Finite Element Navier-Stokes Solver Research Articles

Numerical simulation of particle impact drilling (PID) systems: a one-way coupled approach

A numerical technique based on a CFD-DEM method is presented for the analysis of particle impact drilling (PID) systems. The method is built from a preexisting finite element Navier–Stokes solver for the fluid phase and a discrete element method module for the steel particles which this drilling technology utilizes to enhance the penetration rate. We provide a detailed description of the most relevant implementation issues, including our choice of the hydrodynamic forces appropriate for power-law fluids. We also discuss several critical aspects related to the validity of the simplifying assumptions that will be helpful to simulation engineers. We apply our simple, one-way coupled approach on designs provided by an industrial partner to illustrate its potential as an analysis tool for this promising drilling technology. The goal of this work is, on the one hand, to provide evidence for the usefulness of the numerical approach as a design tool for PID systems, as well as a detailed discussion of the different aspects to be assessed for an effective simulation campaign. On the other hand, a series of modeling aspects that require further work are identified. The focus of the simulation campaign presented is on the particles and fluid flow characteristics within the drill bit.

Assessment of unsteady flow predictions using hybrid deep learning based reduced-order models

In this paper, we present two deep learning-based hybrid data-driven reduced-order models for prediction of unsteady fluid flows. These hybrid models rely on recurrent neural networks (RNNs) to evolve low-dimensional states of unsteady fluid flow. The first model projects the high-fidelity time series data from a finite element Navier–Stokes solver to a low-dimensional subspace via proper orthogonal decomposition (POD). The time-dependent coefficients in the POD subspace are propagated by the recurrent net (closed-loop encoder–decoder updates) and mapped to a high-dimensional state via the mean flow field and the POD basis vectors. This model is referred to as POD-RNN. The second model, referred to as the convolution recurrent autoencoder network (CRAN), employs convolutional neural networks (instead of POD) as layers of linear kernels with nonlinear activations, to extract low-dimensional features from flow field snapshots. The flattened features are advanced using a recurrent (closed-loop manner) net and up-sampled (transpose convoluted) gradually to high-dimensional snapshots. Two benchmark problems of the flow past a cylinder and the flow past side-by-side cylinders are selected as the unsteady flow problems to assess the efficacy of these models. For the problem of the flow past a single cylinder, the performance of both the models is satisfactory and the CRAN model is found to be overkill. However, the CRAN model completely outperforms the POD-RNN model for a more complicated problem of the flow past side-by-side cylinders involving the complex effects of vortex-to-vortex and gap flow interactions. Owing to the scalability of the CRAN model, we introduce an observer-corrector method for calculation of integrated pressure force coefficients on the fluid–solid boundary on a reference grid. This reference grid, typically a structured and uniform grid, is used to interpolate scattered high-dimensional field data as snapshot images. These input images are convenient in training the CRAN model, which motivates us to further explore the application of the CRAN-based models for prediction of fluid flows.

The need for prediction in feedback control of a mixing layer

We present the first application of a Smith predictor in the model-based feedback control of a convectively unstable flow. The two-dimensional incompressible mixing layer is chosen as a plant and integrated with a finite-element Navier–Stokes solver. The flow is actuated by a modulation of the inflow mimicking a pulsed jet actuator. The state is monitored by a downstream velocity sensor. The control goal is to command the fluctuation level at the sensor location. As an additional challenge, the incoming shear-flow profile is perturbed by the small noise level. The starting point of this study is a standard low-order control without prediction. A Smith predictor is included to compensate for the convective delay from actuation to sensing. The closed-loop results with a Smith predictor are distinctly better than without it. The design of the linear robust controllers is performed with an open-loop control. We conjecture that predictors may augment feedback control for a large class of convectively unstable flows with significant time-delay from actuation to sensing.

Oasis: A high-level/high-performance open source Navier–Stokes solver

Oasis is a high-level/high-performance finite element Navier–Stokes solver written from scratch in Python using building blocks from the FEniCS project (fenicsproject.org). The solver is unstructured and targets large-scale applications in complex geometries on massively parallel clusters. Oasis utilizes MPI and interfaces, through FEniCS, to the linear algebra backend PETSc. Oasis advocates a high-level, programmable user interface through the creation of highly flexible Python modules for new problems. Through the high-level Python interface the user is placed in complete control of every aspect of the solver. A version of the solver, that is using piecewise linear elements for both velocity and pressure, is shown to reproduce very well the classical, spectral, turbulent channel simulations of Moser et al. (1999). The computational speed is strongly dominated by the iterative solvers provided by the linear algebra backend, which is arguably the best performance any similar implicit solver using PETSc may hope for. Higher order accuracy is also demonstrated and new solvers may be easily added within the same framework. Program summaryProgram title: OasisCatalogue identifier: AEUW_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEUW_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU Lesser GPL version 3 or any later versionNo. of lines in distributed program, including test data, etc.: 3491No. of bytes in distributed program, including test data, etc.: 266924Distribution format: tar.gzProgramming language: Python/C++.Computer: Any single laptop computer or cluster.Operating system: Any (Linux, OSX, Windows).RAM: a few Megabytes to several hundred GigabytesClassification: 12.External routines: FEniCS 1.3.0 (www.fenicsproject.org, that in turn depends on a number of external libraries like MPI, PETSc, Epetra, Boost and ParMetis)Nature of problem:Incompressible, Newtonian fluid flow.Solution method:The finite element method.Unusual features:FEniCS automatically generates and compiles low-level C++ code based on high-level Python code.Running time:The example provided takes a couple of minutes on a single processor.

A portable OpenCL-based unstructured edge-based finite element Navier–Stokes solver on graphics hardware

The rise of GPUs in modern high-performance systems increases the interest in porting portion of codes to such hardware. The current paper aims to explore the performance of a portable state-of-the-art FE solver on GPU accelerators. Performance evaluation is done by comparing with an existing highly-optimized OpenMP version of the solver. Code portability is ensured by writing the program using the OpenCL 1.1 specifications, while performance portability is sought through an optimization step performed at the beginning of the calculations to find out the optimal parameter set for the solver. The results show that the new implementation can be several times faster than the OpenMP version.

A modular numerical method for implicit 0D/3D coupling in cardiovascular finite element simulations

Implementation of boundary conditions in cardiovascular simulations poses numerical challenges due to the complex dynamic behavior of the circulatory system. The use of elaborate closed-loop lumped parameter network (LPN) models of the heart and the circulatory system as boundary conditions for computational fluid dynamics (CFD) simulations can provide valuable global dynamic information, particularly for patient specific simulations. In this paper, the necessary formulation for coupling an arbitrary LPN to a finite element Navier–Stokes solver is presented. A circuit analogy closed-loop LPN is solved numerically, and pressure and flow information is iteratively passed between the 0D and 3D domains at interface boundaries, resulting in a time-implicit scheme. For Neumann boundaries, an implicit method, regardless of the LPN, is presented to achieve the desired stability and convergence properties. Numerical procedures for passing flow and pressure information between the 0D and 3D domains are described, and implicit, semi-implicit, and explicit quasi-Newton formulations are compared. The issue of divergence in the presence of backflow is addressed via a stabilized boundary formulation. The requirements for coupling Dirichlet boundary conditions are also discussed and this approach is compared in detail to that of the Neumann coupled boundaries. Having the option to select between Dirichlet and Neumann coupled boundary conditions increases the flexibility of current framework by allowing a wide range of components to be used at the 3D–0D interface.

MASSIVELY PARALLEL I/O FOR PARTITIONED SOLVER SYSTEMS

This paper investigates I/O approaches for massively parallel partitioned solver systems. Typically, such systems have synchronized "loops" and write data in a well defined block I/O format consisting of a header and data portion. Our target use for such a parallel I/O subsystem is checkpoint-restart where writing is by far the most common operation and reading typically only happens during either initialization or during a restart operation because of a system failure. We compare four parallel I/O strategies: POSIX File Per Processor (1PFPP), "Poor-Man's" Parallel I/O (PMPIO), a synchronized parallel I/O (syncIO), and a "reduced blocking" strategy (rbIO). Performance tests executed on the Blue Gene/P at Argonne National Laboratory using real CFD solver data from PHASTA (an unstructured grid finite element Navier-Stokes solver) show that the syncIO strategy can achieve a read bandwidth of 47.4 GB/sec and a write bandwidth of 27.5 GB/sec using 128K processors. The "reduced-blocking" rbIO strategy achieves an actual writing performance of 17.8 GB/sec and the perceived writing performance is 166 TB/sec on Blue Gene/P using 128K processors.

Simulation of axisymmetric jets with a finite element Navier–Stokes solver and a multilevel VOF approach

A multilevel VOF approach has been coupled to an accurate finite element Navier–Stokes solver in axisymmetric geometry for the simulation of incompressible liquid jets with high density ratios. The representation of the color function over a fine grid has been introduced to reduce the discontinuity of the interface at the cell boundary. In the refined grid the automatic breakup and coalescence occur at a spatial scale much smaller than the coarse grid spacing. To reduce memory requirements, we have implemented on the fine grid a compact storage scheme which memorizes the color function data only in the mixed cells. The capillary force is computed by using the Laplace–Beltrami operator and a volumetric approach for the two principal curvatures. Several simulations of axisymmetric jets have been performed to show the accuracy and robustness of the proposed scheme.

Numerical simulation of glass fogging and defogging

A numerical procedure for the prediction of fogging and defogging phenomena is presented. The simulation involves the solution of an air flow field along a cold solid surface, the evaluation of the unsteady conduction through the solid itself, and a model for the heat and mass transfer within the thin water layer on the fogged surface. A suite of routines for the unsteady simulation of the water layer evolution is coupled with an equal order finite element Navier Stokes solver and a finite volume conduction code. The procedure is fully independent of the numerical details of the solid and fluid domain solvers. Two different coupling approaches may be followed: A loose one, where the Navier Stokes solution is used only for a steady state estimate of the heat transfer coefficient, or a close one, where the Navier Stokes, conduction and water layer codes are iterated simultaneously. The latter is required for the problem of natural convection, where temperature (and thus the energy balance of the water layer) and flow field are coupled. The water layer is modelled as a collection of closely packed tiny droplets, leaving a portion of dry area among them. The effect of the contact angle is taken into account, and physical assumptions allow to define the local ratio between wet and dry surface for both the fogging and defogging process. As a case study, a comparison with experimental data for a complete fogging and defogging cycle of a glass lens in natural convection is presented.

Turbulence modeling for computing viscous high-Reynolds-number flows on unstructured meshes

This paper develops an unstructured solution algorithm for the computation of compressible Reynolds-averaged Navier–Stokes (RANS) equations using turbulence models. An algebraic turbulence model based on the Baldwin and Lomax model (BLM) and a one-equation Baldwin and Barth model (BBM) have been implemented on fully unstructured meshes. The eddy viscosity is computed using the BLM along turbulence stations normal to the wall. For each turbulence station a number of turbulence sample points are generated. These sample points are used to gather the information required for computing the eddy viscosity. For each time-step, the current flow variables are interpolated from the unstructured mesh onto the turbulence sample points. The BLM is evaluated on the turbulence stations and the resulting eddy viscosity values are stored at each sample point and then interpolated back to the mesh. The alternating digital tree data structure is used to increase the efficiency of the searching for the element in the mesh that contains the sampling point. The implementation of BBM is using a Galerkin finite element approximation with an edge-based data structure. The integration in time of BBM is performed explicitly by the use of a Runge–Kutta multi-stage method. These models are validated using an efficient, unstructured, multigrid finite element Navier–Stokes solver, by comparing the computed results with available theoretical and experimental results.

An arbitrary Lagrangian-Eulerian finite element approach to non-steady state turbulent fluid flow with application to mould filling in casting

This paper presents a two-dimensional Lagrangian–Eulerian finite element approach of non-steady state turbulent fluid flows with free surfaces. The proposed model is based on a velocity–pressure finite element Navier–Stokes solver, including an augmented Lagrangian technique and an iterative resolution of Uzawa type. Turbulent effects are taken into account with the k–e two-equation statistical model. Mesh updating is carried out through an arbitrary Lagrangian–Eulerian (ALE) method in order to describe properly the free surface evolution. Three comparisons between experimental and numerical results illustrate the efficiency of the method. The first one is turbulent flow in an academic geometry, the second one is a mould filling in effective casting conditions and the third one is a precise confrontation to a water model. Copyright © 2000 John Wiley & Sons, Ltd.

Finite element Navier-Stokes solver for unstructured grids

A three-dimensional finite element Navier-Stokes solver has been developed for calculating transonic viscous flow on unstructured grids about complex aerodynamic configurations. The solver employs a second-orderaccurate space discretization of the Navier-Stokes equations obtained from a Galerkin weighted-residual approximation. Time discretization is obtained using either an explicit two-step Lax-Wendroff scheme, or an explicit multistep Runge-Kutta scheme. Boundary conditions are implemented using a procedure based on the method of characteristi cs. The overall solution procedure has been initially validated by calculating two- and three-dimensional inviscid and viscous transonic flows.