David R. Noble

A consistent hydrodynamic boundary condition for the lattice Boltzmann method

A hydrodynamic boundary condition is developed to replace the heuristic bounce‐back boundary condition used in the majority of lattice Boltzmann simulations. This boundary condition is applied to the two‐dimensional, steady flow of an incompressible fluid between two parallel plates. Poiseuille flow with stationary plates, and a constant pressure gradient is simulated to machine accuracy over the full range of relaxation times and pressure gradients. A second problem involves a moving upper plate and the injection of fluid normal to the plates. The bounce‐back boundary condition is shown to be an inferior approach for simulating stationary walls, because it actually mimics boundaries that move with a speed that depends on the relaxation time. When using accurate hydrodynamic boundary conditions, the lattice Boltzmann method is shown to exhibit second‐order accuracy.

A direct simulation method for particle‐fluid systems

A coupled numerical method for the direct simulation of particle‐fluid systems is formulated and implemented. The Navier‐Stokes equations governing fluid flow are solved using the lattice Boltzmann method, while the equations of motion governing particles are solved with the discrete element method. Particle‐fluid coupling is realized through an immersed moving boundary condition. Particle forcing mechanisms represented in the model to at least the first‐order include static and dynamic fluid‐induced forces, and intergranular forces including particle collisions, static contacts, and cementation. The coupling scheme is validated through a comparison of simulation results with the analytical solution of cylindrical Couette flow. Simulation results for the fluid‐induced erosive failure of a cemented particulate constriction are presented to demonstrate the capability of the method.

AN EVALUATION OF THE BOUNCE‐BACK BOUNDARY CONDITION FOR LATTICE BOLTZMANN SIMULATIONS

The bounce-back boundary condition for lattice Boltzmann simulations is evaluated for flow about an infinite periodic array of cylinders. The solution is compared with results from a more accurate boundary condition formulation for the lattice Boltzmann method and with finite difference solutions. The bounce-back boundary condition is used to simulate boundaries of cylinders with both circular and octagonal cross-sections. The convergences of the velocity and total drag associated with this method are slightly sublinear with grid spacing. Error is also a function of relaxation time, increasing exponentially for large relaxation times. However, the accuracy does not exhibit a trend with Reynolds number between 0.1 and 100. The square lattice Boltzmann grid conforms to the octagonal cylinder but only approximates the circular cylinder, and the resulting error associated with the octagonal cylinder is half the error of the circular cylinder.

COMPARISON OF ACCURACY AND PERFORMANCE FOR LATTICE BOLTZMANN AND FINITE DIFFERENCE SIMULATIONS OF STEADY VISCOUS FLOW

The lattice Boltzmann method (LBM) is used to simulate flow in an infinite periodic array of octagonal cylinders. Results are compared with those obtained by a finite difference (FD) simulation solved in terms of streamfunction and vorticity using an alternating direction implicit scheme. Computed velocity profiles are compared along lines common to both the lattice Boltzmann and finite difference grids. Along all such slices, both streamwise and transverse velocity predictions agree to within 0ċ5% of the average streamwise velocity. The local shear on the surface of the cylinders also compares well, with the only deviations occurring in the vicinity of the corners of the cylinders, where the slope of the shear is discontinuous. When a constant dimensionless relaxation time is maintained, LBM exhibits the same convergence behaviour as the FD algorithm, with the time step increasing as the square of the grid size. By adjusting the relaxation time such that a constant Mach number is achieved, the time step of LBM varies linearly with the grid size. The efficiency of LBM on the CM-5 parallel computer at the National Center for Supercomputing Applications (NCSA) is evaluated by examining each part of the algorithm. Overall, a speed of 13ċ9 GFLOPS is obtained using 512 processors for a domain size of 2176×2176.

Direct assessment of lattice Boltzmann hydrodynamics and boundary conditions for recirculating flows

A hydrodynamic boundary condition is developed for lattice Boltzmann hydrodynamics using a square, orthogonal grid. A constraint based on energy considerations is developed to provide closure for the equations which govern the particle distribution at the boundaries. This boundary condition is applied to the two-dimensional, steady flow of an incompressible fluid behind a grid, known as Kovasznay flow. The results are compared to those using alternate boundary conditions using the known exact solution. The hydrodynamic boundary condition produces quadratic spatial convergence, while alternate techniques fail to maintain this second-order accuracy.

Aria 1.5 : user manual.

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes the incompressible Navier-Stokes equations, energy transport equation, species transport equations, nonlinear elastic solid mechanics, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking. Coupled physics problems are solved in several ways including fully-coupled Newtons method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods, fully-coupled Picards method, and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic h-adaptivity and dynamic load balancing are some of Arias more advanced capabilities. Aria is based on the Sierra Framework.

A level set approach to 3D mold filling of Newtonian fluids.

Filling operations, in which a viscous fluid displaces a gas in a complex geometry, occur with surprising frequency in many manufacturing processes. Difficulties in generating accurate models of these processes involve accurately capturing the interfacial boundary as it undergoes large motions and deformations, preventing dispersion and mass-loss during the computation, and robustly accounting for the effects of surface tension and wetting phenomena. This paper presents a numerical capturing algorithm using level set theory and finite element approximation. Important aspects of this work are addressing issues of mass-conservation and the presence of wetting effects. We have applied our methodology to a three-dimension model of a complicated filling problem. The simulated results are compared to experimental flow visualization data taken for filling of UCON oil in the identical geometry. Comparison of simulation and experiment indicates that the simulation conserved mass adequately and the simulated interface shape was in approximate agreement with experiment. Differences seen were largely attributed to inaccuracies in the wetting line model.Copyright

A Coupled DEM-LB Model for the Simulation of Particle-Fluid Systems

Our understanding of particle-fluid dynamics has been severely limited by the nonexistence of a high-fidelity modeling capability. Continuum modeling approaches overlook the microscale particle-fluid interactions from which macroscopic system properties emerge, while experimental inquiries are plagued by high costs and limited resolution. One promising numerical alternative is to simulate particle-fluid systems at the grain-scale, fully resolving the interaction of individual solid particles with other solid particles and the surrounding fluid. Until recently, the direct simulation of these systems has proven computationally intractable. In this research, a robust modeling capability for the direct simulation of particle-fluid systems has been formulated and implemented. The coupled equations of motion governing both the fluid phase and the individual particles comprising the solid phase are solved using a highly efficient numerical scheme based on the discrete-element (DEM) and the lattice-Boltzmann (LB) methods. Particle forcing mechanisms represented in the model to at least the first order include static and dynamic fluid-induced forces, and intergranular forces from particle collisions, static contacts, and cementation. The coupled method has been implemented into a generalized modeling environment for the seamless definition, simulation, and analysis of two-dimensional particle-fluid physics. Extensive numerical testing of the model has demonstrated its accuracy over a wide range of dynamical regimes.

A verified conformal decomposition finite element method for implicit, many-material geometries

Abstract As computing power rapidly increases, quickly creating a representative and accurate discretization of complex geometries arises as a major hurdle towards achieving a next generation simulation capability. Component definitions may be in the form of solid (CAD) models or derived from 3D computed tomography (CT) data, and creating a surface-conformal discretization may be required to resolve complex interfacial physics. The Conformal Decomposition Finite Element Methods (CDFEM) has been shown to be an efficient algorithm for creating conformal tetrahedral discretizations of these implicit geometries without manual mesh generation. In this work we describe an extension to CDFEM to accurately resolve the intersections of many materials within a simulation domain. This capability is demonstrated on both an analytical geometry and an image-based CT mesostructure representation consisting of hundreds of individual particles. Effective geometric and transport properties are the calculated quantities of interest. Solution verification is performed, showing CDFEM to be optimally convergent in nearly all cases. Representative volume element (RVE) size is also explored and per-sample variability quantified. Relatively large domains and small elements are required to reduce uncertainty, with recommended meshes of nearly 10 million elements still containing upwards of 30% uncertainty in certain effective properties. This work instills confidence in the applicability of CDFEM to provide insight into the behaviors of complex composite materials and provides recommendations on domain and mesh requirements.

Multiscale models of nuclear waste reprocessing : from the mesoscale to the plant-scale.

Nuclear waste reprocessing and nonproliferation models are needed to support the renaissance in nuclear energy. This report summarizes an LDRD project to develop predictive capabilities to aid the next-generation nuclear fuel reprocessing, in SIERRA Mechanics, Sandia’s high performance computing multiphysics code suite and Cantera, an open source software product for thermodynamics and kinetic modeling. Much of the focus of the project has been to develop a moving conformal decomposition finite element method (CDFEM) method applicable to mass transport at the water/oil droplet interface that occurs in the turbulent emulsion of droplets within the contactor. Contactor-scale models were developed using SIERRA Mechanics turbulence modeling capability. Unit operations occur at the column-scale where many contactors are connected in series. Population balance models