with a lower training data requirement compared to the benchmark deep learning (DL) method. Next, the dissertation continues with an investigation of the empirical evidence which points to the limitation of PIDL architectures with certain types of PDEs. It presents the challenges in training PIDL architecture by contrasting PIDL performances in learning the first-order scalar hyperbolic LWR conservation law and its second-order parabolic counterpart. The outcome indicates that PIDL experiences challenges in incorporating the hyperbolic LWR equation due to the non-smoothness of its solution. On the other hand, the PIDL architecture with the parabolic version of the PDE, augmented with the diffusion term, leads to the successful reassembly of the density field even with the shockwaves present. Thereafter, the implication of PIDL limitations for traffic state estimation and prediction is commented upon, and readers\u27 attention is directed to potential mitigation strategies. Lastly, a PIDL framework with nonlocal traffic flow physics, capturing the driver reaction to the downstream traffic conditions, is proposed. In summary, this dissertation showcases the vast capability of the developed physics-informed deep learning paradigm for traffic state estimation in terms of efficiently utilizing meager observation for precise reconstruction of the data field. Moreover, it contemplates the practical ramification of PIDL for TSE with the hyperbolic flow conservation law and explores the remedy with sampling strategies of training instances and adding the diffusion term. Ultimately, it paints the picture of potent PIDL applications in TSE with nonlocal physics and suggests future research directions in PIDL for traffic state predictions

Applied Aerodynamics

Aerodynamics, from a modern point of view, is a branch of physics that study physical laws and their applications, regarding the displacement of a body into a fluid, such concept could be applied to any body moving in a fluid at rest or any fluid moving around a body at rest. This Book covers a small part of the numerous cases of stationary and non stationary aerodynamics; wave generation and propagation; wind energy; flow control techniques and, also, sports aerodynamics. It's not an undergraduate text but is thought to be useful for those teachers and/or researchers which work in the several branches of applied aerodynamics and/or applied fluid dynamics, from experiments procedures to computational methods

An open-source hybrid CFD-DSMC solver for high-speed flows

A new open-source hybrid CFD-DSMC solver, called hyperFoam, has been implemented within the OpenFOAM framework. The capabilities of the OpenFOAM computational fluid dynamics (CFD) solver rhoCentralFoam for supersonic simulations were analysed, showing good agreement with state-of-the-art solvers such as DLR-Tau, and then enhanced, by incorporating the local time stepping (LTS) and adaptive mesh refinement (AMR) techniques. These aspects would later be used for the development of the hypersonic CFD code hy2Foam.;hyperFoam relies on hy2Foam and the direct direct simulation Monte Carlo (DSMC) code dsmcFoam to be able to resolve the flow physics while under the slip-transition regime. Using a mixture of Boyd's Gradient-Length-Local Knudsen number and a generalised modified Chapman-Enskog parameter, hyperFoam is capable of identifying the continuum and rarefied zones within the computational domain and solve each with its respective CFD or DSMC solver.;hyperFoam has been used to simulate several Couette flow with heat transfer test cases, each of different complexity. Good agreement was shown between the DSMC and hybrid results for these simulations. The hybrid code was then used to analyse a hypersonic cylinder. Reasonably similar accuracy was found between the DSMC and hybrid results for vibrationless N2 and N2-O2. However, forO2 important discrepancies were found due to an inconsistency between continuum and rarefied vibrational modelling.A new open-source hybrid CFD-DSMC solver, called hyperFoam, has been implemented within the OpenFOAM framework. The capabilities of the OpenFOAM computational fluid dynamics (CFD) solver rhoCentralFoam for supersonic simulations were analysed, showing good agreement with state-of-the-art solvers such as DLR-Tau, and then enhanced, by incorporating the local time stepping (LTS) and adaptive mesh refinement (AMR) techniques. These aspects would later be used for the development of the hypersonic CFD code hy2Foam.;hyperFoam relies on hy2Foam and the direct direct simulation Monte Carlo (DSMC) code dsmcFoam to be able to resolve the flow physics while under the slip-transition regime. Using a mixture of Boyd's Gradient-Length-Local Knudsen number and a generalised modified Chapman-Enskog parameter, hyperFoam is capable of identifying the continuum and rarefied zones within the computational domain and solve each with its respective CFD or DSMC solver.;hyperFoam has been used to simulate several Couette flow with heat transfer test cases, each of different complexity. Good agreement was shown between the DSMC and hybrid results for these simulations. The hybrid code was then used to analyse a hypersonic cylinder. Reasonably similar accuracy was found between the DSMC and hybrid results for vibrationless N2 and N2-O2. However, forO2 important discrepancies were found due to an inconsistency between continuum and rarefied vibrational modelling