Learning the Latent dynamics of Fluid flows from High-Fidelity Numerical Simulations using Parsimonious Diffusion Maps [PDF]
The Physics of FluidsWe use parsimonious diffusion maps (PDMs) to discover the latent dynamics of high-fidelity Navier–Stokes simulations with a focus on the two-dimensional (2D) fluidic pinball problem.
Alessandro Della Pia +3 more
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Accelerated Optimization in the PDE Framework: Formulations for the Manifold of Diffeomorphisms [PDF]
SIAM Journal of Imaging Sciences, 2018 We consider the problem of optimization of cost functionals on the infinite-dimensional manifold of diffeomorphisms. We present a new class of optimization methods, valid for any optimization problem setup on the space of diffeomorphisms by generalizing ...
G. Sundaramoorthi, A. Yezzi
semanticscholar +1 more source
RHEA: an open-source Reproducible Hybrid-architecture flow solver Engineered for Academia
Journal of Open Source Software, 2023 The study of complex multiscale flows (Groen et al., 2014), like for example the motion of small-scale turbulent eddies over large aerodynamic structures (Jofre & Doostan, 2022), microconfined high-pressure supercritical fluids for enhanced energy ...
L. Jofre, A. Abdellatif, G. Oyarzun
semanticscholar +1 more source
Non-Perturbative Hydrodynamic Limits [PDF]
, 2013 We introduce non-perturbative analytical techniques for the derivation of the hydrodynamic manifolds from kinetic equations. The new approach is analogous to the Schwinger-Dyson equation of quantum field theories, and its derivation is demonstrated with the construction of the exact diffusion manifold for a model kinetic equation. The novel approach is
arxiv +1 more source
Scientific Reports, 2020 One potential pathway to find an ultimate rule governing our universe is to hunt for a connection among the fundamental equations in physics. Recently, Ren et al.
X. Zhai, Changyu Huang, Gang Ren
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Method for solving hyperbolic systems with initial data on non-characteristic manifolds with applications to the shallow water wave equations [PDF]
, 2019 We are concerned with hyperbolic systems of order-one linear PDEs originated on non-characteristic manifolds. We put forward a simple but effective method of transforming such initial conditions to standard initial conditions (i.e. when the solution is specified at an initial moment of time). We then show how our method applies in fluid mechanics. More
arxiv +1 more source
Random organization and non-equilibrium hyperuniform fluids on a sphere [PDF]
arXiv, 2023 Random organizing hyperuniform fluid induced by reciprocal activation is a non-equilibrium fluid with vanishing density fluctuations at large length scales like crystals. Here we extend this new state of matter to a closed manifold, namely a spherical surface.
arxiv
Feature Surfaces in Symmetric Tensor Fields Based on Eigenvalue Manifold
IEEE Transactions on Visualization and Computer Graphics, 2016 Three-dimensional symmetric tensor fields have a wide range of applications in solid and fluid mechanics. Recent advances in the (topological) analysis of 3D symmetric tensor fields focus on degenerate tensors which form curves.
Jonathan Palacios +7 more
semanticscholar +1 more source
A simple model of the derivation of fluid mechanics from the Boltzmann equation
, 1969 Q is independent of / > 0 and maps a f unction ƒ belonging to a certain manifold M into a tangent vector Q [f] based at ƒ, so that the flow defined by (1) is a flow on M.
H. McKean
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Extended Hamilton-Jacobi theory, contact manifolds and integrability by quadratures [PDF]
, 2019 A Hamilton-Jacobi theory for general dynamical systems, defined on fibered phase spaces, has been recently developed. In this paper we shall apply such a theory to contact Hamiltonian systems, as those appearing in thermodynamics and on geodesic flows in fluid mechanics. We first study the partial and complete solutions of the Hamilton-Jacobi Equation (
arxiv +1 more source