On improving the performance of large parallel lattice Boltzmann flow simulations in heterogeneous porous media

Classical Cartesian domain decompositions for parallel lattice Boltzmann simulations of fluid flow through heterogeneous porous media are doomed to workload imbalance as the number of processors increases, thus leading to decreasing parallel performance. A one-lattice lattice Boltzmann method (LBM) implementation with vector data structure combined with even fluid node partitioning domain decomposition and fully-optimized data transfer layout is presented. It is found to provide nearly-optimal workload balance, lower memory usage and better computational performance than classical slice decomposition techniques using sparse matrix data structures. Predictive memory usage and parallel performance models are also established and observed to be in very good agreement with data corresponding to numerical fluid flow simulations performed through 3-dimensional packings of cylinders and polydisperse spheres.     

Primal‐Dual Optimization for Fluids

We apply a novel optimization scheme from the image processing and machine learning areas, a fast Primal‐Dual method, to achieve controllable and realistic fluid simulations. While our method is generally applicable to many problems in fluid simulations, we focus on the two topics of fluid guiding and separating solid‐wall boundary conditions. Each problem is posed as an optimization problem and solved using our method, which contains acceleration schemes tailored to each problem. In fluid guiding, we are interested in partially guiding fluid motion to exert control while preserving fluid characteristics. With our method, we achieve explicit control over both large‐scale motions and small‐scale details which is valuable for many applications, such as level‐of‐detail adjustment (after running the coarse simulation), spatially varying guiding strength, domain modification, and resimulation with different fluid parameters. For the separating solid‐wall boundary conditions problem, our method effectively eliminates unrealistic artefacts of fluid crawling up solid walls and sticking to ceilings, requiring few changes to existing implementations. We demonstrate the fast convergence of our Primal‐Dual method with a variety of test cases for both model problems.     

Fast Fluid Simulations with Sparse Volumes on the GPU

We introduce efficient, large scale fluid simulation on GPU hardware using the fluid‐implicit particle (FLIP) method over a sparse hierarchy of grids represented in NVIDIA^® GVDB Voxels. Our approach handles tens of millions of particles within a virtually unbounded simulation domain. We describe novel techniques for parallel sparse grid hierarchy construction and fast incremental updates on the GPU for moving particles. In addition, our FLIP technique introduces sparse, work efficient parallel data gathering from particle to voxel, and a matrix‐free GPU‐based conjugate gradient solver optimized for sparse grids. Our results show that our method can achieve up to an order of magnitude faster simulations on the GPU as compared to FLIP simulations running on the CPU.     

Level-set method for the modelling of liquid bridge formation and break-up

In this paper, a level-set method is used to track the free surface and velocity profile of a Newtonian filament being stretched on an extensional rheometer. The method enables simulations to be performed from initial stretching until after the filament has broken up. The method used also follows the behaviour at the plate-liquid interface, allowing the air–liquid–solid contact point to move freely rather than being pinned at the edge of the plate. The simulations were validated by comparison with analogous experiments with glycerin, with excellent agreement between the two. The simulations were able to track the free surface throughout the experiment, including after the topological change associated with the filament breaking up. For the modelling of the fluid stretching, a novel grid deformation algorithm was introduced which allowed a tailored expansion of the domain, avoiding the need for specialised re-meshing.     

Hybrid atomistic�Ccontinuum simulations of fluid flows involving interfaces

In this work, we use an hybrid atomistic–continuum (HAC) simulation method to study transient and steady isothermal flows of Lennard-Jones fluids near interfaces. Our hybrid method is based on a domain decomposition algorithm. The flow domain is composed of two overlapping regions: an atomistic region described by molecular dynamics, and a continuum region described by a finite volume discretization of the incompressible Navier–Stokes equations. To show the interest of such an hybrid method to compute flows near fluid/solid interface, we first applied our hybrid scheme to the classical Couette flow, where the moving wall is modelled at the atomistic scale. In addition, we also studied an oscillatory shear flow. Then, to compute flows near fluid/fluid interface, we applied our method to a two-phase Couette flow (liquid/gas), where the interface is modelled at the molecular scale. We show that hybrid results can sometimes differ from those provided by analytical solutions deduced from continuum mechanics equations combined with usual boundary/interface relations. For the Couette and oscillatory shear flows, a good agreement is found between hybrid simulations and macroscopic analytical solutions, however, we noticed that the fluid in contact with the wall can be more entailed than what expected. For the liquid/gas Couette flow, the hybrid simulation exhibits an unexpected jump of the velocity in the interfacial region, corresponding to a partial slip between the two fluid phases. Those interesting results highlight the interest of using an HAC method to deal with systems for which surfaces/interfaces effects are important.     

Mesoscale simulations of particulate flows with parallel distributed Lagrange multiplier technique

Fluid particulate flows are common phenomena in nature and industry. Modeling of such flows at micro and macro levels as well establishing relationships between these approaches are needed to understand properties of the particulate matter. We propose a computational technique based on the direct numerical simulation of the particulate flows. The numerical method is based on the distributed Lagrange multiplier technique following the ideas of Glowinski et al. [16] and Patankar [30]. Each particle is explicitly resolved on an Eulerian grid as a separate domain, using solid volume fractions. The fluid equations are solved through the entire computational domain, however, Lagrange multiplier constrains are applied inside the particle domain such that the fluid within any volume associated with a solid particle moves as an incompressible rigid body. Mutual forces for the fluid-particle interactions are internal to the system. Particles interact with the fluid via fluid dynamic equations, resulting in implicit fluid-rigid body coupling relations that produce realistic fluid flow around the particles (i.e., no-slip boundary conditions). The particle-particle interactions are implemented using explicit force-displacement interactions for frictional inelastic particles similar to the DEM method of Cundall et al. [10] with some modifications using a volume of an overlapping region as an input to the contact forces. The method is flexible enough to handle arbitrary particle shapes and size distributions. A parallel implementation of the method is based on the SAMRAI (Structured Adaptive Mesh Refinement Application Infrastructure) library, which allows handling of large amounts of rigid particles and enables local grid refinement. Accuracy and convergence of the presented method has been tested against known solutions for a falling particle as well as by examining fluid flows through stationary particle beds (periodic and cubic packing). To evaluate code performance and validate particle contact physics algorithm, we performed simulations of a representative experiment conducted at the U.C. Berkeley Thermal Hydraulic Lab for pebble flow through a narrow opening.     

基于SPH与FEM的结构入水分析方法

建立基于光滑粒子动力学（smoothed particle hydrodynamics, SPH）、有限元法（finite element method, FEM）和无反射边界耦合的结构入水分析方法,将无限水域利用无反射边界条件截断成有限水域,将有限水域分为流体变形大的SPH区域、流体变形小的FEM区域和声学流体FEM区域,结构用FEM离散。采用通用接触算法模拟SPH与FEM的耦合,采用声固耦合方法处理FEM区域之间的耦合,建立流固耦合的SPH FEM分析方法。该方法结合SPH模拟大变形的优点和FEM的高效性,可实现含自由液面变形、液体飞溅和无限水域等特点的流固耦合问题的模拟,为结构入水分析缩小离散区域、降低自由度和SPH粒子数等提供一种有效的分析方法。     

Distributing and Load Balancing Sparse Fluid Simulations

This paper describes a general algorithm and a system for load balancing sparse fluid simulations. Automatically distributing sparse fluid simulations efficiently is challenging because the computational load varies across the simulation domain and time. A key challenge with load balancing is that optimal decision making requires knowing the fluid distribution across partitions for future time steps, but computing this state for an arbitrary simulation requires running the simulation itself. The key insight of this paper is that it is possible to predict future load by running a speculative low resolution simulation in parallel. We mathematically formulate the problem of load balancing over multiple time steps and present a polynomial time algorithm to compute an approximate solution to it. Our experimental results show that distributing and speculatively load balancing sparse FLIP simulations over 8 nodes speeds them up by 5.3× to 7.9×, and that speculative load balancing generates assignments that perform within 20% of optimal.     

Numerical modelling of interfacial soil erosion with viscous incompressible flows

The aim of this study is to develop a numerical model for simulating surface erosion occurring at a fluid/soil interface subject to a flow process. Balance equations with jump relations are used. A penalization procedure including a fictitious domain method is used to compute the Stokes flow around obstacles, in order to avoid body-fitted unstructured meshes and instead use fast and efficient finite volume approximations on Cartesian meshes. The evolution of the water/soil interface is described by using a level set function. The ability of the model to predict the interfacial erosion of soils is confirmed by several numerical simulations.     

A numerical procedure for predicting the performance of high pressure homogenizing valves

This paper describes a numerical procedure for the prediction of the homogenizing performance of high pressure homogenizing valves used in diary plants. The method is based on a strict interaction between a complex CFD code and a simple homogenizing simulation code developed by the authors. This latter implements a mathematical model for the evaluation of droplets break-up, that needs an accurate evaluation of few significant fluid dynamic parameters in the whole fluid dynamic domain inside the valve. Due to the relevant pressure gradients within the flow and to the possibility of cavitation, particular attention has been paid in defining the fluid model, the mesh and the parameters required for CFD simulations. Notwithstanding the quite simple model of the homogenizing process, comparatively with the complexity of phenomena involved, the first results obtained are in general agreement with the experimental data available. These results point out the potential of the procedure proposed as a starting point for further implementation of more complex effects.     

Domain decomposition and multigrid solvers for flow simulation in porous media on distributed memory parallel processors

Realistic simulations of fluid flow in oil reservoirs have been proven to be computationally intensive. In this work, techniques for solving large sparse systems of linear equations that arise in simulating these processes are developed for parallel computers such as INTEL hypercubes iPSC/2 and iPSC/860. This solver is based on a combined multigrid and domain decomposition approach. The Algorithm uses line corrections solved using a multigrid method, line Jacobi and block incomplete domain decomposition as an overall preconditioner for a conjugate gradient-like acceleration method, ORTHOMIN (k). This is shown to be a factor of ten times faster on a 32-processor hypercube compared to widely used sequential solvers. Three test problems are used to validate the results which include implicit wells and faults: The first is based on highly heterogeneous two-phase flow, the second on the SPE Third Comparative Solution and the third on real production compositional data.     

A study on boundary force model used in multiscale simulations with non-periodic boundary condition

This paper presents an investigation of the non-periodic boundary condition (NPBC) which is often used in multiscale atomistic–continuum simulations. The relationship between the boundary force exerted by the imaginary atoms outside the atomistic domain and the fluid state parameters including density and temperature at the boundary is studied. A fitting formula of the boundary force as a function of the fluid state has been proposed based on the relationship. The accuracy of the fitting formula is verified by the equilibrium molecular dynamics (MD) simulations. Poiseuille flow with viscous dissipation and unsteady heat transfer between two walls is then simulated using the proposed fitting formula. The elimination of density oscillation near the boundary of atomistic region and good agreement of velocity and temperature evolutions with time from pure MD and the multiscale simulations adopting NPBC further confirm the correctness of our fitting formula.     

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

We describe a parallel lattice-Boltzmann code for efficient simulation of fluid flow in complex geometries. The lattice-Boltzmann model and the structure of the code are discussed. The fluid solver is highly optimized and the resulting computational core is very fast. Furthermore, communication is minimized and the novel topology-aware domain decomposition technique is shown to be very effective for large systems, allowing us to tune code execution in geographically distributed cross-site simulations. The benchmarks presented indicate that very high performance can be achieved.     

An efficient parallel algorithm with application to computational fluid dynamics

When solving time-dependent partial differential equations on parallel computers using the nonoverlapping domain decomposition method, one often needs numerical boundary conditions on the boundaries between subdomains. These numerical boundary conditions can significantly affect the stability and accuracy of the final algorithm.In this paper, a stability and accuracy analysis of the existing methods for generating numerical boundary conditions will be presented, and a new approach based on explicit predictors and implicit correctors will be used to solve convection-diffusion equations on parallel computers, with application to aerospace engineering for the solution of Euler equations in computational fluid dynamics simulations. Both theoretical analyses and numerical results demonstrate significant improvement in stability and accuracy by using the new approach.     

Parallel Monte Carlo simulations by asynchronous domain decomposition

A simple general method for performing Metropolis Monte Carlo condensed matter simulations on parallel processors is examined. The method is based on the cyclic generation of temporary discrete domains within the system, which are separated by distances greater than the inter-particle interaction range. Particle configurations within each domain are then sampled independently by an assigned processor, whilst particles outside these domains are held fixed. Results for a simulated Lennard-Jones fluid confirm that the method rigorously satisfies the detailed balance condition, and that the efficiency of configurational sampling scales almost linearly with the number of processors. Furthermore, the number of iterations performed on a given processor can be essentially arbitrary, with very low levels of inter-process communication. Provided the CPU time per step is not state-dependent, the method can then be used to perform large calculations as unsupervised background tasks on heterogeneous networks.     

Efficient high-quality volume rendering of SPH data

High quality volume rendering of SPH data requires a complex order-dependent resampling of particle quantities along the view rays. In this paper we present an efficient approach to perform this task using a novel view-space discretization of the simulation domain. Our method draws upon recent work on GPU-based particle voxelization for the efficient resampling of particles into uniform grids. We propose a new technique that leverages a perspective grid to adaptively discretize the view-volume, giving rise to a continuous level-of-detail sampling structure and reducing memory requirements compared to a uniform grid. In combination with a level-of-detail representation of the particle set, the perspective grid allows effectively reducing the amount of primitives to be processed at run-time. We demonstrate the quality and performance of our method for the rendering of fluid and gas dynamics SPH simulations consisting of many millions of particles.     

Bivariate splines for fluid flows

We discuss numerical approximations of the 2D steady-state Navier-Stokes equations in stream function formulation using bivariate splines of arbitrary degree d and arbitrary smoothness r with r<d. We derive the discrete Navier-Stokes equations in terms of B-coefficients of bivariate splines over a triangulation, with curved boundary edges, of any given domain. Smoothness conditions and boundary conditions are enforced through Lagrange multipliers. The pressure is computed by solving a Poisson equation with Neumann boundary conditions. We have implemented this approach in MATLAB and our numerical experiments show that our method is effective. Numerical simulations of several fluid flows will be included to demonstrate the effectiveness of the bivariate spline method.     

Multi-Level Memory Structures for Simulating and Rendering Smoothed Particle Hydrodynamics

In this paper, we present a novel hash map-based sparse data structure for Smoothed Particle Hydrodynamics, which allows for efficient neighbourhood queries in spatially adaptive simulations as well as direct ray tracing of fluid surfaces. Neighbourhood queries for adaptive simulations are improved by using multiple independent data structures utilizing the same underlying self-similar particle ordering, to significantly reduce non-neighbourhood particle accesses. Direct ray tracing is performed using an auxiliary data structure, with constant memory consumption, which allows for efficient traversal of the hash map-based data structure as well as efficient intersection tests. Overall, our proposed method significantly improves the performance of spatially adaptive fluid simulations and allows for direct ray tracing of the fluid surface with little memory overhead.     

One-Dimensional Turbulence: A new approach to high-fidelity subgrid closure of turbulent flow simulations

Consideration of the requirements for robust, high-fidelity subgrid closure of large-eddy simulations of multiphysics turbulent flows indicates the need for a spatially and temporally resolved representation of fine-scale physical and chemical processes that are coupled to fluid motion. One-Dimensional Turbulence (ODT), a potentially cost-effective approach for this purpose, captures these couplings by means of a stochastic simulation implemented on a one-dimensional domain. A subgrid implementation of ODT is formulated and its potential advantages and limitations are assessed.