Related papers: Machine learning of hidden variables in multiscale…
This work explores the capability of simulating complex fluid flows by directly solving the Boltzmann equation. Due to the high-dimensionality of the governing equation, the substantial computational cost of solving the Boltzmann equation…
Machine learning models are gaining increasing popularity in the domain of fluid dynamics for their potential to accelerate the production of high-fidelity computational fluid dynamics data. However, many recently proposed machine learning…
We consider non-spherical rigid body particles in an incompressible fluid in the regime where the particles are too large to assume that they are simply transported with the fluid without back-coupling and where the particles are also too…
A multi-scale model for the evolution of the velocity gradient tensor in fully developed turbulence is proposed. The model is based on a coupling between a ``Restricted Euler'' dynamics [{\it P. Vieillefosse, Physica A, {\bf 14}, 150…
A machine learning method to predict steady external fluid flows using elliptic input features is introduced. Using data from as few as one high-fidelity simulation, the proposed method produces models generalizable under changes to…
We introduce transfer learning for nonlinear dynamics, which enables efficient predictions of chaotic dynamics by utilizing a small amount of data. For the Lorenz chaos, by optimizing the transfer rate, we accomplish more accurate inference…
Fluids can behave in a highly irregular, turbulent way. It has long been realised that, therefore, some weak notion of solution is required when studying the fundamental partial differential equations of fluid dynamics, such as the…
We introduce a machine-learning-based framework for constructing continuum non-Newtonian fluid dynamics model directly from a micro-scale description. Dumbbell polymer solutions are used as examples to demonstrate the essential ideas. To…
This paper explores the feasibility of quantum simulation for partial differential equations (PDEs) with physical boundary or interface conditions. Semi-discretisation of such problems does not necessarily yield Hamiltonian dynamics and…
The work of Ansumali \textit{et al.}\cite{Ansumali} is extended to Two Dimensional Magnetohydrodynamic (MHD) turbulence in which energy is cascaded to small spatial scales and thus requires subgrid modeling. Applying large eddy simulation…
High-intensity laser plasma interactions create complex computational problems because they involve both fluid and kinetic regimes, which need models that maintain physical precision while keeping computational speed. The research…
The small-scale velocity gradient is connected to fundamental properties of turbulence at the large scales. By neglecting the viscous and nonlocal pressure Hessian terms, we derive a restricted Euler model for the turbulent flow along an…
Nonequilibrium statistical models of point vortex systems are constructed using an optimal closure method, and these models are employed to approximate the relaxation toward equilibrium of systems governed by the two-dimensional Euler…
Engineering design and scientific analysis rely upon computer simulations of turbulent fluid flows using turbulence models. These turbulence models are empirical and approximate, leading to large uncertainties in their predictions that…
Simultaneously detecting hidden solid boundaries and reconstructing flow fields from sparse observations poses a significant inverse challenge in fluid mechanics. This study presents a physics-informed neural network (PINN) framework…
Fluid turbulence is characterized by strong coupling across a broad range of scales. Furthermore, besides the usual local cascades, such coupling may extend to interactions that are non-local in scale-space. As such the computational…
In the variational principle leading to the Euler equation for a perfect fluid, we can use the method of undetermined multiplier for holonomic constraints representing mass conservation and adiabatic condition. For a dissipative fluid, the…
Modeling the subgrid-scale dynamics of reduced models is a long standing open problem that finds application in ocean, atmosphere and climate predictions where direct numerical simulation (DNS) is impossible. While neural networks (NNs)…
Modeling the mechanics of fluid in complex scenes is vital to applications in design, graphics, and robotics. Learning-based methods provide fast and differentiable fluid simulators, however most prior work is unable to accurately model how…
In the present paper we give a brief summary of some recent theoretical advances in the treatment of inhomogeneous fluids and methods which have applications in the study of dynamical properties of liquids in situations of extreme…