A coupled element-based finite-volume method for the solution of incompressible Navier-Stokes equations

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

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

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.

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.

Intelligent computing and simulation of magnetic field influence on Casson 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.

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

Despite significant progress in unstructured grid generation and employment, the robust employment of body-conforming coordinate systems promotes the workers to consider it as a major alternative to treat relatively complex flow fields in irregular geometries. Contrary to the laminar flow treatment, there are many ambiguities around treating turbulent flow on body-fitted coordinate system. The ambiguities are mainly originated from the curvature on the boundaries. Considering the past taken efforts in improving the results of treating turbulent flow on curvilinear coordinate system, we have extended a new formulation on body-fitted coordinate system using physical covariant velocities as the dependent variables in our algorithm. The chosen numerical method is finite volume. To suppress nonphysical solution on non-orthogonal grids, the advantages of staggered grid employment are utilized. To evaluate the performance of the newly developed formulation, we solve turbulent flow in complex geometries using different k-omega and k-epsilon turbulence models and compare their results with each other. The comparison indicates that the current formulation performs well using different turbulence models. In some cases, the results of a turbulence model show extra-ordinary advantages comparing with its employment in the other curvilinear coordinate formulations.

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

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.

A strongly conservative finite-volume procedure is presented for flows in complex geometries. The technique is based on a complete transformation of the governing equations, and physical velocity components, rather than the traditionally used Cartesian velocity components, are used as primitive variables. It was found that projecting the discretized vector transport equation in the direction of the covariant base vectors eliminated two substantial difficulties associated with flows in complex geometries. These difficulties stem from the presence of cross-pressure gradient terms and the need for a transformation between the different types of curvilinear velocity components in the mass conservation equation. It is shown that the present formulation ensures that the computational scheme is diagonally dominant. It was found that partially implicit treatment of nonorthogonal diffusion terms improved the convergence rate primarily for high-cell-Reynolds-number values. For nonstaggered grids, a new sol...

The purpose of this work is to introduce and validate a new staggered control volume method for the simulation of 2D/axisymmetric incompressible flows. The present study introduces a numerical procedure for solving the Navier–Stokes equations using the primitive variable formulation. The proposed method is an extension of the staggered grid methodology to unstructured triangular meshes for a control volume approach which features ease of handling of irregularly shaped domains. Two alternative elements are studied: transported scalars are stored either at the sides of an element or at its vertices, while the pressure is always stored at the centre of an element. Two interpolation functions were investigated for the integration of the momentum equations: a skewed mass-weighted upwind function and a flow-oriented exponential shape function. The momentum equations are solved over the covolume of a side or of a vertex and the pressure–velocity coupling makes use of a localized linear reconstruction of the discontinuous pressure field surrounding an element in order to obtain the pressure gradient terms. The pressure equation is obtained through a discretization of the continuity equation which uses the triangular element itself as the control volume. The method is applied to the simulation of the following test cases: backward-facing step flow, flow over a two-dimensional obstacle and flow in a pipe with sudden contraction of cross-sectional area. All numerical investigations are compared with experimental data from the literature. A grid convergence and error analysis study is also carried out for flow in a driven cavity. Results compared favourably with experimental data and so the new control volume scheme is deemed well suited for the prediction of incompressible flows in complex geometries. © 1997 John Wiley & Sons, Ltd.

We present an approach for the computation of error estimates in output functionals such as lift or drag for an embedded-boundary Cartesian mesh method. The approach relies on the solution of an adjoint equation and provides error estimates that can be used to both improve the accuracy of the functional and guide a mesh refinement procedure. This is a significant step in our research toward automating the simulation process for flows in complex geometries. The accuracy of the approach is verified on an analytic model problem and validated against common results in the literature. The robustness of the approach is examined for two test cases in three dimensions, namely, an isolated wing in transonic flow and a canard-controlled missile in supersonic flow. The results demonstrate that the approach is tolerant of coarse initial meshes. A practical advantage of the approach is that the adaptive mesh refinement may be performed with a fixed surface triangulation. In all cases considered, the approach provided reliable estimates of the output functional on computationally affordable meshes.

A multi-moment constrained finite volume method on arbitrary unstructured grids for incompressible flows