Related papers: A Multiscale Camassa--Holm Equation
We develop a stochastic model for the velocity gradients dynamics along a Lagrangian trajectory. Comparing with different attempts proposed in the literature, the present model, at the cost of introducing a free parameter known in…
In this paper, we propose a local-global multiscale mortar mixed finite element method (MMMFEM) for multiphase transport in heterogeneous media. We consider the two-phase flow system, the pressure equation is solved via the multiscale…
Compressible interfacial multiphase flows (CIMF) are essential to different applications, such as liquid fuel injection in supersonic propulsion systems. Since high-level details in CIMF are often difficult to measure in experiments,…
Geometric data and purpose-built generative models on them have become ubiquitous in high-impact deep learning application domains, ranging from protein backbone generation and computational chemistry to geospatial data. Current geometric…
This paper presents a Crank-Nicolson leap-frog (CNLF) scheme for the unsteady incompressible magnetohydrodynamics (MHD) equations. The spatial discretization adopts the Galerkin finite element method (FEM), and the temporal discretization…
In this paper the two-dimensional Benney system describing long wave propagation of a finite depth fluid motion and the multi-dimensional Russo--Smereka kinetic equation describing a bubbly flow are considered. The Hamiltonian approach…
The transport of heat and particles in the relatively collisional edge regions of magnetically confined plasmas is a scientifically challenging and technologically important problem. Understanding and predicting this transport requires the…
In this study, an implicit scheme for the gas-kinetic scheme (GKS) on the unstructured hybrid mesh is proposed. The Spalart-Allmaras (SA) one equation turbulence model is incorporated into the implicit gas-kinetic scheme (IGKS) to predict…
Quark-gluon plasmas formed in heavy ion collisions at high energies are well described by ideal classical fluid equations with nearly zero viscosity. It is believed that a similar fluid permeated the entire universe at about three…
This paper introduces a novel data driven framework for constructing accurate and general equivariant models of multiscale phenomena which does not rely on specific assumptions about the underlying physics. This framework is illustrated…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
The Navier--Stokes equations for incompressible flows past a two--dimensional sphere are considered in this article. The existence of an inertial form of the equations is established. Furthermore for the first time for fluid equations, we…
We propose a set of generalized incompressible fluid dynamical equations, which interpolates between the Burgers and Navier-Stokes equations in two dimensions and study their properties theoretically and numerically. It is well-known that…
We formulate a coarse-graining approach to the dynamics of magnetohydrodynamic (MHD) fluids at a continuum of length-scales. In this methodology, effective equations are derived for the observable velocity and magnetic fields…
We consider multi-gradient fluids endowed with a volumetric internal energy which is a function of mass density, volumetric entropy and their successive gradients. We obtained the thermodynamic forms of equation of motions and equation of…
This work presents an abstract framework for the design, implementation, and analysis of the multiscale spectral generalized finite element method (MS-GFEM), a particular numerical multiscale method originally proposed in [I. Babuska and R.…
In this paper, we consider the high order geometric flows of a submanifolds $M$ in a complete Riemannian manifold $N$ with $\dim(N)=\dim(M)+1=n+1$, which were introduced by Mantegazza in the case the ambient space is an Euclidean space, and…
A complete analysis is presented for the far-field creeping flow produced by a multipolar force distribution in a fluid confined between two parallel planar walls. We show that at distances larger than several wall separations the flow…
Multiscale correlation functions in high Reynolds number experimental turbulence and synthetic signals are investigated. Fusion Rules predictions as they arise from multiplicative, almost uncorrelated, random processes for the energy…
This paper proposes a simple new closure principle for turbulent shear flows. The turbulent flow field is divided into an outer and an inner region. The inner region is made up of a log-law region and a wall layer. The wall layer is viewed…