Session J25: Computational Fluid Dynamics

Live

Lattice-Boltzmann (LB) simulations have been used extensively over the past several decades in the study of hydrodynamics. LB methods have been coupled with various molecular dynamics (MD) methods to better simulate complex fluids, phase transitions, and their behavior at interfaces. Using a modified Lattice Boltzmann method package from the Large-Scale Atomic/Molecular Massively Parallel Simulator (LAMMPS), we attempt to couple colloidal particles and the LB fluid under critical conditions to study the particle dynamics at the liquid-gas interface. This work is preliminary to studying interfacial behaviour of complex fluid suspensions in LAMMPS, such as that of a liquid crystal (LC) colloid suspension, where distinct defect patterns are known to emerge at the LC-gas interface at equilibrium. We expect these defects to disturb the uniformity of colloidal suspensions.   

Live

Simulation of turbulent flows at high Reynolds number is a computationally challenging task relevant to a large number of engineering and scientific applications in diverse fields such as climate science, aerodynamics, and combustion. Turbulent flows are typically modeled by the Navier-Stokes equations. Direct Numerical Simulation (DNS) of the Navier-Stokes equations with sufficient numerical resolution to capture all the relevant scales of the turbulent motions can be prohibitively expensive. Simulation at lower-resolution on a coarse-grid introduces significant errors. We introduce a machine learning (ML) technique based on a deep neural network architecture that corrects the numerical errors induced by a coarse-grid simulation of turbulent flows at high-Reynolds numbers, while simultaneously recovering an estimate of the high-resolution fields. Our proposed simulation strategy is a hybrid ML-PDE solver that is capable of obtaining a meaningful high-resolution solution trajectory while solving the system PDE at a lower resolution.   

Live

In 1957, Miles proposed a linear theory for the growth of wind-induced small ripples on water. In the framework of hydrodynamic stability, these ripples are regarded as perturbations of the air flow. There is an energy transfer from the wind to the waves in the critical layer, which is the height where the phase speed is equal to the wind speed. We unify the many approaches of Miles' theory and provide a physical mechanism for the wave growth and we develop a simple method to compute the growth rate for an arbitrary wind profile. With this numerical scheme, we revisit the work of Morland and Saffman (1993) on Squire's theorem for the Miles instability, and study various turbulent boundary layer profiles as wind models. Moreover, for short and long waves we obtain uniform approximations of the perturbation stream function by the method of Matched Asymptotic Expansions, and infer approximate formulae for the growth rate. Finally, we simulate a quasi-linear model proposed by Janssen (1982), which takes into account the feedback of growing waves on the wind.   

Live

The dynamic behavior of a partially wetting polymer droplet driven over a nanostructured interface is investigated using molecular dynamics simulations. We consider the bead-spring model to represent a polymeric liquid that partially wets a rough surface composed of a periodic array of spherical particles. It is found that at sufficiently small values of the external force, the droplet remains pinned at the particles’ surface, while above the threshold, its motion consists of alternating periods of pinning and rapid displacements between neighboring particles. The latter process involves large periodic variation of the advancing and receding contact angles due to attachment and detachment of the contact line. Finally, upon increasing external force, the droplet center of mass is displaced steadily but the oscillation amplitude of the receding contact angle as well as the maximum contact angle hysteresis remain relatively unaffected.   

Live

Wave equations are ubiquitous: classical physics, fluid dynamics, relativistic quantum theory. Standard solutions use n-spatial dimensions (n=1,2,3) plus one independent time t dimension. The method of descent connects solutions for n=3 down to n=2 and n=1, the latter solved by D’Alembert with canonical variables p=x+w and m=x-w, where x is position along x-axis, w=Ct and C a relevant speed, see Lessons 17-24 in [1]. Instead, we ascend from the one-dimensional (1D) wave equation in spherical coordinates, with radial distance 0<r instead of -∞<x<+∞. Time is treated here as a novel orientation angle whose tangent is q=w/r. The 1D-wave equation is thus solved as a superposition of a permanent background potential dependent on r only, plus a new entangled potential dependent on q only; meaning of the r-q plane is discussed. Solutions with same structure hold for n>1, with an azimuth angle added in the 2D-plane, plus an additional elevation angle for the 3D-case. First-time explicit closed solutions are reported here for wave equations with n=1,2,3. Our novel solutions are non-harmonic and depend upon two independent variables r and q, plus (n-1) spatial angles. Reference: [1] S. J. Fowler, Partial Differential Equations for Scientists and Engineers (Dover, New York 1992).   

Live

The pseudopotential lattice Boltzmann method has become an alternative tool to simulating multiphase systems. As is typically done, the lattice Boltzmann equation LBE is only used to solve the mass and momentum conservation equations. To solve non-isothermal problems an appropriate energy conservation equation ECE is solved using finite differences. When the LBE is coupled with an ECE, simulations often become more unstable and can be difficult to reach high values of the density ratio. Also, most ECE are written as a discrete equation for temperature, not exactly conserving total energy in a periodic domain. This talk focuses on studying the application of an ECE coupled to the pseudopotential method for multiphase simulation. The goals are: evaluate the presence of discretization errors, violation in the conservation of total energy and analyze current methods stability. A smooth oscillation problem is employed to evaluate the ECE. The comparison between numerical and analytical results revealing that the second order of the numerical scheme is not sufficient to properly model the non-isothermal oscillation problem.   

Live

Experimental investigation of processes occurring in high-energy systems is complicated and expensive. High temperatures and pressures, transience, and nascent toxic gases make mathematical tools demanding in this domain. Hence, using numerical models is a key component for an efficient design of high-energy systems.
In this study, we consider the coupled problem of tracking the burning surface together with calculating flow parameters in high-energy systems. For this purpose, we develop the numerical model that takes into account both complex grain geometry and multidimensional gas flow pattern. We parallelize this algorithm using CUDA technology. It allows us to gain up to 30x acceleration in comparison with consequent implementation.
We test our numerical model on the configuration without nozzle, that is when the nozzle section is made of propellant as well. We prove approximation convergence for the problem and depict the evolution of the propellant burning surface. Also, we show dependencies of thrust, burning surface area, the average speed on the nozzle edge, and maximum pressure on time during the firing. In the end, we present distributions of flow parameters at initial, intermediate, and final time points.   

Live

The Integer Lattice Gas provides a solution to one of the major problems that the Boolean Lattice Gas has by ensuring it recovers the proper Boltzmann Distribution as opposed to the Fermi-Dirac Distribution recovered by the Boolean Lattice Gas. This allows the Integer Lattice Gas to fully recover the Navier-Stokes Equation, something that Boolean Lattice Gasses struggled with. However, the Integer Lattice Gas has, thusfar, been far less computationally efficient than the more commonly used Lattice Boltzmann method, and thus has not been viable for practical utilization. We have created, by sampling from a local equilibrium distribution, a sampling collision operator for the Integer Lattice Gas that allows it to be competative with comparable Fluctuating Lattice Boltzmann Methods. This makes the Integer Lattice Gas a far more viable method, and, although not yet faster than the Lattice Boltzmann method, its stability and non-deterministic nature give several advantages that may make the Integer Lattice Gas a better option for some applications.   

Not Participating

The flow of a thin Newtonian film coating a solid substrate with complex curvature is a challenging problem of interest to many fields, especially biophysics. By a combination of multiple-scale analysis and center manifold techniques, Roy, Roberts and Simpson (2002) were able to develop a general nonlinear interface equation, whose solutions reveal the mechanism responsible for film thinning near regions of high substrate curvature. Here we examine the perturbative response of this equation by investigating an interfacial instability involving capillary driven flow of a thin film on a toroidal substrate. We coin this system the doughnut glazing problem. Results of a generalized linear stability analysis based on non-normal growth of a non-uniform liquid layer reveal the migration patterns of growing modes to the interior surface of the torus. Contrary to expectation, as the torii radii approach infinity, the wavelength of the maximally unstable mode does not asymptote to that of the well-known sinusoidal instablity for a thin film on a solid cylinder (Goren 1962). We demonstrate how the asymmetry inherent in the torus geometry biases the flow to help steer the formation, evolution and growth of unstable non-normal modes.   

Live

Graphene oxides (GO) is used as a particulate surfactant to change the interfacial properties of drops and bubbles. To get insights into the processes governing GO adsorption, we use molecular simulations to simulate GO nanoparticles at the interface between water and vapour. We first extract the free energy profile normal to the interface for a single particle with varying degree of functionalization at the basal plane and varying particle size using umbrella sampling. We found that the affinity of the particle with the interface decreases for increasing degree of functionalization, and that only particles with a degree of functionalization lower than a threshold are interfacially actives. This is in agreement with experimental observations. We then use molecular dynamics to evaluate the behaviour of a single GO particle at the interface and show that, as a consequence of hydrophilic and hydrophobic patches at the particle surface, a GO particle only partially adsorbs to the interface. Finally we evaluate the role of particle-particle interactions on adsorption as well as on the surface tension by exploring the case of multiple GO particles. Implications of our results for drops/bubbles stabilisation will be discussed.   

On Demand

We study the interplay between shear, buoyancy, and phase change on the stability of a flow of a liquid over an inclined, phase-changing plane under the influence of gravity. In the absence of buoyancy and phase change, this flow is known to exhibit a long-wavelength instability – which was first identified by Yih (Phys. Fluids. 6(3), pp. 321-334, 1963) – and a short-wavelength shear-mode instability – identified by Kelly (Phys. Fluids. A: Fluid Dynamics 1(5), pp. 819-828, 1989). We use a combination of linear stability and asymptotic analyses to study the effects of stratification and phase boundary on these instabilities, and find that they significantly affect the flow dynamics