1,466 research outputs found
The role of forebody topology on aerodynamics and aeroacoustics characteristics of squareback vehicles using Computational Aeroacoustics (CAA)
This study investigates the influence of forebody configuration on aerodynamic noise generation and radiation in standard squareback vehicles, employing a hybrid computational aeroacoustics approach. Initially, a widely used standard squareback body is employed to establish grid-independent solutions and validate the applied methodology against previously published experimental data. Six distinct configurations are examined, consisting of three bodies with A-pillars and three without A-pillars. Throughout these configurations, the reference area, length, and height remain consistent, while systematic alterations to the forebody are implemented. The findings reveal that changes in the forebody design exert a substantial influence on both the overall aerodynamics and aeroacoustics performance of the vehicle. Notably, bodies without A-pillars exhibit a significant reduction in downforce compared to their A-pillar counterparts. For all configurations, the flow characteristics around the side-view mirror and the side window exhibit an asymmetrical horseshoe vortex with high-intensity pressure fluctuations, primarily within the confines of this vortex and the mirror wake. Side windows on bodies with A-pillars experience more pronounced pressure fluctuations, rendering these configurations distinctly impactful in terms of radiated noise. However, despite forebody-induced variations in pressure fluctuations impacting the side window and side-view mirror, the fundamental structure of the radiated noise remains relatively consistent. The noise pattern transitions from a cardioid-like shape to a monopole-like pattern as the probing distance from the vehicle increases
Molecular kinetic modelling of non-equilibrium transport of confined van der Waals fluids
A thermodynamically consistent kinetic model is proposed for the non-equilibrium transport of confined van der Waals fluids, where the long-range molecular attraction is considered by a mean-field term in the transport equation, and the transport coefficients are tuned to match the experimental data. The equation of state of the van der Waals fluids can be obtained from an appropriate choice of the pair correlation function. By contrast, the modified Enskog theory predicts non-physical negative transport coefficients near the critical temperature and may not be able to recover the Boltzmann equation in the dilute limit. In addition, the shear viscosity and thermal conductivity are predicted more accurately by taking gas molecular attraction into account, while the softened Enskog formula for hard-sphere molecules performs better in predicting the bulk viscosity. The present kinetic model agrees with the Boltzmann model in the dilute limit and with the Navier-Stokes equations in the continuum limit, indicating its capability in modelling dilute-to-dense and continuum-to-non-equilibrium flows. The new model is examined thoroughly and validated by comparing it with the molecular dynamics simulation results. In contrast to the previous studies, our simulation results reveal the importance of molecular attraction even for high temperatures, which holds the molecules to the bulk while the hard-sphere model significantly overestimates the density near the wall. Because the long-range molecular attraction is considered appropriately in the present model, the velocity slip and temperature jump at the surface for the more realistic van der Waals fluids can be predicted accurately
An Arbitrarily High Order and Asymptotic Preserving Kinetic Scheme in Compressible Fluid Dynamic
We present a class of arbitrarily high order fully explicit kinetic numerical methods in compressible fluid dynamics, both in time and space, which include the relaxation schemes by Jin and Xin. These methods can use the CFL number larger or equal to unity on regular Cartesian meshes for the multi-dimensional case. These kinetic models depend on a small parameter that can be seen as a “Knudsen” number. The method is asymptotic preserving in this Knudsen number. Also, the computational costs of the method are of the same order of a fully explicit scheme. This work is the extension of Abgrall et al. (2022) [3] to multi-dimensional systems. We have assessed our method on several problems for two-dimensional scalar problems and Euler equations and the scheme has proven to be robust and to achieve the theoretically predicted high order of accuracy on smooth solutions
Swarm Reinforcement Learning For Adaptive Mesh Refinement
The Finite Element Method, an important technique in engineering, is aided by
Adaptive Mesh Refinement (AMR), which dynamically refines mesh regions to allow
for a favorable trade-off between computational speed and simulation accuracy.
Classical methods for AMR depend on task-specific heuristics or expensive error
estimators, hindering their use for complex simulations. Recent learned AMR
methods tackle these problems, but so far scale only to simple toy examples. We
formulate AMR as a novel Adaptive Swarm Markov Decision Process in which a mesh
is modeled as a system of simple collaborating agents that may split into
multiple new agents. This framework allows for a spatial reward formulation
that simplifies the credit assignment problem, which we combine with Message
Passing Networks to propagate information between neighboring mesh elements. We
experimentally validate the effectiveness of our approach, Adaptive Swarm Mesh
Refinement (ASMR), showing that it learns reliable, scalable, and efficient
refinement strategies on a set of challenging problems. Our approach
significantly speeds up computation, achieving up to 30-fold improvement
compared to uniform refinements in complex simulations. Additionally, we
outperform learned baselines and achieve a refinement quality that is on par
with a traditional error-based AMR strategy without expensive oracle
information about the error signal.Comment: Version 1 of this paper is a preliminary workshop version that was
accepted as a workshop paper in the ICLR 2023 Workshop on Physics for Machine
Learnin
High order asymptotic preserving scheme for linear kinetic equations with diffusive scaling
In this work, high order asymptotic preserving schemes are constructed and
analysed for kinetic equations under a diffusive scaling. The framework enables
to consider different cases: the diffusion equation, the advection-diffusion
equation and the presence of inflow boundary conditions. Starting from the
micro-macro reformulation of the original kinetic equation, high order time
integrators are introduced. This class of numerical schemes enjoys the
Asymptotic Preserving (AP) property for arbitrary initial data and degenerates
when goes to zero into a high order scheme which is implicit for the
diffusion term, which makes it free from the usual diffusion stability
condition. The space discretization is also discussed and high order methods
are also proposed based on classical finite differences schemes. The Asymptotic
Preserving property is analysed and numerical results are presented to
illustrate the properties of the proposed schemes in different regimes
Asymptotic Preserving Discontinuous Galerkin Methods for a Linear Boltzmann Semiconductor Model
A key property of the linear Boltzmann semiconductor model is that as the
collision frequency tends to infinity, the phase space density
converges to an isotropic function , called the drift-diffusion
limit, where is a Maxwellian and the physical density satisfies a
second-order parabolic PDE known as the drift-diffusion equation. Numerical
approximations that mirror this property are said to be asymptotic preserving.
In this paper we build two discontinuous Galerkin methods to the semiconductor
model: one with the standard upwinding flux and the other with a
-scaled Lax-Friedrichs flux, where 1/ is the scale of
the collision frequency. We show that these schemes are uniformly stable in
and are asymptotic preserving. In particular, we discuss what
properties the discrete Maxwellian must satisfy in order for the schemes to
converge in to an accurate -approximation of the drift
diffusion limit. Discrete versions of the drift-diffusion equation and error
estimates in several norms with respect to and the spacial
resolution are also included
Data-driven deep-learning methods for the accelerated simulation of Eulerian fluid dynamics
Deep-learning (DL) methods for the fast inference of the temporal evolution of fluid-dynamics systems, based on the previous recognition of features underlying large sets of fluid-dynamics data, have been studied. Specifically, models based on convolution neural networks (CNNs) and graph neural networks (GNNs) were proposed and discussed.
A U-Net, a popular fully-convolutional architecture, was trained to infer wave dynamics on liquid surfaces surrounded by walls, given as input the system state at previous time-points. A term for penalising the error of the spatial derivatives was added to the loss function, which resulted in a suppression of spurious oscillations and a more accurate location and length of the
predicted wavefronts. This model proved to accurately generalise to complex wall geometries not seen during training.
As opposed to the image data-structures processed by CNNs, graphs offer higher freedom on how data is organised and processed. This motivated the use of graphs to represent the state of fluid-dynamic systems discretised by unstructured sets of nodes, and GNNs to process such graphs. Graphs have enabled more accurate representations of curvilinear geometries and higher resolution placement exclusively in areas where physics is more challenging to resolve. Two novel
GNN architectures were designed for fluid-dynamics inference: the MuS-GNN, a multi-scale GNN, and the REMuS-GNN, a rotation-equivariant multi-scale GNN. Both architectures work by repeatedly passing messages from each node to its nearest nodes in the graph. Additionally, lower-resolutions graphs, with a reduced number of nodes, are defined from the original graph,
and messages are also passed from finer to coarser graphs and vice-versa. The low-resolution graphs allowed for efficiently capturing physics encompassing a range of lengthscales.
Advection and fluid flow, modelled by the incompressible Navier-Stokes equations, were the two types of problems used to assess the proposed GNNs. Whereas a single-scale GNN was sufficient to achieve high generalisation accuracy in advection simulations, flow simulation highly benefited from an increasing number of low-resolution graphs. The generalisation and long-term accuracy of these simulations were further improved by the REMuS-GNN architecture, which
processes the system state independently of the orientation of the coordinate system thanks to a rotation-invariant representation and carefully designed components. To the best of the author’s knowledge, the REMuS-GNN architecture was the first rotation-equivariant and multi-scale GNN.
The simulations were accelerated between one (in a CPU) and three (in a GPU) orders of magnitude with respect to a CPU-based numerical solver. Additionally, the parallelisation of multi-scale GNNs resulted in a close-to-linear speedup with the number of CPU cores or GPUs.Open Acces
JAX-DIPS: Neural bootstrapping of finite discretization methods and application to elliptic problems with discontinuities
We present a scalable strategy for development of mesh-free hybrid
neuro-symbolic partial differential equation solvers based on existing
mesh-based numerical discretization methods. Particularly, this strategy can be
used to efficiently train neural network surrogate models of partial
differential equations by (i) leveraging the accuracy and convergence
properties of advanced numerical methods, solvers, and preconditioners, as well
as (ii) better scalability to higher order PDEs by strictly limiting
optimization to first order automatic differentiation. The presented neural
bootstrapping method (hereby dubbed NBM) is based on evaluation of the finite
discretization residuals of the PDE system obtained on implicit Cartesian cells
centered on a set of random collocation points with respect to trainable
parameters of the neural network. Importantly, the conservation laws and
symmetries present in the bootstrapped finite discretization equations inform
the neural network about solution regularities within local neighborhoods of
training points. We apply NBM to the important class of elliptic problems with
jump conditions across irregular interfaces in three spatial dimensions. We
show the method is convergent such that model accuracy improves by increasing
number of collocation points in the domain and predonditioning the residuals.
We show NBM is competitive in terms of memory and training speed with other
PINN-type frameworks. The algorithms presented here are implemented using
\texttt{JAX} in a software package named \texttt{JAX-DIPS}
(https://github.com/JAX-DIPS/JAX-DIPS), standing for differentiable interfacial
PDE solver. We open sourced \texttt{JAX-DIPS} to facilitate research into use
of differentiable algorithms for developing hybrid PDE solvers
Adaptive dynamical networks
It is a fundamental challenge to understand how the function of a network is related to its structural organization. Adaptive dynamical networks represent a broad class of systems that can change their connectivity over time depending on their dynamical state. The most important feature of such systems is that their function depends on their structure and vice versa. While the properties of static networks have been extensively investigated in the past, the study of adaptive networks is much more challenging. Moreover, adaptive dynamical networks are of tremendous importance for various application fields, in particular, for the models for neuronal synaptic plasticity, adaptive networks in chemical, epidemic, biological, transport, and social systems, to name a few. In this review, we provide a detailed description of adaptive dynamical networks, show their applications in various areas of research, highlight their dynamical features and describe the arising dynamical phenomena, and give an overview of the available mathematical methods developed for understanding adaptive dynamical networks
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