Related papers: Random vortex dynamics and Monte-Carlo simulations…
We establish stochastic functional integral representations for incompressible fluid flows occupying wall-bounded domains using the conditional law duality for a class of diffusion processes. These representations are used to derive a…
In this paper we establish a mathematical framework which may be used to design Monte-Carlo simulations for a class of time irreversible dynamic systems, such as incompressible fluid flows, including turbulent flows in wall-bounded regions,…
In this paper a Monte-Carlo method for simulating the motion of fluid flow moving along a solid wall is proposed. The random vortex method in the present paper is established by using the reflection technology and perturbation technique.…
The dynamical equation of the boundary vorticity has been obtained, which shows that the viscosity at a solid wall is doubled as if the fluid became more viscous at the boundary. For certain viscous flows the boundary vorticity can be…
In this paper we present a novel, closed three-dimensional (3D) random vortex dynamics system, which is equivalent to the Navier--Stokes equations for incompressible viscous fluid flows. The new random vortex dynamics system consists of a…
In this paper, we propose an approach for simulating wall-bounded incompressible turbulent flows by integrating the technology of random vortex method with the core principles of large-eddy simulations (LES). In particular, we employ the…
We develop a numerical method for simulation of incompressible viscous flows by integrating the technology of random vortex method with the core idea of Large Eddy Simulation (LES). Specifically, we utilize the filtering method in LES,…
We develop numerical multiscale methods for viscous boundary layer flow. The goal is to derive effective boundary conditions, or wall laws, through high resolution simulations localized to the boundary coupled to a coarser simulation in the…
We propose a suitable analytical framework to perform numerical analysis of problems arising in compressible fluid models with uncertain data. We discuss both weak and strong stochastic approach, where the former is based on the knowledge…
The paper presents numerical methods for unsteady flows of a viscous incompressible fluid in internal domains with many inlet/outlet sections. The novel variants of dissipative boundary conditions augmented by the inertia terms are used at…
In this paper, we consider turbulence from a geometric perspective based on the vorticity equations for incompressible viscous fluid flows. We derive several quantitative statements about the statistics of turbulent flows. In particular we…
Recent experimental and computational studies indicate that near wall turbulent flows can be characterized by universal small scale autonomous dynamics that are modulated by large scale structures. We formulate numerical simulations of near…
By using a formulation of a class of compressible viscous flows with a heat source via vorticity and expansion-rate, we study the Oberbeck-Boussinesq flows. To this end we establish a new integral representation for solutions of parabolic…
We perform direct numerical simulations (DNS) of a turbulent channel flow over porous walls. In the fluid region the flow is governed by the incompressible Navier--Stokes (NS) equations, while in the porous layers the Volume-Averaged…
To produce a vortex, a torque must be applied to the fluid. In viscous fluids, the torques that produce turbulent vortices result from the loss of symmetry of the stress tensor, once the viscous friction exceeds the shear stress resistance…
Periodic travelling waves at the free surface of an incompressible inviscid fluid in two dimensions under gravity are numerically computed for an arbitrary vorticity distribution. The fluid domain over one period is conformally mapped from…
In this technical note, we demonstrate the robustness of our numerical scheme of vorticity iteration in dealing with the dipole-wall interaction at small viscosity, with emphasis on mesh convergence, boundary vorticity as well as wall…
Interfaces between two fluids are ubiquitous and of special importance for industrial applications, e.g., stabilisation of emulsions. The dynamics of fluid-fluid interfaces is difficult to study because these interfaces are usually…
This work presents a novel numerical investigation of the dynamics of free-boundary flows of viscoelastic liquid membranes. The governing equation describes the balance of linear momentum, in which the stresses include the viscoelastic…
We present a velocity-based Monte Carlo fluid solver that overcomes the limitations of its existing vorticity-based counterpart. Because the velocity-based formulation is more commonly used in graphics, our Monte Carlo solver can be readily…