HemeLB: A high performance parallel lattice-Boltzmann code for large scale fluid flow in complex geometries

Recently, meshless methods have become popular in numerically solving partial differential equations and have been employed to solve equations governing fluid flows, heat transfer, and species transport. In the present study, a numerical solver is developed employing the meshless framework to efficiently compute the hydrodynamic stability of fluid flows in complex geometries. The developed method is tested on two cases of Taylor–Couette flows. The concentric case represents the parallel flow assumption incorporated in the Orr–Sommerfeld model and the eccentric Taylor–Couette flow incorporates a non-parallel base flow with separation bubbles. The method was validated against earlier works by Marcus [“Simulation of Taylor-Couette flow. Part 1. Numerical methods and comparison with experiment,” J. Fluid Mech. 146, 45–64 (1984)], Oikawa et al. [“Stability of flow between eccentric rotating cylinders,” J. Phys. Soc. Jpn. 58, 2355–2364 (1989)], Leclercq et al. [“Temporal stability of eccentric Taylor–Couette–Poiseuille flow,” J. Fluid Mech. 733, 68–99 (2013)], and Mittal et al. [“A finite element formulation for global linear stability analysis of a nominally two-dimensional base flow,” Numer. Methods Fluids 75, 295–312 (2014)]. The results for the two cases and the effectiveness of the method are discussed in detail. The method is then applied to Taylor–Couette flow in an elliptical enclosure and the stability of the flow is investigated.

A lattice Boltzmann (LB) framework is developed for simulation of three-phase viscoelastic fluid flows in complex geometries. This model is based on a Rothman-Keller type model for immiscible multiphase flows which ensures mass conservation of each component in porous media even for a high density ratio. To account for the viscoelastic effects, the Maxwell constitutive relation is correctly introduced into the momentum equation, which leads to a modified lattice Boltzmann evolution equation for Maxwell fluids by removing the normal but excess viscous term. Our simulation tests indicate that this excess viscous term may induce significant errors. After three benchmark cases, the displacement processes of oil by dispersed polymer are studied as a typical example of three-phase viscoelastic fluid flow. The results show that increasing either the polymer intrinsic viscosity or the elastic modulus will enhance the oil recovery.

The generation of an orthogonal grid by the use of a boundary integral technique

The BEACON code is a Best Estimate Advanced Containment code which being developed by EG and G, Idaho, Inc., at the Idaho National Engineering Laboratory. The program is designed to perform a best estimate analysis of the flow of a mixture of air, water, and steam in a nuclear reactor containment system under loss-of-coolant accident conditions. The code can simulate two-component, two-phase fluid flow in complex geometries using a combination of two-dimensional, one-dimensional, and lumped-parameter representations for the various parts of the system. The current version of BEACON, which is designated BEACON/MOD2A, contains mass and heat transfer models for wall film and for wall conduction. It is suitable for the evaluation of short term transients in PWR dry containment systems. This manual describes the models employed in BEACON/MOD2A and specifies code implementation requirements. It provides application information for input data preparation and for output data interpretation.

The spectral-element method (SEM), is a high-order numerical method with the ability to accurately simulate fluid flows in complex geometries. SEM has opened the possibility to study – in great detail – fluid phenomena known to be very sensitive to discretization errors, e.g. flows undergoing pressureinduced separation [4]. Recently, Cherry et al. [1] performed experiments using Magnetic Resonance Velocimetry (MRV) of turbulent diffuser flow exhibiting unsteady three-dimensional separation at Re = 10 000 based on bulk velocity and height of the inflow duct. Two geometries with different opening angles were investigated and it was found that the flow was extremely sensitive to slight changes in the geometrical setup. To understand this sensitivity and to analyze its causes, we present a direct numerical simulation (DNS) of one of these cases (denoted by “Diffuser 1“ in [1]) by means of the SEM. Here, we focus on careful analysis of mean flow results in order to assess the quality of the simulation data.KeywordsDirect Numerical SimulationDiscretization ErrorGeometrical SetupMagnetic Resonance VelocimetryFriction Reynolds NumberThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

ABSTRACTThis article presents a new element-based finite-volume discretization approach for the solution of incompressible flow problems on co-located grids. The proposed method, called the method of proper closure equations (MPCE), employs a proper set of physically relevant equations to constrain the velocity and pressure at integration points. These equations provide a proper coupling between the nodal values of pressure and velocity. The final algebraic equations are not segregated in this study and are solved in a fully coupled manner. To show the applicability and performance of the method, it is tested on several steady two-dimensional laminar-flow benchmark cases. The results indicate that the method simulates the fluid flow in complex geometries and on nonorthogonal computational grids accurately. Also, it is shown that the method is robust in the sense that it does not require severe underrelaxation even at relatively high Reynolds numbers. In each test case, the required underrelaxation parameter, the number of iterations, and the corresponding CPU time are reported.

Intelligent computing and simulation of magnetic field influence on Casson fluid flow in complex geometries

Prediction of Heat and Fluid Flow in Complex Geometries Using General Orthogonal Coordinates

An immersed boundary method for direct and large eddy simulation of stratified flows in complex geometry

Fluid mechanics simulation of steady state flow in complex geometries has many applications, from the micro-scale (cell membranes, filters, rocks) to macro-scale (groundwater, hydrocarbon reservoirs, and geothermal) and beyond. Direct simulation of steady state flow in such porous media requires significant computational resources to solve within reasonable timeframes. This study outlines an integrated method combining predictions of fluid flow (fast, limited accuracy) with direct flow simulation (slow, high accuracy) is outlined that reduces computation time by an order of magnitude without loss of accuracy. A convolutional neural network (CNNs) is trained with various configurations on simulations in 2D and 3D porous media to estimate steady state velocity fields. Permeability estimation (as an average of the field) is accurate, but the velocity fields themselves are error prone, unsuitable for further transport studies. This estimate can either be used as an indicative prediction, or as initial conditions in direct simulation to reach a fully accurate result in a fraction of the compute time. Using Deep Learning predictions (or potentially any other approximation method) to accelerate flow simulation to steady state in complex structures shows promise as a technique to push the boundaries fluid flow modelling.

Numerical simulation of a square cavity was conducted to validate an implementation of an Immersed Boundary Method (IBM). The cavity consists of two differentially heated side walls and adiabatic top and bottom walls. A Cartesian grid is used with a finite volume, fractional step pressure correction method. Simulations use Dirichlet boundaries for vertical walls and Neumann boundaries for horizontal walls. The Immersed Boundary Method involves modifying the Navier--Stokes equations to include a forcing function in the momentum and energy equations that creates a virtual boundary. This method is useful because the boundary does not necessarily have to coincide with grid points; however, it is much less computationally expensive than other similar methods such as the cut cell method. The IBM is commonly used in simulations involving complex objects and can also accommodate moving boundaries. A standard numerical simulation with grid aligned with the boundary is first compared with previous results. The same geometry is then simulated by tilting the grid at various angles and using the IBM for each of the walls, and comparing these results with those initially obtained. We detail the implementation method and common problems associated with this. Velocity and temperature profiles are presented and the IBM is shown to maintain second order spatial accuracy. References E. A. Fadlun, R. Verzicco, P. Orlandi, and J. Mohd-Yusof. Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. Journal of Computational Physics, 161(1):35--60, 2000. doi:10.1006/jcph.2000.6484 T. Gao, Y. H. Tseng, and X. Y. Lu. An improved hybrid cartesian/immersed boundary method for fluid-solid flows. International Journal for Numerical Methods in Fluids, 55(12):1189--1211, 2007. doi:10.1002/fld.1522 M. P. Kirkpatrick and S. W. Armfield. Experimental and large eddy simulation results for the purging of salt water from a cavity by an overflow of fresh water. International Journal of Heat and Mass Transfer, 48(2):341--359, 2005. doi:10.1016/j.ijheatmasstransfer.2004.08.016 M. P. Kirkpatrick, S. W. Armfield, and J. H. Kent. A representation of curved boundaries for the solution of the navier-stokes equations on a staggered three-dimensional cartesian grid. Journal of Computational Physics, 184(1):1--36, 2003. doi:10.1016/S0021-9991(02)00013-X B. P. Leonard and Simin Mokhtari. Beyond first-order upwinding: The ultra-sharp alternative for non-oscillatory steady-state simulation of convection. International Journal for Numerical Methods in Engineering, 30(4):729--766, 1990. doi:10.1002/nme.1620300412 S. H. Peng and L. Davidson. Large eddy simulation for turbulent buoyant flow in a confined cavity. volume 22, pages 323--331, 2001. doi:10.1016/S0142-727X(01)00095-9 C. S. Peskin. Numerical-analysis of blood-flow in heart. Journal of Computational Physics, 25(3):220--252, 1977. doi:10.1016/0021-9991(77)90100-0 J. Salat, S. Xin, P. Joubert, A. Sergent, F. Penot, and P. Le Quere. Experimental and numerical investigation of turbulent natural convection in a large air-filled cavity. International Journal of Heat and Fluid Flow, 25:824--832, 2004. doi:10.1016/j.ijheatfluidflow.2004.04.003 Y. H. Tseng and J. H. Ferziger. A ghost-cell immersed boundary method for flow in complex geometry. Journal of Computational Physics, 192(2):593--623, 2003. doi:10.1016/j/jcp.2003.07.024 N. Zhang and Z. C. Zheng. An improved direct-forcing immersed-boundary method for finite difference applications. Journal of Computational Physics, 221(1):250--268, 2007. doi:10.1016/j.jcp.2006.06.012 N. Zhang, Z. C. Zheng, and S. Eckels. Study of heat-transfer on the surface of a circular cylinder in flow using an immersed-boundary method. International Journal of Heat and Fluid Flow, 29(6):1558--1566, 2008. doi:10.1016/j.ijheatfluidflow.2008.08.009

A cellular automata method for the prediction of incompressible fluid flows is presented and its practical relevance is investigated by comparing it with a standard finite volume solver. The cellular automata approach is based on an advanced lattice Boltzmann technique for a discrete microscopic description of the fluid flow. The finite volume solution procedure solves the macroscopic Navier-Stokes equations by means of an advanced multigrid pressure-correction technique on block-structured grids. Advantages and disadvantages of the cellular automata technique are discussed and quantitative comparative results related to accuracy, convergence properties and computing times are given for test cases with varying geometrical complexity. As a practical application of the method, results for the numerical simulation of the flow in a porous sedimentary layer are given

This document contains a summary of the work performed under the LDRD project entitled 'Interface Physics in Microporous Media'. The presence of fluid-fluid interfaces, which can carry non-zero stresses, distinguishes multiphase flows from more readily understood single-phase flows. In this work the physics active at these interfaces has been examined via a combined experimental and computational approach. One of the major difficulties of examining true microporous systems of the type found in filters, membranes, geologic media, etc. is the geometric uncertainty. To help facilitate the examination of transport at the pore-scale without this complication, a significant effort has been made in the area of fabrication of both two-dimensional and three-dimensional micromodels. Using these micromodels, multiphase flow experiments have been performed for liquid-liquid and liquid-gas systems. Laser scanning confocal microscopy has been utilized to provide high resolution, three-dimensional reconstructions as well as time resolved, two-dimensional reconstructions. Computational work has focused on extending lattice Boltzmann (LB) and finite element methods for probing the interface physics at the pore scale. A new LB technique has been developed that provides over 100x speed up for steady flows in complex geometries. A new LB model has been developed that allows for arbitrary density ratios, which has been a significant obstacle in applying LB to air-water flows. A new reduced order model has been developed and implemented in finite element code for examining non-equilibrium wetting in microchannel systems. These advances will enhance Sandia's ability to quantitatively probe the rich interfacial physics present in microporous systems.

Large scale unsteady motions in many practical engineering flows play a very important role and it is very unlikely that these unsteady flow features can be captured within the framework of Reynolds averaged Navier–Stokes approach. Large‐eddy simulation (LES) has become, arguably, the only practical numerical tool for predicting those flows more accurately since it is still not realistic to apply DNS to practical engineering flows with the current and near future available computing power.Numerical methods for the LES of turbulent flows in complex geometry have been developed and applied to predict practical engineering flows successfully. The method is based on body‐fitted curvilinear co‐ordinates with the contravariant velocity components of the general Navier–Stokes equations discretized on a staggered orthogonal mesh. For incompressible flow simulations the main source of computational expense is due to the solution of a Poisson equation for pressure. This is especially true for flows in complex geometry. A multigrid 3D pressure solver is developed to speed up the solution. In addition, the Poisson equation for pressure takes a simpler form with no cross‐derivatives when orthogonal mesh is used and hence resulting in increased convergence rate and producing more accurate solutions. Copyright © 2004 John Wiley & Sons, Ltd.

In the present study, the dynamic Vreman model based on the global equilibrium between the subgrid-scale dissipation and the viscous dissipation with a global model coefficient are applied to large eddy simulation of turbulent flow in complex geometries. Distributions of pressure, velocity and vorticity as well as some flow structure are gained, which is helpful to examine the performance of SGS model and understand the flow characters in complex geometries.