Incompressible Navier-Stokes inverse design method based on adaptive unstructured meshes
International Nuclear Information System (INIS)
Rahmati, M.T.; Charlesworth, D.; Zangeneh, M.
2005-01-01
An inverse method for blade design based on Navier-Stokes equations on adaptive unstructured meshes has been developed. In the method, unlike the method based on inviscid equations, the effect of viscosity is directly taken into account. In the method, the pressure (or pressure loading) is prescribed. The design method then computes the blade shape that would accomplish the target prescribed pressure distribution. The method is implemented using a cell-centered finite volume method, which solves the incompressible Navier-Stokes equations on unstructured meshes. An adaptive unstructured mesh method based on grid subdivision and local adaptive mesh method is utilized for increasing the accuracy. (author)
Parallelization of Unsteady Adaptive Mesh Refinement for Unstructured Navier-Stokes Solvers
Schwing, Alan M.; Nompelis, Ioannis; Candler, Graham V.
2014-01-01
This paper explores the implementation of the MPI parallelization in a Navier-Stokes solver using adaptive mesh re nement. Viscous and inviscid test problems are considered for the purpose of benchmarking, as are implicit and explicit time advancement methods. The main test problem for comparison includes e ects from boundary layers and other viscous features and requires a large number of grid points for accurate computation. Ex- perimental validation against double cone experiments in hypersonic ow are shown. The adaptive mesh re nement shows promise for a staple test problem in the hypersonic com- munity. Extension to more advanced techniques for more complicated ows is described.
Unstructured Navier-Stokes Analysis of Full TCA Configuration
Frink, Neal T.; Pirzadeh, Shahyar Z.
1999-01-01
This paper presents an Unstructured Navier-Stokes Analysis of Full TCA (Technology Concept Airplane) Configuration. The topics include: 1) Motivation; 2) Milestone and approach; 3) Overview of the unstructured-grid system; 4) Results on full TCA W/B/N/D/E configuration; 5) Concluding remarks; and 6) Future directions.
Finite volume methods for the incompressible Navier-Stokes equations on unstructured grids
Energy Technology Data Exchange (ETDEWEB)
Meese, Ernst Arne
1998-07-01
Most solution methods of computational fluid dynamics (CFD) use structured grids based on curvilinear coordinates for compliance with complex geometries. In a typical industry application, about 80% of the time used to produce the results is spent constructing computational grids. Recently the use of unstructured grids has been strongly advocated. For unstructured grids there are methods for generating them automatically on quite complex domains. This thesis focuses on the design of Navier-Stokes solvers that can cope with unstructured grids and ''low quality grids'', thus reducing the need for human intervention in the grid generation.
Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi
2016-05-01
A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.
A third-order gas-kinetic CPR method for the Euler and Navier-Stokes equations on triangular meshes
Zhang, Chao; Li, Qibing; Fu, Song; Wang, Z. J.
2018-06-01
A third-order accurate gas-kinetic scheme based on the correction procedure via reconstruction (CPR) framework is developed for the Euler and Navier-Stokes equations on triangular meshes. The scheme combines the accuracy and efficiency of the CPR formulation with the multidimensional characteristics and robustness of the gas-kinetic flux solver. Comparing with high-order finite volume gas-kinetic methods, the current scheme is more compact and efficient by avoiding wide stencils on unstructured meshes. Unlike the traditional CPR method where the inviscid and viscous terms are treated differently, the inviscid and viscous fluxes in the current scheme are coupled and computed uniformly through the kinetic evolution model. In addition, the present scheme adopts a fully coupled spatial and temporal gas distribution function for the flux evaluation, achieving high-order accuracy in both space and time within a single step. Numerical tests with a wide range of flow problems, from nearly incompressible to supersonic flows with strong shocks, for both inviscid and viscous problems, demonstrate the high accuracy and efficiency of the present scheme.
Tavelli, Maurizio; Dumbser, Michael
2017-07-01
We propose a new arbitrary high order accurate semi-implicit space-time discontinuous Galerkin (DG) method for the solution of the two and three dimensional compressible Euler and Navier-Stokes equations on staggered unstructured curved meshes. The method is pressure-based and semi-implicit and is able to deal with all Mach number flows. The new DG scheme extends the seminal ideas outlined in [1], where a second order semi-implicit finite volume method for the solution of the compressible Navier-Stokes equations with a general equation of state was introduced on staggered Cartesian grids. Regarding the high order extension we follow [2], where a staggered space-time DG scheme for the incompressible Navier-Stokes equations was presented. In our scheme, the discrete pressure is defined on the primal grid, while the discrete velocity field and the density are defined on a face-based staggered dual grid. Then, the mass conservation equation, as well as the nonlinear convective terms in the momentum equation and the transport of kinetic energy in the energy equation are discretized explicitly, while the pressure terms appearing in the momentum and energy equation are discretized implicitly. Formal substitution of the discrete momentum equation into the total energy conservation equation yields a linear system for only one unknown, namely the scalar pressure. Here the equation of state is assumed linear with respect to the pressure. The enthalpy and the kinetic energy are taken explicitly and are then updated using a simple Picard procedure. Thanks to the use of a staggered grid, the final pressure system is a very sparse block five-point system for three dimensional problems and it is a block four-point system in the two dimensional case. Furthermore, for high order in space and piecewise constant polynomials in time, the system is observed to be symmetric and positive definite. This allows to use fast linear solvers such as the conjugate gradient (CG) method. In
Rubin, S. G.
1982-01-01
Recent developments with finite-difference techniques are emphasized. The quotation marks reflect the fact that any finite discretization procedure can be included in this category. Many so-called finite element collocation and galerkin methods can be reproduced by appropriate forms of the differential equations and discretization formulas. Many of the difficulties encountered in early Navier-Stokes calculations were inherent not only in the choice of the different equations (accuracy), but also in the method of solution or choice of algorithm (convergence and stability, in the manner in which the dependent variables or discretized equations are related (coupling), in the manner that boundary conditions are applied, in the manner that the coordinate mesh is specified (grid generation), and finally, in recognizing that for many high Reynolds number flows not all contributions to the Navier-Stokes equations are necessarily of equal importance (parabolization, preferred direction, pressure interaction, asymptotic and mathematical character). It is these elements that are reviewed. Several Navier-Stokes and parabolized Navier-Stokes formulations are also presented.
International Nuclear Information System (INIS)
Vidovic, D.; Segal, A.; Wesseling, P.
2004-01-01
A method for linear reconstruction of staggered vector fields with special treatment of the divergence is presented. An upwind-biased finite volume scheme for solving the unsteady incompressible Navier-Stokes equations on staggered unstructured triangular grids that uses this reconstruction is described. The scheme is applied to three benchmark problems and is found to be superlinearly convergent in space
Duque, Earl P. N.; Biswas, Rupak; Strawn, Roger C.
1995-01-01
This paper summarizes a method that solves both the three dimensional thin-layer Navier-Stokes equations and the Euler equations using overset structured and solution adaptive unstructured grids with applications to helicopter rotor flowfields. The overset structured grids use an implicit finite-difference method to solve the thin-layer Navier-Stokes/Euler equations while the unstructured grid uses an explicit finite-volume method to solve the Euler equations. Solutions on a helicopter rotor in hover show the ability to accurately convect the rotor wake. However, isotropic subdivision of the tetrahedral mesh rapidly increases the overall problem size.
Three-Dimensional Navier-Stokes Calculations Using the Modified Space-Time CESE Method
Chang, Chau-lyan
2007-01-01
The space-time conservation element solution element (CESE) method is modified to address the robustness issues of high-aspect-ratio, viscous, near-wall meshes. In this new approach, the dependent variable gradients are evaluated using element edges and the corresponding neighboring solution elements while keeping the original flux integration procedure intact. As such, the excellent flux conservation property is retained and the new edge-based gradients evaluation significantly improves the robustness for high-aspect ratio meshes frequently encountered in three-dimensional, Navier-Stokes calculations. The order of accuracy of the proposed method is demonstrated for oblique acoustic wave propagation, shock-wave interaction, and hypersonic flows over a blunt body. The confirmed second-order convergence along with the enhanced robustness in handling hypersonic blunt body flow calculations makes the proposed approach a very competitive CFD framework for 3D Navier-Stokes simulations.
Wang, Zhiheng
2014-12-10
A meshless local radial basis function method is developed for two-dimensional incompressible Navier-Stokes equations. The distributed nodes used to store the variables are obtained by the philosophy of an unstructured mesh, which results in two main advantages of the method. One is that the unstructured nodes generation in the computational domain is quite simple, without much concern about the mesh quality; the other is that the localization of the obtained collocations for the discretization of equations is performed conveniently with the supporting nodes. The algebraic system is solved by a semi-implicit pseudo-time method, in which the convective and source terms are explicitly marched by the Runge-Kutta method, and the diffusive terms are implicitly solved. The proposed method is validated by several benchmark problems, including natural convection in a square cavity, the lid-driven cavity flow, and the natural convection in a square cavity containing a circular cylinder, and very good agreement with the existing results are obtained.
Directory of Open Access Journals (Sweden)
Yuan Li
2013-01-01
Full Text Available This paper presents two-level iteration penalty finite element methods to approximate the solution of the Navier-Stokes equations with friction boundary conditions. The basic idea is to solve the Navier-Stokes type variational inequality problem on a coarse mesh with mesh size H in combining with solving a Stokes, Oseen, or linearized Navier-Stokes type variational inequality problem for Stokes, Oseen, or Newton iteration on a fine mesh with mesh size h. The error estimate obtained in this paper shows that if H, h, and ε can be chosen appropriately, then these two-level iteration penalty methods are of the same convergence orders as the usual one-level iteration penalty method.
Unstructured mesh adaptivity for urban flooding modelling
Hu, R.; Fang, F.; Salinas, P.; Pain, C. C.
2018-05-01
Over the past few decades, urban floods have been gaining more attention due to their increase in frequency. To provide reliable flooding predictions in urban areas, various numerical models have been developed to perform high-resolution flood simulations. However, the use of high-resolution meshes across the whole computational domain causes a high computational burden. In this paper, a 2D control-volume and finite-element flood model using adaptive unstructured mesh technology has been developed. This adaptive unstructured mesh technique enables meshes to be adapted optimally in time and space in response to the evolving flow features, thus providing sufficient mesh resolution where and when it is required. It has the advantage of capturing the details of local flows and wetting and drying front while reducing the computational cost. Complex topographic features are represented accurately during the flooding process. For example, the high-resolution meshes around the buildings and steep regions are placed when the flooding water reaches these regions. In this work a flooding event that happened in 2002 in Glasgow, Scotland, United Kingdom has been simulated to demonstrate the capability of the adaptive unstructured mesh flooding model. The simulations have been performed using both fixed and adaptive unstructured meshes, and then results have been compared with those published 2D and 3D results. The presented method shows that the 2D adaptive mesh model provides accurate results while having a low computational cost.
Baseline Validation of Unstructured Grid Reynolds-Averaged Navier-Stokes Toward Flow Control
Joslin, Ronald D.; Viken, Sally A.
2001-01-01
The value of the use of the Reynolds-averaged Navier-Stokes methodology for active flow control applications is assessed. An experimental flow control database exists for a NACA0015 airfoil modified at the leading edge to implement a fluidic actuator; hence, this configuration is used. Computational results are documented for the baseline wing configuration (no control) with the experimental results and assumes two-dimensional flow. The baseline wing configuration has discontinuities at the leading edge, trailing edge, and aft of midchord on the upper surface. A limited number of active flow control applications have been tested in the laboratory and in flight. These applications include dynamic stall control using a deformable leading edge, separation control for takeoff and landing flight conditions using piezoelectric devices, pulsed vortex generators, zero-net-mass oscillations, and thrust vectoring with zero-net-mass piezoelectric-driven oscillatory actuation. As yet, there is no definitive comparison with experimental data that indicates current computational capabilities can quantitatively predict the large aerodynamic performance gains achieved with active flow control in the laboratory. However, one study using the Reynolds-averaged Navier-Stokes (RANS) methodology has shown good quantitative agreement with experimental results for an isolated zero-net-mass actuator. In addition, some recent studies have used RANS to demonstrate qualitative performance gains compared with the experimental data for separation control on an airfoil. Those quantitative comparisons for both baseline and flow control cases indicated that computational results were in poor quantitative agreement with the experiments. The current research thrust will investigate the potential use of an unstructured grid RANS approach to predict aerodynamic performance for active flow control applications building on the early studies. First the computational results must quantitatively match
Koren, B.
2013-01-01
De Navier-Stokes-vergelijkingen behoren tot de meest gebruikte vergelijkingen voor de berekening van gas- en vloeistofstromingen. Op de Vakantiecursus 2013 van het Platform Wiskunde Nederland vertelt Barry Koren over de Navier-Stokes-vergelijkingen, over stromingsleer en over openstaande
Carpenter, Mark H.; Parsani, Matteo; Fisher, Travis C.; Nielsen, Eric J.
2015-01-01
Staggered grid, entropy stable discontinuous spectral collocation operators of any order are developed for Burgers' and the compressible Navier-Stokes equations on unstructured hexahedral elements. This generalization of previous entropy stable spectral collocation work [1, 2], extends the applicable set of points from tensor product, Legendre-Gauss-Lobatto (LGL) to a combination of tensor product Legendre-Gauss (LG) and LGL points. The new semi-discrete operators discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality for both Burgers' and the compressible Navier-Stokes equations in three spatial dimensions. They are valid for smooth as well as discontinuous flows. The staggered LG and conventional LGL point formulations are compared on several challenging test problems. The staggered LG operators are significantly more accurate, although more costly to implement. The LG and LGL operators exhibit similar robustness, as is demonstrated using test problems known to be problematic for operators that lack a nonlinearly stability proof for the compressible Navier-Stokes equations (e.g., discontinuous Galerkin, spectral difference, or flux reconstruction operators).
Finite Macro-Element Mesh Deformation in a Structured Multi-Block Navier-Stokes Code
Bartels, Robert E.
2005-01-01
A mesh deformation scheme is developed for a structured multi-block Navier-Stokes code consisting of two steps. The first step is a finite element solution of either user defined or automatically generated macro-elements. Macro-elements are hexagonal finite elements created from a subset of points from the full mesh. When assembled, the finite element system spans the complete flow domain. Macro-element moduli vary according to the distance to the nearest surface, resulting in extremely stiff elements near a moving surface and very pliable elements away from boundaries. Solution of the finite element system for the imposed boundary deflections generally produces smoothly varying nodal deflections. The manner in which distance to the nearest surface has been found to critically influence the quality of the element deformation. The second step is a transfinite interpolation which distributes the macro-element nodal deflections to the remaining fluid mesh points. The scheme is demonstrated for several two-dimensional applications.
Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations
Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi
2017-01-01
A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy
MPI to Coarray Fortran: Experiences with a CFD Solver for Unstructured Meshes
Directory of Open Access Journals (Sweden)
Anuj Sharma
2017-01-01
Full Text Available High-resolution numerical methods and unstructured meshes are required in many applications of Computational Fluid Dynamics (CFD. These methods are quite computationally expensive and hence benefit from being parallelized. Message Passing Interface (MPI has been utilized traditionally as a parallelization strategy. However, the inherent complexity of MPI contributes further to the existing complexity of the CFD scientific codes. The Partitioned Global Address Space (PGAS parallelization paradigm was introduced in an attempt to improve the clarity of the parallel implementation. We present our experiences of converting an unstructured high-resolution compressible Navier-Stokes CFD solver from MPI to PGAS Coarray Fortran. We present the challenges, methodology, and performance measurements of our approach using Coarray Fortran. With the Cray compiler, we observe Coarray Fortran as a viable alternative to MPI. We are hopeful that Intel and open-source implementations could be utilized in the future.
Navier-Stokes Aerodynamic Simulation of the V-22 Osprey on the Intel Paragon MPP
Vadyak, Joseph; Shrewsbury, George E.; Narramore, Jim C.; Montry, Gary; Holst, Terry; Kwak, Dochan (Technical Monitor)
1995-01-01
The paper will describe the Development of a general three-dimensional multiple grid zone Navier-Stokes flowfield simulation program (ENS3D-MPP) designed for efficient execution on the Intel Paragon Massively Parallel Processor (MPP) supercomputer, and the subsequent application of this method to the prediction of the viscous flowfield about the V-22 Osprey tiltrotor vehicle. The flowfield simulation code solves the thin Layer or full Navier-Stoke's equation - for viscous flow modeling, or the Euler equations for inviscid flow modeling on a structured multi-zone mesh. In the present paper only viscous simulations will be shown. The governing difference equations are solved using a time marching implicit approximate factorization method with either TVD upwind or central differencing used for the convective terms and central differencing used for the viscous diffusion terms. Steady state or Lime accurate solutions can be calculated. The present paper will focus on steady state applications, although time accurate solution analysis is the ultimate goal of this effort. Laminar viscosity is calculated using Sutherland's law and the Baldwin-Lomax two layer algebraic turbulence model is used to compute the eddy viscosity. The Simulation method uses an arbitrary block, curvilinear grid topology. An automatic grid adaption scheme is incorporated which concentrates grid points in high density gradient regions. A variety of user-specified boundary conditions are available. This paper will present the application of the scalable and superscalable versions to the steady state viscous flow analysis of the V-22 Osprey using a multiple zone global mesh. The mesh consists of a series of sheared cartesian grid blocks with polar grids embedded within to better simulate the wing tip mounted nacelle. MPP solutions will be shown in comparison to equivalent Cray C-90 results and also in comparison to experimental data. Discussions on meshing considerations, wall clock execution time
Shen, Hua
2018-05-28
We construct positivity-preserving space–time conservation element and solution element (CE/SE) schemes for solving the compressible Euler and Navier–Stokes equations on hybrid unstructured meshes consisting of triangular and rectangular elements. The schemes use an a posteriori limiter to prevent negative densities and pressures based on the premise of preserving optimal accuracy. The limiter enforces a constraint for spatial derivatives and does not change the conservative property of CE/SE schemes. Several numerical examples suggest that the proposed schemes preserve accuracy for smooth flows and strictly preserve positivity of densities and pressures for the problems involving near vacuum and very strong discontinuities.
Unsteady Navier-Stokes computations over airfoils using both fixed and dynamic meshes
Rumsey, Christopher L.; Anderson, W. Kyle
1989-01-01
A finite volume implicit approximate factorization method which solves the thin layer Navier-Stokes equations was used to predict unsteady turbulent flow airfoil behavior. At a constant angle of attack of 16 deg, the NACA 0012 airfoil exhibits an unsteady periodic flow field with the lift coefficient oscillating between 0.89 and 1.60. The Strouhal number is 0.028. Results are similar at 18 deg, with a Strouhal number of 0.033. A leading edge vortex is shed periodically near maximum lift. Dynamic mesh solutions for unstalled airfoil flows show general agreement with experimental pressure coefficients. However, moment coefficients and the maximum lift value are underpredicted. The deep stall case shows some agreement with experiment for increasing angle of attack, but is only qualitatively comparable past stall and for decreasing angle of attack.
Venkatachari, Balaji Shankar; Streett, Craig L.; Chang, Chau-Lyan; Friedlander, David J.; Wang, Xiao-Yen; Chang, Sin-Chung
2016-01-01
Despite decades of development of unstructured mesh methods, high-fidelity time-accurate simulations are still predominantly carried out on structured, or unstructured hexahedral meshes by using high-order finite-difference, weighted essentially non-oscillatory (WENO), or hybrid schemes formed by their combinations. In this work, the space-time conservation element solution element (CESE) method is used to simulate several flow problems including supersonic jet/shock interaction and its impact on launch vehicle acoustics, and direct numerical simulations of turbulent flows using tetrahedral meshes. This paper provides a status report for the continuing development of the space-time conservation element solution element (CESE) numerical and software framework under the Revolutionary Computational Aerosciences (RCA) project. Solution accuracy and large-scale parallel performance of the numerical framework is assessed with the goal of providing a viable paradigm for future high-fidelity flow physics simulations.
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Johnston, Hans; Liu Jianguo
2004-01-01
We present numerical schemes for the incompressible Navier-Stokes equations based on a primitive variable formulation in which the incompressibility constraint has been replaced by a pressure Poisson equation. The pressure is treated explicitly in time, completely decoupling the computation of the momentum and kinematic equations. The result is a class of extremely efficient Navier-Stokes solvers. Full time accuracy is achieved for all flow variables. The key to the schemes is a Neumann boundary condition for the pressure Poisson equation which enforces the incompressibility condition for the velocity field. Irrespective of explicit or implicit time discretization of the viscous term in the momentum equation the explicit time discretization of the pressure term does not affect the time step constraint. Indeed, we prove unconditional stability of the new formulation for the Stokes equation with explicit treatment of the pressure term and first or second order implicit treatment of the viscous term. Systematic numerical experiments for the full Navier-Stokes equations indicate that a second order implicit time discretization of the viscous term, with the pressure and convective terms treated explicitly, is stable under the standard CFL condition. Additionally, various numerical examples are presented, including both implicit and explicit time discretizations, using spectral and finite difference spatial discretizations, demonstrating the accuracy, flexibility and efficiency of this class of schemes. In particular, a Galerkin formulation is presented requiring only C 0 elements to implement
Time evolution of the eddy viscosity in two-dimensional navier-stokes flow
Chaves; Gama
2000-02-01
The time evolution of the eddy viscosity associated with an unforced two-dimensional incompressible Navier-Stokes flow is analyzed by direct numerical simulation. The initial condition is such that the eddy viscosity is isotropic and negative. It is shown by concrete examples that the Navier-Stokes dynamics stabilizes negative eddy viscosity effects. In other words, this dynamics moves monotonically the initial negative eddy viscosity to positive values before relaxation due to viscous term occurs.
Samtaney, Ravi; Mohamed, Mamdouh; Hirani, Anil
2015-11-01
We present examples of numerical solutions of incompressible flow on 2D curved domains. The Navier-Stokes equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. A conservative discretization of Navier-Stokes equations on simplicial meshes is developed based on discrete exterior calculus (DEC). The discretization is then carried out by substituting the corresponding discrete operators based on the DEC framework. By construction, the method is conservative in that both the discrete divergence and circulation are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step. Numerical examples include Taylor vortices on a sphere, Stuart vortices on a sphere, and flow past a cylinder on domains with varying curvature. Supported by the KAUST Office of Competitive Research Funds under Award No. URF/1/1401-01.
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Batcho, P.F.; Karniadakis, G.E.
1994-01-01
The present study focuses on the solution of the incompressible Navier-Stokes equations in general, non-separable domains, and employs a Galerkin projection of divergence-free vector functions as a trail basis. This basis is obtained from the solution of a generalized constrained Stokes eigen-problem in the domain of interest. Faster convergence can be achieved by constructing a singular Stokes eigen-problem in which the Stokes operator is modified to include a variable coefficient which vanishes at the domain boundaries. The convergence properties of such functions are advantageous in a least squares sense and are shown to produce significantly better approximations to the solution of the Navier-Stokes equations in post-critical states where unsteadiness characterizes the flowfield. Solutions for the eigen-systems are efficiently accomplished using a combined Lanczos-Uzawa algorithm and spectral element discretizations. Results are presented for different simulations using these global spectral trial basis on non-separable and multiply-connected domains. It is confirmed that faster convergence is obtained using the singular eigen-expansions in approximating stationary Navier-Stokes solutions in general domains. It is also shown that 100-mode expansions of time-dependent solutions based on the singular Stokes eigenfunctions are sufficient to accurately predict the dynamics of flows in such domains, including Hopf bifurcations, intermittency, and details of flow structures
Torre, F. la; Kenjeres, S.; Kleijn, C.R.; Moerel, J.L.P.A.
2009-01-01
Both the particle based Direct Simulation Monte Carlo (DSMC) method and a compressible Navier-Stokes based continuum method are used to investigate the flow inside micronozzles and to predict the performance of such devices. For the Navier-Stokes approach, both slip and no-slip boundary conditions
Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations
Mohamed, Mamdouh S.
2017-05-23
A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy otherwise. The mimetic character of many of the DEC operators provides exact conservation of both mass and vorticity, in addition to superior kinetic energy conservation. The employment of barycentric Hodge star allows the discretization to admit arbitrary simplicial meshes. The discretization scheme is presented along with various numerical test cases demonstrating its main characteristics.
Development and verification of unstructured adaptive mesh technique with edge compatibility
International Nuclear Information System (INIS)
Ito, Kei; Ohshima, Hiroyuki; Kunugi, Tomoaki
2010-01-01
In the design study of the large-sized sodium-cooled fast reactor (JSFR), one key issue is suppression of gas entrainment (GE) phenomena at a gas-liquid interface. Therefore, the authors have been developed a high-precision CFD algorithm to evaluate the GE phenomena accurately. The CFD algorithm has been developed on unstructured meshes to establish an accurate modeling of JSFR system. For two-phase interfacial flow simulations, a high-precision volume-of-fluid algorithm is employed. It was confirmed that the developed CFD algorithm could reproduce the GE phenomena in a simple GE experiment. Recently, the authors have been developed an important technique for the simulation of the GE phenomena in JSFR. That is an unstructured adaptive mesh technique which can apply fine cells dynamically to the region where the GE occurs in JSFR. In this paper, as a part of the development, a two-dimensional unstructured adaptive mesh technique is discussed. In the two-dimensional adaptive mesh technique, each cell is refined isotropically to reduce distortions of the mesh. In addition, connection cells are formed to eliminate the edge incompatibility between refined and non-refined cells. The two-dimensional unstructured adaptive mesh technique is verified by solving well-known lid-driven cavity flow problem. As a result, the two-dimensional unstructured adaptive mesh technique succeeds in providing a high-precision solution, even though poor-quality distorted initial mesh is employed. In addition, the simulation error on the two-dimensional unstructured adaptive mesh is much less than the error on the structured mesh with a larger number of cells. (author)
Unstructured Finite Elements and Dynamic Meshing for Explicit Phase Tracking in Multiphase Problems
Chandra, Anirban; Yang, Fan; Zhang, Yu; Shams, Ehsan; Sahni, Onkar; Oberai, Assad; Shephard, Mark
2017-11-01
Multi-phase processes involving phase change at interfaces, such as evaporation of a liquid or combustion of a solid, represent an interesting class of problems with varied applications. Large density ratio across phases, discontinuous fields at the interface and rapidly evolving geometries are some of the inherent challenges which influence the numerical modeling of multi-phase phase change problems. In this work, a mathematically consistent and robust computational approach to address these issues is presented. We use stabilized finite element methods on mixed topology unstructured grids for solving the compressible Navier-Stokes equations. Appropriate jump conditions derived from conservations laws across the interface are handled by using discontinuous interpolations, while the continuity of temperature and tangential velocity is enforced using a penalty parameter. The arbitrary Lagrangian-Eulerian (ALE) technique is utilized to explicitly track the interface motion. Mesh at the interface is constrained to move with the interface while elsewhere it is moved using the linear elasticity analogy. Repositioning is applied to the layered mesh that maintains its structure and normal resolution. In addition, mesh modification is used to preserve the quality of the volumetric mesh. This work is supported by the U.S. Army Grants W911NF1410301 and W911NF16C0117.
Parsani, Matteo
2016-10-04
Staggered grid, entropy stable discontinuous spectral collocation operators of any order are developed for the compressible Euler and Navier--Stokes equations on unstructured hexahedral elements. This generalization of previous entropy stable spectral collocation work [M. H. Carpenter, T. C. Fisher, E. J. Nielsen, and S. H. Frankel, SIAM J. Sci. Comput., 36 (2014), pp. B835--B867, M. Parsani, M. H. Carpenter, and E. J. Nielsen, J. Comput. Phys., 292 (2015), pp. 88--113], extends the applicable set of points from tensor product, Legendre--Gauss--Lobatto (LGL), to a combination of tensor product Legendre--Gauss (LG) and LGL points. The new semidiscrete operators discretely conserve mass, momentum, energy, and satisfy a mathematical entropy inequality for the compressible Navier--Stokes equations in three spatial dimensions. They are valid for smooth as well as discontinuous flows. The staggered LG and conventional LGL point formulations are compared on several challenging test problems. The staggered LG operators are significantly more accurate, although more costly from a theoretical point of view. The LG and LGL operators exhibit similar robustness, as is demonstrated using test problems known to be problematic for operators that lack a nonlinear stability proof for the compressible Navier--Stokes equations (e.g., discontinuous Galerkin, spectral difference, or flux reconstruction operators).
Homogenization of Stokes and Navier-Stokes equations
International Nuclear Information System (INIS)
Allaire, G.
1990-04-01
This thesis is devoted to homogenization of Stokes and Navier-Stokes equations with a Dirichlet boundary condition in a domain containing many tiny obstacles. Tipycally those obstacles are distributed at the modes of a periodic lattice with same small period in each axe's direction, and their size is always asymptotically smaller than the lattice's step. With the help of the energy method, and thanks to a suitable pressure's extension, we prove the convergence of the homogenization process when the lattice's step tends to zero (and thus the number of obstacles tends to infinity). For a so-called critical size of the obstacles, the homogenized problem turns out to be a Brinkman's law (i.e. Stokes or Navier-Stokes equation plus a linear zero-order term for the velocity in the momentum equation). For obstacles which have a size smaller than the critical one, the limit problem reduces to the initial Stokes or Navier-Stokes equations, while for larger sizes the homogenized problem a Darcy's law. Furthermore, those results have been extended to the case of obstacles included in a hyperplane, and we establish a simple model of fluid flows through grids, which is based on a special form of Brinkman's law [fr
MHD simulations on an unstructured mesh
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Strauss, H.R.; Park, W.
1996-01-01
We describe work on a full MHD code using an unstructured mesh. MH3D++ is an extension of the PPPL MH3D resistive full MHD code. MH3D++ replaces the structured mesh and finite difference / fourier discretization of MH3D with an unstructured mesh and finite element / fourier discretization. Low level routines which perform differential operations, solution of PDEs such as Poisson's equation, and graphics, are encapsulated in C++ objects to isolate the finite element operations from the higher level code. The high level code is the same, whether it is run in structured or unstructured mesh versions. This allows the unstructured mesh version to be benchmarked against the structured mesh version. As a preliminary example, disruptions in DIIID reverse shear equilibria are studied numerically with the MH3D++ code. Numerical equilibria were first produced starting with an EQDSK file containing equilibrium data of a DIII-D L-mode negative central shear discharge. Using these equilibria, the linearized equations are time advanced to get the toroidal mode number n = 1 linear growth rate and eigenmode, which is resistively unstable. The equilibrium and linear mode are used to initialize 3D nonlinear runs. An example shows poloidal slices of 3D pressure surfaces: initially, on the left, and at an intermediate time, on the right
Isogeometric analysis of the isothermal Navier-Stokes-Korteweg equations
Gomez, Hector
2010-05-01
This paper is devoted to the numerical simulation of the Navier-Stokes-Korteweg equations, a phase-field model for water/water-vapor two-phase flows. We develop a numerical formulation based on isogeometric analysis that permits straightforward treatment of the higher-order partial-differential operator that represents capillarity. We introduce a new refinement methodology that desensitizes the numerical solution to the computational mesh and achieves mesh invariant solutions. Finally, we present several numerical examples in two and three dimensions that illustrate the effectiveness and robustness of our approach. © 2010 Elsevier B.V.
Perturbation of eigenvalues of preconditioned Navier-Stokes operators
Energy Technology Data Exchange (ETDEWEB)
Elman, H.C. [Univ. of Maryland, College Park, MD (United States)
1996-12-31
We study the sensitivity of algebraic eigenvalue problems associated with matrices arising from linearization and discretization of the steady-state Navier-Stokes equations. In particular, for several choices of preconditioners applied to the system of discrete equations, we derive upper bounds on perturbations of eigenvalues as functions of the viscosity and discretization mesh size. The bounds suggest that the sensitivity of the eigenvalues is at worst linear in the inverse of the viscosity and quadratic in the inverse of the mesh size, and that scaling can be used to decrease the sensitivity in some cases. Experimental results supplement these results and confirm the relatively mild dependence on viscosity. They also indicate a dependence on the mesh size of magnitude smaller than the analysis suggests.
Maljaars, Jakob M.; Labeur, Robert Jan; Möller, Matthias
2018-04-01
A generic particle-mesh method using a hybridized discontinuous Galerkin (HDG) framework is presented and validated for the solution of the incompressible Navier-Stokes equations. Building upon particle-in-cell concepts, the method is formulated in terms of an operator splitting technique in which Lagrangian particles are used to discretize an advection operator, and an Eulerian mesh-based HDG method is employed for the constitutive modeling to account for the inter-particle interactions. Key to the method is the variational framework provided by the HDG method. This allows to formulate the projections between the Lagrangian particle space and the Eulerian finite element space in terms of local (i.e. cellwise) ℓ2-projections efficiently. Furthermore, exploiting the HDG framework for solving the constitutive equations results in velocity fields which excellently approach the incompressibility constraint in a local sense. By advecting the particles through these velocity fields, the particle distribution remains uniform over time, obviating the need for additional quality control. The presented methodology allows for a straightforward extension to arbitrary-order spatial accuracy on general meshes. A range of numerical examples shows that optimal convergence rates are obtained in space and, given the particular time stepping strategy, second-order accuracy is obtained in time. The model capabilities are further demonstrated by presenting results for the flow over a backward facing step and for the flow around a cylinder.
International Nuclear Information System (INIS)
Rosenfeld, M.; Kwak, D.; Vinokur, M.
1988-01-01
A solution method based on a fractional step approach is developed for obtaining time-dependent solutions of the three-dimensional, incompressible Navier-Stokes equations in generalized coordinate systems. The governing equations are discretized conservatively by finite volumes using a staggered mesh system. The primitive variable formulation uses the volume fluxes across the faces of each computational cell as dependent variables. This procedure, combined with accurate and consistent approximations of geometric parameters, is done to satisfy the discretized mass conservation equation to machine accuracy as well as to gain favorable convergence properties of the Poisson solver. The discretized equations are second-order-accurate in time and space and no smoothing terms are added. An approximate-factorization scheme is implemented in solving the momentum equations. A novel ZEBRA scheme with four-color ordering is devised for the efficient solution of the Poisson equation. Several two and three-dimensional solutions are compared with other numerical and experimental results to validate the present method. 23 references
Stochastic 2-D Navier-Stokes Equation
International Nuclear Information System (INIS)
Menaldi, J.L.; Sritharan, S.S.
2002-01-01
In this paper we prove the existence and uniqueness of strong solutions for the stochastic Navier-Stokes equation in bounded and unbounded domains. These solutions are stochastic analogs of the classical Lions-Prodi solutions to the deterministic Navier-Stokes equation. Local monotonicity of the nonlinearity is exploited to obtain the solutions in a given probability space and this significantly improves the earlier techniques for obtaining strong solutions, which depended on pathwise solutions to the Navier-Stokes martingale problem where the probability space is also obtained as a part of the solution
Chang, Sin-Chung; Chang, Chau-Lyan; Yen, Joseph C.
2013-01-01
In the multidimensional CESE development, triangles and tetrahedra turn out to be the most natural building blocks for 2D and 3D spatial meshes. As such the CESE method is compatible with the simplest unstructured meshes and thus can be easily applied to solve problems with complex geometries. However, because the method uses space-time staggered stencils, solution decoupling may become a real nuisance in applications involving unstructured meshes. In this paper we will describe a simple and general remedy which, according to numerical experiments, has removed any possibility of solution decoupling. Moreover, in a real-world viscous flow simulation near a solid wall, one often encounters a case where a boundary with high curvature or sharp corner is surrounded by triangular/tetrahedral meshes of extremely high aspect ratio (up to 106). For such an extreme case, the spatial projection of a space-time compounded conservation element constructed using the original CESE design may become highly concave and thus its centroid (referred to as a spatial solution point) may lie far outside of the spatial projection. It could even be embedded beyond a solid wall boundary and causes serious numerical difficulties. In this paper we will also present a new procedure for constructing conservation elements and solution elements which effectively overcomes the difficulties associated with the original design. Another difficulty issue which was addressed more recently is the wellknown fact that accuracy of gradient computations involving triangular/tetrahedral grids deteriorates rapidly as the aspect ratio of grid cells increases. The root cause of this difficulty was clearly identified and several remedies to overcome it were found through a rigorous mathematical analysis. However, because of the length of the current paper and the complexity of mathematics involved, this new work will be presented in another paper.
International Nuclear Information System (INIS)
Liu Miaoer; Ren Yuxin; Zhang Hanxin
2004-01-01
In this paper, a continuous projection method is designed and analyzed. The continuous projection method consists of a set of partial differential equations which can be regarded as an approximation of the Navier-Stokes (N-S) equations in each time interval of a given time discretization. The local truncation error (LTE) analysis is applied to the continuous projection methods, which yields a sufficient condition for the continuous projection methods to be temporally second order accurate. Based on this sufficient condition, a fully second order accurate discrete projection method is proposed. A heuristic stability analysis is performed to this projection method showing that the present projection method can be stable. The stability of the present scheme is further verified through numerical experiments. The second order accuracy of the present projection method is confirmed by several numerical test cases
International Nuclear Information System (INIS)
Pontaza, J.P.; Reddy, J.N.
2004-01-01
We consider least-squares finite element models for the numerical solution of the non-stationary Navier-Stokes equations governing viscous incompressible fluid flows. The paper presents a formulation where the effects of space and time are coupled, resulting in a true space-time least-squares minimization procedure, as opposed to a space-time decoupled formulation where a least-squares minimization procedure is performed in space at each time step. The formulation is first presented for the linear advection-diffusion equation and then extended to the Navier-Stokes equations. The formulation has no time step stability restrictions and is spectrally accurate in both space and time. To allow the use of practical C 0 element expansions in the resulting finite element model, the Navier-Stokes equations are expressed as an equivalent set of first-order equations by introducing vorticity as an additional independent variable and the least-squares method is used to develop the finite element model of the governing equations. High-order element expansions are used to construct the discrete model. The discrete model thus obtained is linearized by Newton's method, resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method in matrix-free form. Spectral convergence of the L 2 least-squares functional and L 2 error norms in space-time is verified using a smooth solution to the two-dimensional non-stationary incompressible Navier-Stokes equations. Numerical results are presented for impulsively started lid-driven cavity flow, oscillatory lid-driven cavity flow, transient flow over a backward-facing step, and flow around a circular cylinder; the results demonstrate the predictive capability and robustness of the proposed formulation. Even though the space-time coupled formulation is emphasized, we also present the formulation and numerical results for least
From Petrov-Einstein to Navier-Stokes
Lysov, Vyacheslav
The fluid/gravity correspondence relates solutions of the incompressible Navier-Stokes equation to metrics which solve the Einstein equations. We propose propose two possible approaches to establish this correspondence: perturbative expansion for shear modes and large mean curvature expansion for algebraically special metrics. We show by explicit construction that for every solution of the incompressible Navier-Stokes equation in p+1 dimensions, there is an associated "dual" solution of the vacuum Einstein equations in p+2 dimensions. The dual geometry has an intrinsically flat time-like boundary segment whose extrinsic curvature is given by the stress tensor of the Navier-Stokes fluid. We consider a "near-horizon" limit in which hypersurface becomes highly accelerated. The near-horizon expansion in gravity is shown to be mathematically equivalent to the hydrodynamic expansion in fluid dynamics, and the Einstein equation reduces to the incompressible Navier-Stokes equation. It is shown that imposing a Petrov type I condition on the hypersurface geometry reduces the degrees of freedom in the extrinsic curvature to those of a fluid. Moreover, expanding around a limit in which the mean curvature of the embedding diverges, the leading-order Einstein constraint equations on hypersurface are shown to reduce to the non-linear incompressible Navier-Stokes equation for a fluid moving in hypersurface. We extend the fluid/gravity correspondence to include the magnetohydrodynamics/gravity correspondence, which translates solutions of the equations of magnetohydrodynamics (describing charged fluids) into geometries that satisfy the Einstein-Maxwell equations. We present an explicit example of this new correspondence in the context of flat Minkowski space. We show that a perturbative deformation of the Rindler wedge satisfies the Einstein-Maxwell equations provided that the parameters appearing in the expansion, which we interpret as fluid fields, satisfy the
Self-similarity in incompressible Navier-Stokes equations.
Ercan, Ali; Kavvas, M Levent
2015-12-01
The self-similarity conditions of the 3-dimensional (3D) incompressible Navier-Stokes equations are obtained by utilizing one-parameter Lie group of point scaling transformations. It is found that the scaling exponents of length dimensions in i = 1, 2, 3 coordinates in 3-dimensions are not arbitrary but equal for the self-similarity of 3D incompressible Navier-Stokes equations. It is also shown that the self-similarity in this particular flow process can be achieved in different time and space scales when the viscosity of the fluid is also scaled in addition to other flow variables. In other words, the self-similarity of Navier-Stokes equations is achievable under different fluid environments in the same or different gravity conditions. Self-similarity criteria due to initial and boundary conditions are also presented. Utilizing the proposed self-similarity conditions of the 3D hydrodynamic flow process, the value of a flow variable at a specified time and space can be scaled to a corresponding value in a self-similar domain at the corresponding time and space.
Yang, Xiaoquan; Cheng, Jian; Liu, Tiegang; Luo, Hong
2015-11-01
The direct discontinuous Galerkin (DDG) method based on a traditional discontinuous Galerkin (DG) formulation is extended and implemented for solving the compressible Navier-Stokes equations on arbitrary grids. Compared to the widely used second Bassi-Rebay (BR2) scheme for the discretization of diffusive fluxes, the DDG method has two attractive features: first, it is simple to implement as it is directly based on the weak form, and therefore there is no need for any local or global lifting operator; second, it can deliver comparable results, if not better than BR2 scheme, in a more efficient way with much less CPU time. Two approaches to perform the DDG flux for the Navier- Stokes equations are presented in this work, one is based on conservative variables, the other is based on primitive variables. In the implementation of the DDG method for arbitrary grid, the definition of mesh size plays a critical role as the formation of viscous flux explicitly depends on the geometry. A variety of test cases are presented to demonstrate the accuracy and efficiency of the DDG method for discretizing the viscous fluxes in the compressible Navier-Stokes equations on arbitrary grids.
Parallel adaptive simulations on unstructured meshes
International Nuclear Information System (INIS)
Shephard, M S; Jansen, K E; Sahni, O; Diachin, L A
2007-01-01
This paper discusses methods being developed by the ITAPS center to support the execution of parallel adaptive simulations on unstructured meshes. The paper first outlines the ITAPS approach to the development of interoperable mesh, geometry and field services to support the needs of SciDAC application in these areas. The paper then demonstrates the ability of unstructured adaptive meshing methods built on such interoperable services to effectively solve important physics problems. Attention is then focused on ITAPs' developing ability to solve adaptive unstructured mesh problems on massively parallel computers
Simulation of time-dependent free-surface Navier-Stokes flows
International Nuclear Information System (INIS)
Muldowney, G.P.
1989-01-01
Two numerical methods for simulation of time-dependent free-surface Navier-Stokes flows are developed. Both techniques are based on semi-implicit time advancement of the momentum equations, integral formulation of the spatial problem at each timestep, and spectral-element discretization to solve the resulting integral equation. Central to each algorithm is a boundary-specific solution step which permits the spatial treatment in two dimensions to be performed in O(N 3 ) operations per timestep despite the presence of deforming geometry. The first approach is a domain-integral formulation involving integrals over the entire flow domain of kernel functions which arise in time-differencing the Navier-Stokes equations. The second is a particular-solution formulation which replaces domain integration with an iterative scheme to generate particular velocity and pressure fields on individual elements, followed by a patching step to produce a particular solution continuous over the full domain. Two of the most difficult aspects of viscous free-surface flow simulations, namely time-dependent geometry and nontrivial boundary conditions, are well accommodated by these integral equation techniques. In addition the methods offer spectral accuracy in space and admit arbitrarily high-order discretization in time. For large-scale computations and/or long-term time advancement the domain-integral algorithm must be executed on a supercomputer to deliver results in reasonable processing time. A detailed simulation of gas liquid flow with full resolution of the free phase boundary requires approximately five CPU hours at 80 megaflops
Analyticity estimates for the Navier-Stokes equations
DEFF Research Database (Denmark)
Herbst, I.; Skibsted, Erik
We study spatial analyticity properties of solutions of the Navier-Stokes equation and obtain new growth rate estimates for the analyticity radius. We also study stability properties of strong global solutions of the Navier-Stokes equation with data in and prove a stability result...
Lee-Rausch, Elizabeth M.; Hammond, Dana P.; Nielsen, Eric J.; Pirzadeh, S. Z.; Rumsey, Christopher L.
2010-01-01
FUN3D Navier-Stokes solutions were computed for the 4th AIAA Drag Prediction Workshop grid convergence study, downwash study, and Reynolds number study on a set of node-based mixed-element grids. All of the baseline tetrahedral grids were generated with the VGRID (developmental) advancing-layer and advancing-front grid generation software package following the gridding guidelines developed for the workshop. With maximum grid sizes exceeding 100 million nodes, the grid convergence study was particularly challenging for the node-based unstructured grid generators and flow solvers. At the time of the workshop, the super-fine grid with 105 million nodes and 600 million elements was the largest grid known to have been generated using VGRID. FUN3D Version 11.0 has a completely new pre- and post-processing paradigm that has been incorporated directly into the solver and functions entirely in a parallel, distributed memory environment. This feature allowed for practical pre-processing and solution times on the largest unstructured-grid size requested for the workshop. For the constant-lift grid convergence case, the convergence of total drag is approximately second-order on the finest three grids. The variation in total drag between the finest two grids is only 2 counts. At the finest grid levels, only small variations in wing and tail pressure distributions are seen with grid refinement. Similarly, a small wing side-of-body separation also shows little variation at the finest grid levels. Overall, the FUN3D results compare well with the structured-grid code CFL3D. The FUN3D downwash study and Reynolds number study results compare well with the range of results shown in the workshop presentations.
Computing Flows Using Chimera and Unstructured Grids
Liou, Meng-Sing; Zheng, Yao
2006-01-01
DRAGONFLOW is a computer program that solves the Navier-Stokes equations of flows in complexly shaped three-dimensional regions discretized by use of a direct replacement of arbitrary grid overlapping by nonstructured (DRAGON) grid. A DRAGON grid (see figure) is a combination of a chimera grid (a composite of structured subgrids) and a collection of unstructured subgrids. DRAGONFLOW incorporates modified versions of two prior Navier-Stokes-equation-solving programs: OVERFLOW, which is designed to solve on chimera grids; and USM3D, which is used to solve on unstructured grids. A master module controls the invocation of individual modules in the libraries. At each time step of a simulated flow, DRAGONFLOW is invoked on the chimera portion of the DRAGON grid in alternation with USM3D, which is invoked on the unstructured subgrids of the DRAGON grid. The USM3D and OVERFLOW modules then immediately exchange their solutions and other data. As a result, USM3D and OVERFLOW are coupled seamlessly.
Large Time Behavior for Weak Solutions of the 3D Globally Modified Navier-Stokes Equations
Directory of Open Access Journals (Sweden)
Junbai Ren
2014-01-01
Full Text Available This paper is concerned with the large time behavior of the weak solutions for three-dimensional globally modified Navier-Stokes equations. With the aid of energy methods and auxiliary decay estimates together with Lp-Lq estimates of heat semigroup, we derive the optimal upper and lower decay estimates of the weak solutions for the globally modified Navier-Stokes equations as C1(1+t-3/4≤uL2≤C2(1+t-3/4, t>1. The decay rate is optimal since it coincides with that of heat equation.
Toward An Unstructured Mesh Database
Rezaei Mahdiraji, Alireza; Baumann, Peter Peter
2014-05-01
Unstructured meshes are used in several application domains such as earth sciences (e.g., seismology), medicine, oceanography, cli- mate modeling, GIS as approximate representations of physical objects. Meshes subdivide a domain into smaller geometric elements (called cells) which are glued together by incidence relationships. The subdivision of a domain allows computational manipulation of complicated physical structures. For instance, seismologists model earthquakes using elastic wave propagation solvers on hexahedral meshes. The hexahedral con- tains several hundred millions of grid points and millions of hexahedral cells. Each vertex node in the hexahedrals stores a multitude of data fields. To run simulation on such meshes, one needs to iterate over all the cells, iterate over incident cells to a given cell, retrieve coordinates of cells, assign data values to cells, etc. Although meshes are used in many application domains, to the best of our knowledge there is no database vendor that support unstructured mesh features. Currently, the main tool for querying and manipulating unstructured meshes are mesh libraries, e.g., CGAL and GRAL. Mesh li- braries are dedicated libraries which includes mesh algorithms and can be run on mesh representations. The libraries do not scale with dataset size, do not have declarative query language, and need deep C++ knowledge for query implementations. Furthermore, due to high coupling between the implementations and input file structure, the implementations are less reusable and costly to maintain. A dedicated mesh database offers the following advantages: 1) declarative querying, 2) ease of maintenance, 3) hiding mesh storage structure from applications, and 4) transparent query optimization. To design a mesh database, the first challenge is to define a suitable generic data model for unstructured meshes. We proposed ImG-Complexes data model as a generic topological mesh data model which extends incidence graph model to multi
Torner, Benjamin; Konnigk, Lucas; Hallier, Sebastian; Kumar, Jitendra; Witte, Matthias; Wurm, Frank-Hendrik
2018-06-01
Numerical flow analysis (computational fluid dynamics) in combination with the prediction of blood damage is an important procedure to investigate the hemocompatibility of a blood pump, since blood trauma due to shear stresses remains a problem in these devices. Today, the numerical damage prediction is conducted using unsteady Reynolds-averaged Navier-Stokes simulations. Investigations with large eddy simulations are rarely being performed for blood pumps. Hence, the aim of the study is to examine the viscous shear stresses of a large eddy simulation in a blood pump and compare the results with an unsteady Reynolds-averaged Navier-Stokes simulation. The simulations were carried out at two operation points of a blood pump. The flow was simulated on a 100M element mesh for the large eddy simulation and a 20M element mesh for the unsteady Reynolds-averaged Navier-Stokes simulation. As a first step, the large eddy simulation was verified by analyzing internal dissipative losses within the pump. Then, the pump characteristics and mean and turbulent viscous shear stresses were compared between the two simulation methods. The verification showed that the large eddy simulation is able to reproduce the significant portion of dissipative losses, which is a global indication that the equivalent viscous shear stresses are adequately resolved. The comparison with the unsteady Reynolds-averaged Navier-Stokes simulation revealed that the hydraulic parameters were in agreement, but differences for the shear stresses were found. The results show the potential of the large eddy simulation as a high-quality comparative case to check the suitability of a chosen Reynolds-averaged Navier-Stokes setup and turbulence model. Furthermore, the results lead to suggest that large eddy simulations are superior to unsteady Reynolds-averaged Navier-Stokes simulations when instantaneous stresses are applied for the blood damage prediction.
Boundary Shape Control of the Navier-Stokes Equations and Applications
Institute of Scientific and Technical Information of China (English)
Kaitai LI; Jian SU; Aixiang HUANG
2010-01-01
In this paper,the geometrical design for the blade's surface(s)in an impeller or for the profile of an aircraft,is modeled from the mathematical point of view by a boundary shape control problem for the Navier-Stokes equations.The objective function is the sum of a global dissipative function and the power of the fluid.The control variables are the geometry of the boundary and the state equations are the Navier-Stokes equations.The Euler-Lagrange equations of the optimal control problem are derived,which are an elliptic boundary value system of fourth order,coupled with the Navier-Stokes equations.The authors also prove the existence of the solution of the optimal control problem,the existence of the solution of the Navier-Stokes equations with mixed boundary conditions,the weak continuity of the solution of the Navier-Stokes equations with respect to the geometry shape of the blade's surface and the existence of solutions of the equations for the G(a)teaux derivative of the solution of the Navier-Stokes equations with respect to the geometry of the boundary.
Strong plasma shock structures based on the Navier--Stokes equations
International Nuclear Information System (INIS)
Abe, K.
1975-01-01
The structure of a plasma collisional shock wave is examined on the basis of the Navier--Stokes equations and simultaneously on the basis of the Fokker--Planck equation. The resultant structures are compared to check the validity of the Navier--Stokes equations applied to the structures of strong shock waves. The Navier--Stokes equations give quite correct structures for weak shock waves. For the strong shock waves, the detailed structures obtained from the Navier--Stokes equations differ from the results of the Fokker--Planck equation, but the shock thicknesses of the two shock waves are in relatively close agreement
Balsara, Dinshaw S.; Dumbser, Michael
2015-10-01
Several advances have been reported in the recent literature on divergence-free finite volume schemes for Magnetohydrodynamics (MHD). Almost all of these advances are restricted to structured meshes. To retain full geometric versatility, however, it is also very important to make analogous advances in divergence-free schemes for MHD on unstructured meshes. Such schemes utilize a staggered Yee-type mesh, where all hydrodynamic quantities (mass, momentum and energy density) are cell-centered, while the magnetic fields are face-centered and the electric fields, which are so useful for the time update of the magnetic field, are centered at the edges. Three important advances are brought together in this paper in order to make it possible to have high order accurate finite volume schemes for the MHD equations on unstructured meshes. First, it is shown that a divergence-free WENO reconstruction of the magnetic field can be developed for unstructured meshes in two and three space dimensions using a classical cell-centered WENO algorithm, without the need to do a WENO reconstruction for the magnetic field on the faces. This is achieved via a novel constrained L2-projection operator that is used in each time step as a postprocessor of the cell-centered WENO reconstruction so that the magnetic field becomes locally and globally divergence free. Second, it is shown that recently-developed genuinely multidimensional Riemann solvers (called MuSIC Riemann solvers) can be used on unstructured meshes to obtain a multidimensionally upwinded representation of the electric field at each edge. Third, the above two innovations work well together with a high order accurate one-step ADER time stepping strategy, which requires the divergence-free nonlinear WENO reconstruction procedure to be carried out only once per time step. The resulting divergence-free ADER-WENO schemes with MuSIC Riemann solvers give us an efficient and easily-implemented strategy for divergence-free MHD on
Discrete Adjoint-Based Design Optimization of Unsteady Turbulent Flows on Dynamic Unstructured Grids
Nielsen, Eric J.; Diskin, Boris; Yamaleev, Nail K.
2009-01-01
An adjoint-based methodology for design optimization of unsteady turbulent flows on dynamic unstructured grids is described. The implementation relies on an existing unsteady three-dimensional unstructured grid solver capable of dynamic mesh simulations and discrete adjoint capabilities previously developed for steady flows. The discrete equations for the primal and adjoint systems are presented for the backward-difference family of time-integration schemes on both static and dynamic grids. The consistency of sensitivity derivatives is established via comparisons with complex-variable computations. The current work is believed to be the first verified implementation of an adjoint-based optimization methodology for the true time-dependent formulation of the Navier-Stokes equations in a practical computational code. Large-scale shape optimizations are demonstrated for turbulent flows over a tiltrotor geometry and a simulated aeroelastic motion of a fighter jet.
International Nuclear Information System (INIS)
Wang, G.; Ye, Z.
2005-01-01
It is well known that the aerodynamic interference flows widely exist between the components of conventional transport airplane, for example, the wing-fuselage juncture flow, wing-pylon-nacelle flow and tail-fuselage juncture flow. The main characteristic of these aerodynamic interferences is flow separation, which will increase the drag, reduce the lift and cause adverse influence on the stability and controllability of the airplane. Therefore, the modern civil transport designers should do their best to eliminate negative effects of aerodynamic interferences, which demands that the aerodynamic interferences between the aircraft components should be predicted and analyzed accurately. Today's CFD techniques provide us powerful and efficient analysis tools to achieve this objective. In this paper, computational investigations of the interferences between transport aircraft components have been carried out by using a viscous flow solver based on mixed element type unstructured meshes. (author)
On convergence of trajectory attractors of the 3D Navier-Stokes-α model as α approaches 0
International Nuclear Information System (INIS)
Vishik, M I; Chepyzhov, V V; Titi, E S
2007-01-01
We study the relations between the long-time dynamics of the Navier-Stokes-α model and the exact 3D Navier-Stokes system. We prove that bounded sets of solutions of the Navier-Stokes-α model converge to the trajectory attractor A 0 of the 3D Navier-Stokes system as the time approaches infinity and α approaches zero. In particular, we show that the trajectory attractor A α of the Navier-Stokes-α model converges to the trajectory attractor A 0 of the 3D Navier-Stokes system as α→0+. We also construct the minimal limit A min (subset or equal A 0 ) of the trajectory attractor A α as α→0+ and prove that the set A min is connected and strictly invariant. Bibliography: 35 titles.
p-Euler equations and p-Navier-Stokes equations
Li, Lei; Liu, Jian-Guo
2018-04-01
We propose in this work new systems of equations which we call p-Euler equations and p-Navier-Stokes equations. p-Euler equations are derived as the Euler-Lagrange equations for the action represented by the Benamou-Brenier characterization of Wasserstein-p distances, with incompressibility constraint. p-Euler equations have similar structures with the usual Euler equations but the 'momentum' is the signed (p - 1)-th power of the velocity. In the 2D case, the p-Euler equations have streamfunction-vorticity formulation, where the vorticity is given by the p-Laplacian of the streamfunction. By adding diffusion presented by γ-Laplacian of the velocity, we obtain what we call p-Navier-Stokes equations. If γ = p, the a priori energy estimates for the velocity and momentum have dual symmetries. Using these energy estimates and a time-shift estimate, we show the global existence of weak solutions for the p-Navier-Stokes equations in Rd for γ = p and p ≥ d ≥ 2 through a compactness criterion.
Cavitation Modeling in Euler and Navier-Stokes Codes
Deshpande, Manish; Feng, Jinzhang; Merkle, Charles L.
1993-01-01
Many previous researchers have modeled sheet cavitation by means of a constant pressure solution in the cavity region coupled with a velocity potential formulation for the outer flow. The present paper discusses the issues involved in extending these cavitation models to Euler or Navier-Stokes codes. The approach taken is to start from a velocity potential model to ensure our results are compatible with those of previous researchers and available experimental data, and then to implement this model in both Euler and Navier-Stokes codes. The model is then augmented in the Navier-Stokes code by the inclusion of the energy equation which allows the effect of subcooling in the vicinity of the cavity interface to be modeled to take into account the experimentally observed reduction in cavity pressures that occurs in cryogenic fluids such as liquid hydrogen. Although our goal is to assess the practicality of implementing these cavitation models in existing three-dimensional, turbomachinery codes, the emphasis in the present paper will center on two-dimensional computations, most specifically isolated airfoils and cascades. Comparisons between velocity potential, Euler and Navier-Stokes implementations indicate they all produce consistent predictions. Comparisons with experimental results also indicate that the predictions are qualitatively correct and give a reasonable first estimate of sheet cavitation effects in both cryogenic and non-cryogenic fluids. The impact on CPU time and the code modifications required suggests that these models are appropriate for incorporation in current generation turbomachinery codes.
Navier-Stokes Computations With One-Equation Turbulence Model for Flows Along Concave Wall Surfaces
Wang, Chi R.
2005-01-01
This report presents the use of a time-marching three-dimensional compressible Navier-Stokes equation numerical solver with a one-equation turbulence model to simulate the flow fields developed along concave wall surfaces without and with a downstream extension flat wall surface. The 3-D Navier- Stokes numerical solver came from the NASA Glenn-HT code. The one-equation turbulence model was derived from the Spalart and Allmaras model. The computational approach was first calibrated with the computations of the velocity and Reynolds shear stress profiles of a steady flat plate boundary layer flow. The computational approach was then used to simulate developing boundary layer flows along concave wall surfaces without and with a downstream extension wall. The author investigated the computational results of surface friction factors, near surface velocity components, near wall temperatures, and a turbulent shear stress component in terms of turbulence modeling, computational mesh configurations, inlet turbulence level, and time iteration step. The computational results were compared with existing measurements of skin friction factors, velocity components, and shear stresses of the developing boundary layer flows. With a fine computational mesh and a one-equation model, the computational approach could predict accurately the skin friction factors, near surface velocity and temperature, and shear stress within the flows. The computed velocity components and shear stresses also showed the vortices effect on the velocity variations over a concave wall. The computed eddy viscosities at the near wall locations were also compared with the results from a two equation turbulence modeling technique. The inlet turbulence length scale was found to have little effect on the eddy viscosities at locations near the concave wall surface. The eddy viscosities, from the one-equation and two-equation modeling, were comparable at most stream-wise stations. The present one
Time-Filtered Navier-Stokes Approach and Emulation of Turbulence-Chemistry Interaction
Liu, Nan-Suey; Wey, Thomas; Shih, Tsan-Hsing
2013-01-01
This paper describes the time-filtered Navier-Stokes approach capable of capturing unsteady flow structures important for turbulent mixing and an accompanying subgrid model directly accounting for the major processes in turbulence-chemistry interaction. They have been applied to the computation of two-phase turbulent combustion occurring in a single-element lean-direct-injection combustor. Some of the preliminary results from this computational effort are presented in this paper.
Tip loss correction for actuator / Navier Stokes computations
DEFF Research Database (Denmark)
Shen, Wen Zhong; Sørensen, Jens Nørkær; Mikkelsen, Robert Flemming
2004-01-01
The new tip loss correction, initially developed for ID BEM computations [1], is now extended to 2D Actuator Disc / Navier-Stokes (AD/NS) computations and 3D Actuator Line / Navier-Stokes (AL/NS) computations. As shown in the paper, the tip loss correction is an important and necessary step...
Assessment of the Unstructured Grid Software TetrUSS for Drag Prediction of the DLR-F4 Configuration
Pirzadeh, Shahyar Z.; Frink, Neal T.
2002-01-01
An application of the NASA unstructured grid software system TetrUSS is presented for the prediction of aerodynamic drag on a transport configuration. The paper briefly describes the underlying methodology and summarizes the results obtained on the DLR-F4 transport configuration recently presented in the first AIAA computational fluid dynamics (CFD) Drag Prediction Workshop. TetrUSS is a suite of loosely coupled unstructured grid CFD codes developed at the NASA Langley Research Center. The meshing approach is based on the advancing-front and the advancing-layers procedures. The flow solver employs a cell-centered, finite volume scheme for solving the Reynolds Averaged Navier-Stokes equations on tetrahedral grids. For the present computations, flow in the viscous sublayer has been modeled with an analytical wall function. The emphasis of the paper is placed on the practicality of the methodology for accurately predicting aerodynamic drag data.
Towards an ideal preconditioner for linearized Navier-Stokes problems
Energy Technology Data Exchange (ETDEWEB)
Murphy, M.F. [Univ. of Bristol (United Kingdom)
1996-12-31
Discretizing certain linearizations of the steady-state Navier-Stokes equations gives rise to nonsymmetric linear systems with indefinite symmetric part. We show that for such systems there exists a block diagonal preconditioner which gives convergence in three GMRES steps, independent of the mesh size and viscosity parameter (Reynolds number). While this {open_quotes}ideal{close_quotes} preconditioner is too expensive to be used in practice, it provides a useful insight into the problem. We then consider various approximations to the ideal preconditioner, and describe the eigenvalues of the preconditioned systems. Finally, we compare these preconditioners numerically, and present our conclusions.
Aithal, Abhiram; Ferrante, Antonino
2017-11-01
In order to perform direct numerical simulations (DNS) of turbulent flows over curved surfaces and axisymmetric bodies, we have developed the numerical methodology to solve the incompressible Navier-Stokes (NS) equations in curvilinear coordinates for orthogonal meshes. The orthogonal meshes are generated by solving a coupled system of non-linear Poisson equations. The NS equations in orthogonal curvilinear coordinates are discretized in space on a staggered mesh using second-order central-difference scheme and are solved with an FFT-based pressure-correction method. The momentum equation is integrated in time using the second-order Adams-Bashforth scheme. The velocity field is advanced in time by applying the pressure correction to the approximate velocity such that it satisfies the divergence free condition. The novelty of the method stands in solving the variable coefficient Poisson equation for pressure using an FFT-based Poisson solver rather than the slower multigrid methods. We present the verification and validation results of the new numerical method and the DNS results of transitional flow over a curved axisymmetric body.
Solutions of Navier-Stokes Equation with Coriolis Force
Directory of Open Access Journals (Sweden)
Sunggeun Lee
2017-01-01
Full Text Available We investigate the Navier-Stokes equation in the presence of Coriolis force in this article. First, the vortex equation with the Coriolis effect is discussed. It turns out that the vorticity can be generated due to a rotation coming from the Coriolis effect, Ω. In both steady state and two-dimensional flow, the vorticity vector ω gets shifted by the amount of -2Ω. Second, we consider the specific expression of the velocity vector of the Navier-Stokes equation in two dimensions. For the two-dimensional potential flow v→=∇→ϕ, the equation satisfied by ϕ is independent of Ω. The remaining Navier-Stokes equation reduces to the nonlinear partial differential equations with respect to the velocity and the corresponding exact solution is obtained. Finally, the steady convective diffusion equation is considered for the concentration c and can be solved with the help of Navier-Stokes equation for two-dimensional potential flow. The convective diffusion equation can be solved in three dimensions with a simple choice of c.
Incompressible Navier-Stokes equations. Theory and practice
Energy Technology Data Exchange (ETDEWEB)
Gjesdal, T.
1996-12-31
This paper contains notes from a seminar presented at the Dept. of Mathematics in the University of Bergen, Norway, Oct. 1996. It first introduces the theory of existence and uniqueness of solutions to the incompressible Navier-Stokes equation and defines a well-posed initial-boundary value problem. It then discusses different methods for solving numerically the Navier-Stokes equations in velocity-pressure formulation. The emphasis is on pressure correction methods. 19 refs.
Parabolized Navier-Stokes solutions of separation and trailing-edge flows
Brown, J. L.
1983-01-01
A robust, iterative solution procedure is presented for the parabolized Navier-Stokes or higher order boundary layer equations as applied to subsonic viscous-inviscid interaction flows. The robustness of the present procedure is due, in part, to an improved algorithmic formulation. The present formulation is based on a reinterpretation of stability requirements for this class of algorithms and requires only second order accurate backward or central differences for all streamwise derivatives. Upstream influence is provided for through the algorithmic formulation and iterative sweeps in x. The primary contribution to robustness, however, is the boundary condition treatment, which imposes global constraints to control the convergence path. Discussed are successful calculations of subsonic, strong viscous-inviscid interactions, including separation. These results are consistent with Navier-Stokes solutions and triple deck theory.
Solutions to three-dimensional Navier-Stokes equations for incompressible fluids
Directory of Open Access Journals (Sweden)
Jorma Jormakka
2010-07-01
Full Text Available This article gives explicit solutions to the space-periodic Navier-Stokes problem with non-periodic pressure. These type of solutions are not unique and by using such solutions one can construct a periodic, smooth, divergence-free initial vector field allowing a space-periodic and time-bounded external force such that there exists a smooth solution to the 3-dimensional Navier-Stokes equations for incompressible fluid with those initial conditions, but the solution cannot be continued to the whole space.
The incompressible non-relativistic Navier-Stokes equation from gravity
International Nuclear Information System (INIS)
Bhattacharyya, Sayantani; Minwalla, Shiraz; Wadia, Spenta R.
2009-01-01
We note that the equations of relativistic hydrodynamics reduce to the incompressible Navier-Stokes equations in a particular scaling limit. In this limit boundary metric fluctuations of the underlying relativistic system turn into a forcing function identical to the action of a background electromagnetic field on the effectively charged fluid. We demonstrate that special conformal symmetries of the parent relativistic theory descend to 'accelerated boost' symmetries of the Navier-Stokes equations, uncovering a conformal symmetry structure of these equations. Applying our scaling limit to holographically induced fluid dynamics, we find gravity dual descriptions of an arbitrary solution of the forced non-relativistic incompressible Navier-Stokes equations. In the holographic context we also find a simple forced steady state shear solution to the Navier-Stokes equations, and demonstrate that this solution turns unstable at high enough Reynolds numbers, indicating a possible eventual transition to turbulence.
Cyranka, Jacek; Mucha, Piotr B.; Titi, Edriss S.; Zgliczyński, Piotr
2018-04-01
The paper studies the issue of stability of solutions to the forced Navier-Stokes and damped Euler systems in periodic boxes. It is shown that for large, but fixed, Grashoff (Reynolds) number the turbulent behavior of all Leray-Hopf weak solutions of the three-dimensional Navier-Stokes equations, in periodic box, is suppressed, when viewed in the right frame of reference, by large enough average flow of the initial data; a phenomenon that is similar in spirit to the Landau damping. Specifically, we consider an initial data which have large enough spatial average, then by means of the Galilean transformation, and thanks to the periodic boundary conditions, the large time independent forcing term changes into a highly oscillatory force; which then allows us to employ some averaging principles to establish our result. Moreover, we also show that under the action of fast oscillatory-in-time external forces all two-dimensional regular solutions of the Navier-Stokes and the damped Euler equations converge to a unique time-periodic solution.
Thamareerat, N; Luadsong, A; Aschariyaphotha, N
2016-01-01
In this paper, we present a numerical scheme used to solve the nonlinear time fractional Navier-Stokes equations in two dimensions. We first employ the meshless local Petrov-Galerkin (MLPG) method based on a local weak formulation to form the system of discretized equations and then we will approximate the time fractional derivative interpreted in the sense of Caputo by a simple quadrature formula. The moving Kriging interpolation which possesses the Kronecker delta property is applied to construct shape functions. This research aims to extend and develop further the applicability of the truly MLPG method to the generalized incompressible Navier-Stokes equations. Two numerical examples are provided to illustrate the accuracy and efficiency of the proposed algorithm. Very good agreement between the numerically and analytically computed solutions can be observed in the verification. The present MLPG method has proved its efficiency and reliability for solving the two-dimensional time fractional Navier-Stokes equations arising in fluid dynamics as well as several other problems in science and engineering.
MHD simulations on an unstructured mesh
International Nuclear Information System (INIS)
Strauss, H.R.; Park, W.; Belova, E.; Fu, G.Y.; Sugiyama, L.E.
1998-01-01
Two reasons for using an unstructured computational mesh are adaptivity, and alignment with arbitrarily shaped boundaries. Two codes which use finite element discretization on an unstructured mesh are described. FEM3D solves 2D and 3D RMHD using an adaptive grid. MH3D++, which incorporates methods of FEM3D into the MH3D generalized MHD code, can be used with shaped boundaries, which might be 3D
Approximate controllability of the Navier-Stokes system in unbounded domains
International Nuclear Information System (INIS)
Shorygin, P O
2003-01-01
The question of the approximate controllability for the 2- and the 3-dimensional Navier-Stokes system defined in the exterior of a bounded domain ω or in the entire space is studied. It is shown that one can find boundary controls or locally distributed controls (having support in a prescribed bounded domain) defined on the right-hand side of the system such that in prescribed time the solution of the Navier-Stokes system becomes arbitrarily close to an arbitrary prescribed divergence-free vector field
On time-periodic Navier-Stokes flows with fast spatial decay in the whole space
Czech Academy of Sciences Publication Activity Database
Nakatsuka, Tomoyuki
2018-01-01
Roč. 4, č. 1 (2018), s. 51-67 ISSN 2296-9020 Institutional support: RVO:67985840 Keywords : Navier-Stokes equation * time-periodic solution * asymptotic property Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics https://link.springer.com/article/10. 1007 %2Fs41808-018-0011-8
On time-periodic Navier-Stokes flows with fast spatial decay in the whole space
Czech Academy of Sciences Publication Activity Database
Nakatsuka, Tomoyuki
2018-01-01
Roč. 4, č. 1 (2018), s. 51-67 ISSN 2296-9020 Institutional support: RVO:67985840 Keywords : Navier-Stokes equation * time-periodic solution * asymptotic property Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics https://link.springer.com/article/10.1007%2Fs41808-018-0011-8
Multiphase flow of immiscible fluids on unstructured moving meshes
DEFF Research Database (Denmark)
Misztal, Marek Krzysztof; Erleben, Kenny; Bargteil, Adam
2012-01-01
In this paper, we present a method for animating multiphase flow of immiscible fluids using unstructured moving meshes. Our underlying discretization is an unstructured tetrahedral mesh, the deformable simplicial complex (DSC), that moves with the flow in a Lagrangian manner. Mesh optimization op...
Multiphase Flow of Immiscible Fluids on Unstructured Moving Meshes
DEFF Research Database (Denmark)
Misztal, Marek Krzysztof; Erleben, Kenny; Bargteil, Adam
2013-01-01
In this paper, we present a method for animating multiphase flow of immiscible fluids using unstructured moving meshes. Our underlying discretization is an unstructured tetrahedral mesh, the deformable simplicial complex (DSC), that moves with the flow in a Lagrangian manner. Mesh optimization op...
Reynolds-averaged Navier-Stokes based ice accretion for aircraft wings
Lashkajani, Kazem Hasanzadeh
This thesis addresses one of the current issues in flight safety towards increasing icing simulation capabilities for prediction of complex 2D and 3D glaze ice shapes over aircraft surfaces. During the 1980's and 1990's, the field of aero-icing was established to support design and certification of aircraft flying in icing conditions. The multidisciplinary technologies used in such codes were: aerodynamics (panel method), droplet trajectory calculations (Lagrangian framework), thermodynamic module (Messinger model) and geometry module (ice accretion). These are embedded in a quasi-steady module to simulate the time-dependent ice accretion process (multi-step procedure). The objectives of the present research are to upgrade the aerodynamic module from Laplace to Reynolds-Average Navier-Stokes equations solver. The advantages are many. First, the physical model allows accounting for viscous effects in the aerodynamic module. Second, the solution of the aero-icing module directly provides the means for characterizing the aerodynamic effects of icing, such as loss of lift and increased drag. Third, the use of a finite volume approach to solving the Partial Differential Equations allows rigorous mesh and time convergence analysis. Finally, the approaches developed in 2D can be easily transposed to 3D problems. The research was performed in three major steps, each providing insights into the overall numerical approaches. The most important realization comes from the need to develop specific mesh generation algorithms to ensure feasible solutions in very complex multi-step aero-icing calculations. The contributions are presented in chronological order of their realization. First, a new framework for RANS based two-dimensional ice accretion code, CANICE2D-NS, is developed. A multi-block RANS code from U. of Liverpool (named PMB) is providing the aerodynamic field using the Spalart-Allmaras turbulence model. The ICEM-CFD commercial tool is used for the iced airfoil
Optimal control of compressible Navier-Stokes equations
International Nuclear Information System (INIS)
Ito, K.; Ravindran, S.S.
1994-01-01
Optimal control for the viscous incompressible flows, which are governed by incompressible Navier-Stokes equations, has been the subject of extensive study in recent years, see, e.g., [AT], [GHS], [IR], and [S]. In this paper we consider the optimal control of compressible isentropic Navier-Stokes equations. We develop the weak variational formulation and discuss the existence and necessary optimality condition characterizing the optimal control. A numerical method based on the mixed-finite element method is also discussed to compute the control and numerical results are presented
Implications of Navier-Stokes turbulence theory for plasma turbulence
International Nuclear Information System (INIS)
Montgomery, David
1977-01-01
A brief discussion of Navier-Stokes turbulence theory is given with particular reference to the two dimensional case. The MHD turbulence is introduced with possible applications of techniques developed in Navier-Stokes theory. Turbulence in Vlasov plasma is also discussed from the point of view of the ''direct interaction approximation'' (DIA). (A.K.)
Multigrid time-accurate integration of Navier-Stokes equations
Arnone, Andrea; Liou, Meng-Sing; Povinelli, Louis A.
1993-01-01
Efficient acceleration techniques typical of explicit steady-state solvers are extended to time-accurate calculations. Stability restrictions are greatly reduced by means of a fully implicit time discretization. A four-stage Runge-Kutta scheme with local time stepping, residual smoothing, and multigridding is used instead of traditional time-expensive factorizations. Some applications to natural and forced unsteady viscous flows show the capability of the procedure.
Development Of A Navier-Stokes Computer Code
Yoon, Seokkwan; Kwak, Dochan
1993-01-01
Report discusses aspects of development of CENS3D computer code, solving three-dimensional Navier-Stokes equations of compressible, viscous, unsteady flow. Implements implicit finite-difference or finite-volume numerical-integration scheme, called "lower-upper symmetric-Gauss-Seidel" (LU-SGS), offering potential for very low computer time per iteration and for fast convergence.
On analytical solution of the Navier-Stokes equations
International Nuclear Information System (INIS)
Scheffel, J.
2001-04-01
An analytical method for solving the dissipative, nonlinear and non-stationary Navier-Stokes equations is presented. Velocity and pressure is expanded in power series of cartesian coordinates and time. The method is applied to 2-D incompressible gravitational flow in a bounded, rectangular domain
On large-time energy concentration in solutions to the Navier-Stokes equations in general domains
Czech Academy of Sciences Publication Activity Database
Skalák, Zdeněk
2011-01-01
Roč. 91, č. 9 (2011), s. 724-732 ISSN 0044-2267 R&D Projects: GA AV ČR IAA100190905 Institutional research plan: CEZ:AV0Z20600510 Keywords : Navier-Stokes equations * large-time behavior * energy concentration Subject RIV: BA - General Mathematics Impact factor: 0.863, year: 2011
A Liouville Problem for the Stationary Fractional Navier-Stokes-Poisson System
Wang, Y.; Xiao, J.
2017-06-01
This paper deals with a Liouville problem for the stationary fractional Navier-Stokes-Poisson system whose special case k=0 covers the compressible and incompressible time-independent fractional Navier-Stokes systems in R^{N≥2} . An essential difficulty raises from the fractional Laplacian, which is a non-local operator and thus makes the local analysis unsuitable. To overcome the difficulty, we utilize a recently-introduced extension-method in Wang and Xiao (Commun Contemp Math 18(6):1650019, 2016) which develops Caffarelli-Silvestre's technique in Caffarelli and Silvestre (Commun Partial Diff Equ 32:1245-1260, 2007).
On Critical Spaces for the Navier-Stokes Equations
Prüss, Jan; Wilke, Mathias
2017-10-01
The abstract theory of critical spaces developed in Prüss and Wilke (J Evol Equ, 2017. doi: 10.1007/s00028-017-0382-6), Prüss et al. (Critical spaces for quasilinear parabolic evolution equations and applications, 2017) is applied to the Navier-Stokes equations in bounded domains with Navier boundary conditions as well as no-slip conditions. Our approach unifies, simplifies and extends existing work in the L_p -L_q setting, considerably. As an essential step, it is shown that the strong and weak Stokes operators with Navier conditions admit an H^∞-calculus with H^∞-angle 0, and the real and complex interpolation spaces of these operators are identified.
About Navier-Stokes Equation in the Theory of Convective Heat Transfer
Davidzon, M. Y.
2017-10-01
A system of differential equations (Navier-Stokes, continuity, heat conductivity) is used to solve convective heat transfer problems. While solving Navier-Stokes equation, it is usually assumed that tangent stress is proportional to the velocity gradient. This assumption is valid with a small velocity gradient, for example, near an axis of the channel, but velocity gradient can be very large near the channel wall. Our paper shows that if we accept power law instead of linear law for tangential stress, then the velocity profile for creeping, laminar, and turbulent flow in the channel can be calculated without using Navier-Stokes equation. Also, in this case Navier-Stokes equation itself changes: the coefficient of dynamic viscosity changes its value from normal (in case of the creeping flow) to tending to infinity (in case of the well-developed turbulent flow).
Simulations of transition and turbulence on the Navier-Stokes computer
International Nuclear Information System (INIS)
Krist, S.E.; Zang, T.A.
1987-01-01
The Navier-Stokes Computer (NSC) consists of multiple local memory parallel processors interconnected in a hypercube network. Efficient implementation of algorithms on the NSC thus requires the effective utilization of both the coarse and fine grain paralelism inherent in the architectural design. The basic approach to implementing an algorithm on the NSC is presented herein. The particular finite-difference algorithm considered was developed for performing transition and turbulence simulations by direct solution of the time-dependent incompressible Navier-Stokes equations. The suitability of this algorithm for performing simulations of the isotropic turbulence problem is verified from computations performed on a Cray 2. Projected timing results for the algorithm on the NSC itself are presented for both the isotropic turbulence and laminar turbulent transition problems. 7 references
Spatial Fourier modes controlling Navier-Stokes flow
International Nuclear Information System (INIS)
Treve, Y.M.
1982-01-01
As shown by Foias and Prodi in the limit of infinite times the solutions of the two-dimensional Navier-Stokes equations depend only on a finite number of modes, a number for which rigorous estimates can be obtained. A survey of these results is given together with further developments, notably in connection with the numerical approximation to the exact solutions. (Auth.)
Incompressible limit of compressible Navier-Stokes equations
International Nuclear Information System (INIS)
Bessaih, H.
1994-01-01
In this paper we study the system which describes the motion of compressible viscous fluid in a bounded domain Ω of R 3 . When we introduce a parameter λ, that is the inverse of the Mach number, we prove, under small initial data and external force (for barotropic flows), that the solution of Navier-Stokes equations is the incompressible limit of the solution of compressible Navier-Stokes equations, as the Mach number becomes small. For this, we show the existence of a solution verifying estimates independent of λ. Compactness argument allow us to pass to the limit on λ in the nonlinear terms. (author). 17 refs
Mohamed, Mamdouh S.
2016-02-11
A conservative discretization of incompressible Navier–Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.
Quasineutral limit for the quantum Navier-Stokes-Poisson equation
Li, Min; Pu, Xueke; Wang, Shu
2015-01-01
In this paper, we study the quasineutral limit and asymptotic behaviors for the quantum Navier-Stokes-Possion equation. We apply a formal expansion according to Debye length and derive the neutral incompressible Navier-Stokes equation. To establish this limit mathematically rigorously, we derive uniform (in Debye length) estimates for the remainders, for well-prepared initial data. It is demonstrated that the quantum effect do play important roles in the estimates and the norm introduced depe...
Parallel Performance Optimizations on Unstructured Mesh-based Simulations
Energy Technology Data Exchange (ETDEWEB)
Sarje, Abhinav; Song, Sukhyun; Jacobsen, Douglas; Huck, Kevin; Hollingsworth, Jeffrey; Malony, Allen; Williams, Samuel; Oliker, Leonid
2015-01-01
© The Authors. Published by Elsevier B.V. This paper addresses two key parallelization challenges the unstructured mesh-based ocean modeling code, MPAS-Ocean, which uses a mesh based on Voronoi tessellations: (1) load imbalance across processes, and (2) unstructured data access patterns, that inhibit intra- and inter-node performance. Our work analyzes the load imbalance due to naive partitioning of the mesh, and develops methods to generate mesh partitioning with better load balance and reduced communication. Furthermore, we present methods that minimize both inter- and intranode data movement and maximize data reuse. Our techniques include predictive ordering of data elements for higher cache efficiency, as well as communication reduction approaches. We present detailed performance data when running on thousands of cores using the Cray XC30 supercomputer and show that our optimization strategies can exceed the original performance by over 2×. Additionally, many of these solutions can be broadly applied to a wide variety of unstructured grid-based computations.
Reactor physics verification of the MCNP6 unstructured mesh capability
International Nuclear Information System (INIS)
Burke, T. P.; Kiedrowski, B. C.; Martz, R. L.; Martin, W. R.
2013-01-01
The Monte Carlo software package MCNP6 has the ability to transport particles on unstructured meshes generated from the Computed-Aided Engineering software Abaqus. Verification is performed using benchmarks with features relevant to reactor physics - Big Ten and the C5G7 computational benchmark. Various meshing strategies are tested and results are compared to reference solutions. Computational performance results are also given. The conclusions show MCNP6 is capable of producing accurate calculations for reactor physics geometries and the computational requirements for small lattice benchmarks are reasonable on modern computing platforms. (authors)
Reactor physics verification of the MCNP6 unstructured mesh capability
Energy Technology Data Exchange (ETDEWEB)
Burke, T. P. [Department of Nuclear Engineering and Radiological Sciences, University of Michigan, 2355 Bonisteel Boulevard, Ann Arbor, MI 48109 (United States); Kiedrowski, B. C.; Martz, R. L. [X-Computational Physics Division, Monte Carlo Codes Group, Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, NM 87545 (United States); Martin, W. R. [Department of Nuclear Engineering and Radiological Sciences, University of Michigan, 2355 Bonisteel Boulevard, Ann Arbor, MI 48109 (United States)
2013-07-01
The Monte Carlo software package MCNP6 has the ability to transport particles on unstructured meshes generated from the Computed-Aided Engineering software Abaqus. Verification is performed using benchmarks with features relevant to reactor physics - Big Ten and the C5G7 computational benchmark. Various meshing strategies are tested and results are compared to reference solutions. Computational performance results are also given. The conclusions show MCNP6 is capable of producing accurate calculations for reactor physics geometries and the computational requirements for small lattice benchmarks are reasonable on modern computing platforms. (authors)
Impact of the inherent separation of scales in the Navier-Stokes- alphabeta equations.
Kim, Tae-Yeon; Cassiani, Massimo; Albertson, John D; Dolbow, John E; Fried, Eliot; Gurtin, Morton E
2009-04-01
We study the effect of the length scales alpha and beta in the Navier-Stokes- alphabeta equations on the energy spectrum and the alignment between the vorticity and the eigenvectors of the stretching tensor in three-dimensional homogeneous and isotropic turbulent flows in a periodic cubic domain, including the limiting cases of the Navier-Stokes- alpha and Navier-Stokes equations. A significant increase in the accuracy of the energy spectrum at large wave numbers arises for betaNavier-Stokes- alphabeta equations also improve as beta decreases away from alpha . However, optimal choices for alpha and beta depend not only on the problem of interest but also on the grid resolution.
Discrete adjoint of fractional step Navier-Stokes solver in generalized coordinates
Wang, Mengze; Mons, Vincent; Zaki, Tamer
2017-11-01
Optimization and control in transitional and turbulent flows require evaluation of gradients of the flow state with respect to the problem parameters. Using adjoint approaches, these high-dimensional gradients can be evaluated with a similar computational cost as the forward Navier-Stokes simulations. The adjoint algorithm can be obtained by discretizing the continuous adjoint Navier-Stokes equations or by deriving the adjoint to the discretized Navier-Stokes equations directly. The latter algorithm is necessary when the forward-adjoint relations must be satisfied to machine precision. In this work, our forward model is the fractional step solution to the Navier-Stokes equations in generalized coordinates, proposed by Rosenfeld, Kwak & Vinokur. We derive the corresponding discrete adjoint equations. We also demonstrate the accuracy of the combined forward-adjoint model, and its application to unsteady wall-bounded flows. This work has been partially funded by the Office of Naval Research (Grant N00014-16-1-2542).
Pan, Liang; Xu, Kun; Li, Qibing; Li, Jiequan
2016-12-01
For computational fluid dynamics (CFD), the generalized Riemann problem (GRP) solver and the second-order gas-kinetic scheme (GKS) provide a time-accurate flux function starting from a discontinuous piecewise linear flow distributions around a cell interface. With the adoption of time derivative of the flux function, a two-stage Lax-Wendroff-type (L-W for short) time stepping method has been recently proposed in the design of a fourth-order time accurate method for inviscid flow [21]. In this paper, based on the same time-stepping method and the second-order GKS flux function [42], a fourth-order gas-kinetic scheme is constructed for the Euler and Navier-Stokes (NS) equations. In comparison with the formal one-stage time-stepping third-order gas-kinetic solver [24], the current fourth-order method not only reduces the complexity of the flux function, but also improves the accuracy of the scheme. In terms of the computational cost, a two-dimensional third-order GKS flux function takes about six times of the computational time of a second-order GKS flux function. However, a fifth-order WENO reconstruction may take more than ten times of the computational cost of a second-order GKS flux function. Therefore, it is fully legitimate to develop a two-stage fourth order time accurate method (two reconstruction) instead of standard four stage fourth-order Runge-Kutta method (four reconstruction). Most importantly, the robustness of the fourth-order GKS is as good as the second-order one. In the current computational fluid dynamics (CFD) research, it is still a difficult problem to extend the higher-order Euler solver to the NS one due to the change of governing equations from hyperbolic to parabolic type and the initial interface discontinuity. This problem remains distinctively for the hypersonic viscous and heat conducting flow. The GKS is based on the kinetic equation with the hyperbolic transport and the relaxation source term. The time-dependent GKS flux function
Application of thin-layer Navier-Stokes equations near maximum lift
Anderson, W. K.; Thomas, J. L.; Rumsey, C. L.
1984-01-01
The flowfield about a NACA 0012 airfoil at a Mach number of 0.3 and Reynolds number of 1 million is computed through an angle of attack range, up to 18 deg, corresponding to conditions up to and beyond the maximum lift coefficient. Results obtained using the compressible thin-layer Navier-Stokes equations are presented as well as results from the compressible Euler equations with and without a viscous coupling procedure. The applicability of each code is assessed and many thin-layer Navier-Stokes benchmark solutions are obtained which can be used for comparison with other codes intended for use at high angles of attack. Reasonable agreement of the Navier-Stokes code with experiment and the viscous-inviscid interaction code is obtained at moderate angles of attack. An unsteady solution is obtained with the thin-layer Navier-Stokes code at the highest angle of attack considered. The maximum lift coefficient is overpredicted, however, in comparison to experimental data, which is attributed to the presence of a laminar separation bubble near the leading edge not modeled in the computations. Two comparisons with experimental data are also presented at a higher Mach number.
Nearly Interactive Parabolized Navier-Stokes Solver for High Speed Forebody and Inlet Flows
Benson, Thomas J.; Liou, May-Fun; Jones, William H.; Trefny, Charles J.
2009-01-01
A system of computer programs is being developed for the preliminary design of high speed inlets and forebodies. The system comprises four functions: geometry definition, flow grid generation, flow solver, and graphics post-processor. The system runs on a dedicated personal computer using the Windows operating system and is controlled by graphical user interfaces written in MATLAB (The Mathworks, Inc.). The flow solver uses the Parabolized Navier-Stokes equations to compute millions of mesh points in several minutes. Sample two-dimensional and three-dimensional calculations are demonstrated in the paper.
Reproductive solutions for the g-Navier-Stokes and g-Kelvin-Voight equations
Directory of Open Access Journals (Sweden)
Luis Friz
2016-01-01
Full Text Available This article presents the existence of reproductive solutions of g-Navier-Stokes and g-Kelvin-Voight equations. In this way, for weak solutions, we reach basically the same result as for classic Navier-Stokes equations.
Navier-Stokes dynamics on a differential one-form
Story, Troy L.
2006-11-01
After transforming the Navier-Stokes dynamic equation into a characteristic differential one-form on an odd-dimensional differentiable manifold, exterior calculus is used to construct a pair of differential equations and tangent vector(vortex vector) characteristic of Hamiltonian geometry. A solution to the Navier-Stokes dynamic equation is then obtained by solving this pair of equations for the position x^k and the conjugate to the position bk as functions of time. The solution bk is shown to be divergence-free by contracting the differential 3-form corresponding to the divergence of the gradient of the velocity with a triple of tangent vectors, implying constraints on two of the tangent vectors for the system. Analysis of the solution bk shows it is bounded since it remains finite as | x^k | ->,, and is physically reasonable since the square of the gradient of the principal function is bounded. By contracting the characteristic differential one-form with the vortex vector, the Lagrangian is obtained.
Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations.
Vorobev, Anatoliy
2010-11-01
We use the Cahn-Hilliard approach to model the slow dissolution dynamics of binary mixtures. An important peculiarity of the Cahn-Hilliard-Navier-Stokes equations is the necessity to use the full continuity equation even for a binary mixture of two incompressible liquids due to dependence of mixture density on concentration. The quasicompressibility of the governing equations brings a short time-scale (quasiacoustic) process that may not affect the slow dynamics but may significantly complicate the numerical treatment. Using the multiple-scale method we separate the physical processes occurring on different time scales and, ultimately, derive the equations with the filtered-out quasiacoustics. The derived equations represent the Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations. This approximation can be further employed as a universal theoretical model for an analysis of slow thermodynamic and hydrodynamic evolution of the multiphase systems with strongly evolving and diffusing interfacial boundaries, i.e., for the processes involving dissolution/nucleation, evaporation/condensation, solidification/melting, polymerization, etc.
Boscheri, Walter; Dumbser, Michael
2017-10-01
Lagrangian formulations that are based on a fixed computational grid and which instead evolve the mapping of the reference configuration to the current one. Our new Lagrangian-type DG scheme adopts the novel a posteriori sub-cell finite volume limiter method recently developed in [62] for fixed unstructured grids. In this approach, the validity of the candidate solution produced in each cell by an unlimited ADER-DG scheme is verified against a set of physical and numerical detection criteria, such as the positivity of pressure and density, the absence of floating point errors (NaN) and the satisfaction of a relaxed discrete maximum principle (DMP) in the sense of polynomials. Those cells which do not satisfy all of the above criteria are flagged as troubled cells and are recomputed at the aid of a more robust second order TVD finite volume scheme. To preserve the subcell resolution capability of the original DG scheme, the FV limiter is run on a sub-grid that is 2 N + 1 times finer compared to the mesh of the original unlimited DG scheme. The new subcell averages are then gathered back into a high order DG polynomial by a usual conservative finite volume reconstruction operator. The numerical convergence rates of the new ALE ADER-DG schemes are studied up to fourth order in space and time and several test problems are simulated in order to check the accuracy and the robustness of the proposed numerical method in the context of the Euler and Navier-Stokes equations for compressible gas dynamics, considering both inviscid and viscous fluids. Finally, an application inspired by Inertial Confinement Fusion (ICF) type flows is considered by solving the Euler equations and the PDE of viscous and resistive magnetohydrodynamics (VRMHD).
An adaptive Petrov-Galerkin formulation for solving the compressible Euler and Navier-Stokes
International Nuclear Information System (INIS)
Almeida, Regina Celia Cerqueira de
1993-01-01
A space-time finite element finite element formulation for the compressible Euler and Navier-Stokes equations is proposed. The present work develops a stable generalized CAU method which represents shocks and boundary-layers accurately. An h-adaptive remeshing refinement, which takes into account directional stretching and stretching ratio, is used leading to a very good way to indicate and refine the flow regions with singularities. Numerical experiment were conducted for some steady and unsteady problems and the performance of the proposed methods is discussed. (author)
International Nuclear Information System (INIS)
Makhalov, A S; Nikolaenko, V P
2003-01-01
This paper is a survey of results concerning the three-dimensional Navier-Stokes and Euler equations with initial data characterized by uniformly large vorticity. The existence of regular solutions of the three-dimensional Navier-Stokes equations on an unbounded time interval is proved for large initial data both in R 3 and in bounded cylindrical domains. Moreover, the existence of smooth solutions on large finite time intervals is established for the three-dimensional Euler equations. These results are obtained without additional assumptions on the behaviour of solutions for t>0. Any smooth solution is not close to any two-dimensional manifold. Our approach is based on the computation of singular limits of rapidly oscillating operators, non-linear averaging, and a consideration of the mutual absorption of non-linear oscillations of the vorticity field. The use of resonance conditions, methods from the theory of small divisors, and non-linear averaging of almost periodic functions leads to the limit resonant Navier-Stokes equations. Global solubility of these equations is proved without any conditions on the three-dimensional initial data. The global regularity of weak solutions of three-dimensional Navier-Stokes equations with uniformly large vorticity at t=0 is proved by using the regularity of weak solutions and the strong convergence
A local level set method based on a finite element method for unstructured meshes
International Nuclear Information System (INIS)
Ngo, Long Cu; Choi, Hyoung Gwon
2016-01-01
A local level set method for unstructured meshes has been implemented by using a finite element method. A least-square weighted residual method was employed for implicit discretization to solve the level set advection equation. By contrast, a direct re-initialization method, which is directly applicable to the local level set method for unstructured meshes, was adopted to re-correct the level set function to become a signed distance function after advection. The proposed algorithm was constructed such that the advection and direct reinitialization steps were conducted only for nodes inside the narrow band around the interface. Therefore, in the advection step, the Gauss–Seidel method was used to update the level set function using a node-by-node solution method. Some benchmark problems were solved by using the present local level set method. Numerical results have shown that the proposed algorithm is accurate and efficient in terms of computational time
A local level set method based on a finite element method for unstructured meshes
Energy Technology Data Exchange (ETDEWEB)
Ngo, Long Cu; Choi, Hyoung Gwon [School of Mechanical Engineering, Seoul National University of Science and Technology, Seoul (Korea, Republic of)
2016-12-15
A local level set method for unstructured meshes has been implemented by using a finite element method. A least-square weighted residual method was employed for implicit discretization to solve the level set advection equation. By contrast, a direct re-initialization method, which is directly applicable to the local level set method for unstructured meshes, was adopted to re-correct the level set function to become a signed distance function after advection. The proposed algorithm was constructed such that the advection and direct reinitialization steps were conducted only for nodes inside the narrow band around the interface. Therefore, in the advection step, the Gauss–Seidel method was used to update the level set function using a node-by-node solution method. Some benchmark problems were solved by using the present local level set method. Numerical results have shown that the proposed algorithm is accurate and efficient in terms of computational time.
An analytical solution of the Navier-Stokes equation for internal flows
International Nuclear Information System (INIS)
Lyberg, Mats D; Tryggeson, Henrik
2007-01-01
This paper derives a solution to the Navier-Stokes equation by considering vorticity generated at system boundaries. The result is an explicit expression for the velocity. The Navier-Stokes equation is reformulated as a divergence and integrated, giving a tensor equation that splits into a symmetric and a skew-symmetric part. One equation gives an algebraic system of quadratic equations involving velocity components. A system of nonlinear partial differential equations is reduced to algebra. The velocity is then explicitly calculated and shown to depend on boundary conditions only. This removes the need to solve the Navier-Stokes equation by a 3D numerical computation, replacing it by computation of 2D surface integrals over the boundary. (fast track communication)
Diamantopoulos, Theodore; Rowe, Kristopher; Diamessis, Peter
2017-11-01
The Collocation Penalty Method (CPM) solves a PDE on the interior of a domain, while weakly enforcing boundary conditions at domain edges via penalty terms, and naturally lends itself to high-order and multi-domain discretization. Such spectral multi-domain penalty methods (SMPM) have been used to solve the Navier-Stokes equations. Bounds for penalty coefficients are typically derived using the energy method to guarantee stability for time-dependent problems. The choice of collocation points and penalty parameter can greatly affect the conditioning and accuracy of a solution. Effort has been made in recent years to relate various high-order methods on multiple elements or domains under the umbrella of the Correction Procedure via Reconstruction (CPR). Most applications of CPR have focused on solving the compressible Navier-Stokes equations using explicit time-stepping procedures. A particularly important aspect which is still missing in the context of the SMPM is a study of the Helmholtz equation arising in many popular time-splitting schemes for the incompressible Navier-Stokes equations. Stability and convergence results for the SMPM for the Helmholtz equation will be presented. Emphasis will be placed on the efficiency and accuracy of high-order methods.
An efficient approach to unstructured mesh hydrodynamics on the cell broadband engine
Energy Technology Data Exchange (ETDEWEB)
Ferenbaugh, Charles R [Los Alamos National Laboratory
2010-01-01
Unstructured mesh physics for the Cell Broadband Engine (CBE) has received little or no attention to date, largely because the CBE architecture poses particular challenges for unstructured mesh algorithms. The most common SPU memory management strategies cannot be applied to the irregular memory access patterns of unstructured meshes, and the SPU vector instruction set does not support the indirect addressing needed by connectivity arrays. This paper presents an approach to unstructured mesh physics that addresses these challenges, by creating a new mesh data structure and reorganizing code to give efficient CBE performance. The approach is demonstrated on the FLAG production hydrodynamics code using standard test problems, and results show an average speedup of more than 5x over the original code.
Chen, Xuemei; Fried, Eliot
2008-10-01
Lundgren's vortex model for the intermittent fine structure of high-Reynolds-number turbulence is applied to the Navier-Stokes alphabeta equations and specialized to the Navier-Stokes alpha equations. The Navier-Stokes alphabeta equations involve dispersive and dissipative length scales alpha and beta, respectively. Setting beta equal to alpha reduces the Navier-Stokes alphabeta equations to the Navier-Stokes alpha equations. For the Navier-Stokes alpha equations, the energy spectrum is found to obey Kolmogorov's -5/3 law in a range of wave numbers identical to that determined by Lundgren for the Navier-Stokes equations. For the Navier-Stokes alphabeta equations, Kolmogorov's -5/3 law is also recovered. However, granted that beta Navier-Stokes alphabeta equations may have the potential to resolve features smaller than those obtainable using the Navier-Stokes alpha equations.
Scaling properties of the two-dimensional randomly stirred Navier-Stokes equation.
Mazzino, Andrea; Muratore-Ginanneschi, Paolo; Musacchio, Stefano
2007-10-05
We inquire into the scaling properties of the 2D Navier-Stokes equation sustained by a force field with Gaussian statistics, white noise in time, and with a power-law correlation in momentum space of degree 2 - 2 epsilon. This is at variance with the setting usually assumed to derive Kraichnan's classical theory. We contrast accurate numerical experiments with the different predictions provided for the small epsilon regime by Kraichnan's double cascade theory and by renormalization group analysis. We give clear evidence that for all epsilon, Kraichnan's theory is consistent with the observed phenomenology. Our results call for a revision in the renormalization group analysis of (2D) fully developed turbulence.
Kwon, Young-Sam; Li, Fucai
2018-03-01
In this paper we study the incompressible limit of the degenerate quantum compressible Navier-Stokes equations in a periodic domain T3 and the whole space R3 with general initial data. In the periodic case, by applying the refined relative entropy method and carrying out the detailed analysis on the oscillations of velocity, we prove rigorously that the gradient part of the weak solutions (velocity) of the degenerate quantum compressible Navier-Stokes equations converge to the strong solution of the incompressible Navier-Stokes equations. Our results improve considerably the ones obtained by Yang, Ju and Yang [25] where only the well-prepared initial data case is considered. While for the whole space case, thanks to the Strichartz's estimates of linear wave equations, we can obtain the convergence of the weak solutions of the degenerate quantum compressible Navier-Stokes equations to the strong solution of the incompressible Navier-Stokes/Euler equations with a linear damping term. Moreover, the convergence rates are also given.
Salinas, P.; Pavlidis, D.; Jacquemyn, C.; Lei, Q.; Xie, Z.; Pain, C.; Jackson, M.
2017-12-01
It is well known that the pressure gradient into a production well increases with decreasing distance to the well. To properly capture the local pressure drawdown into the well a high grid or mesh resolution is required; moreover, the location of the well must be captured accurately. In conventional simulation models, the user must interact with the model to modify grid resolution around wells of interest, and the well location is approximated on a grid defined early in the modelling process.We report a new approach for improved simulation of near wellbore flow in reservoir scale models through the use of dynamic mesh optimisation and the recently presented double control volume finite element method. Time is discretized using an adaptive, implicit approach. Heterogeneous geologic features are represented as volumes bounded by surfaces. Within these volumes, termed geologic domains, the material properties are constant. Up-, cross- or down-scaling of material properties during dynamic mesh optimization is not required, as the properties are uniform within each geologic domain. A given model typically contains numerous such geologic domains. Wells are implicitly coupled with the domain, and the fluid flows is modelled inside the wells. The method is novel for two reasons. First, a fully unstructured tetrahedral mesh is used to discretize space, and the spatial location of the well is specified via a line vector, ensuring its location even if the mesh is modified during the simulation. The well location is therefore accurately captured, the approach allows complex well trajectories and wells with many laterals to be modelled. Second, computational efficiency is increased by use of dynamic mesh optimization, in which an unstructured mesh adapts in space and time to key solution fields (preserving the geometry of the geologic domains), such as pressure, velocity or temperature, this also increases the quality of the solutions by placing higher resolution where required
On Coupled System of Navier-Stokes Equations and Temperature
African Journals Online (AJOL)
Dr. Anthony Peter
ABSTRACT. This paper deals with the coupled system of Navier-Stokes equations and temperature (Thermohydraulics) in a strip in the class of spatially non-decaying (infinite-energy) solutions belonging to the properly chosen uniformly local Sobolev spaces. The global well-posedness and dissipativity of the Navier- ...
Status for the two-dimensional Navier-Stokes solver EllipSys2D
Energy Technology Data Exchange (ETDEWEB)
Bertagnolio, F.; Soerensen, N.; Johansen, J.
2001-08-01
This report sets up an evaluation of two-dimensional Navier-Stokes solver EllipSys2D in its present state. This code is used for blade aerodynamics simulations in the Aeroelastic Design group at Risoe. Two airfoils are investigated by computing the flow at several angles of attack ranging from the linear to the stalled region. The computational data are compared to experimental data and numerical results from other computational codes. Several numerical aspects are studied, as mesh dependency, convective scheme, steady state versus unsteady computations, transition modelling. Some general conclusions intended to help in using this code for numerical simulations are given. (au)
Mesh Adaptation and Shape Optimization on Unstructured Meshes, Phase I
National Aeronautics and Space Administration — In this SBIR CRM proposes to implement the entropy adjoint method for solution adaptive mesh refinement into the Loci/CHEM unstructured flow solver. The scheme will...
Simulating variable-density flows with time-consistent integration of Navier-Stokes equations
Lu, Xiaoyi; Pantano, Carlos
2017-11-01
In this talk, we present several features of a high-order semi-implicit variable-density low-Mach Navier-Stokes solver. A new formulation to solve pressure Poisson-like equation of variable-density flows is highlighted. With this formulation of the numerical method, we are able to solve all variables with a uniform order of accuracy in time (consistent with the time integrator being used). The solver is primarily designed to perform direct numerical simulations for turbulent premixed flames. Therefore, we also address other important elements, such as energy-stable boundary conditions, synthetic turbulence generation, and flame anchoring method. Numerical examples include classical non-reacting constant/variable-density flows, as well as turbulent premixed flames.
An efficient numerical technique for solving navier-stokes equations for rotating flows
International Nuclear Information System (INIS)
Haroon, T.; Shah, T.M.
2000-01-01
This paper simulates an industrial problem by solving compressible Navier-Stokes equations. The time-consuming tri-angularization process of a large-banded matrix, performed by memory economical Frontal Technique. This scheme successfully reduces the time for I/O operations even for as large as (40, 000 x 40, 000) matrix. Previously, this industrial problem can solved by using modified Newton's method with Gaussian elimination technique for the large matrix. In the present paper, the proposed Frontal Technique is successfully used, together with Newton's method, to solve compressible Navier-Stokes equations for rotating cylinders. By using the Frontal Technique, the method gives the solution within reasonably acceptance computational time. Results are compared with the earlier works done, and found computationally very efficient. Some features of the solution are reported here for the rotating machines. (author)
Energy Technology Data Exchange (ETDEWEB)
Wu Hongchun [Nuclear Engineering Department, Xi' an Jiaotong University, Xi' an 710049, Shaanxi (China)]. E-mail: hongchun@mail.xjtu.edu.cn; Liu Pingping [Nuclear Engineering Department, Xi' an Jiaotong University, Xi' an 710049, Shaanxi (China); Zhou Yongqiang [Nuclear Engineering Department, Xi' an Jiaotong University, Xi' an 710049, Shaanxi (China); Cao Liangzhi [Nuclear Engineering Department, Xi' an Jiaotong University, Xi' an 710049, Shaanxi (China)
2007-01-15
In the advanced reactor, the fuel assembly or core with unstructured geometry is frequently used and for calculating its fuel assembly, the transmission probability method (TPM) has been used widely. However, the rectangle or hexagon meshes are mainly used in the TPM codes for the normal core structure. The triangle meshes are most useful for expressing the complicated unstructured geometry. Even though finite element method and Monte Carlo method is very good at solving unstructured geometry problem, they are very time consuming. So we developed the TPM code based on the triangle meshes. The TPM code based on the triangle meshes was applied to the hybrid fuel geometry, and compared with the results of the MCNP code and other codes. The results of comparison were consistent with each other. The TPM with triangle meshes would thus be expected to be able to apply to the two-dimensional arbitrary fuel assembly.
The Navier-Stokes equations on a bounded domain
International Nuclear Information System (INIS)
Scheffer, V.
1980-01-01
Suppose U is an open bounded subset of 3-space such that the boundary of U has Lebesgue measure zero. Then for any initial condition with finite kinetic energy we can find a global (i.e. for all time) weak solution u to the time dependent Navier-Stokes equations of incompressible fluid flow in U such that the curl of u is continuous outside a locally closed set whose 5/3 dimensional Hausdorff measure is finite. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Almeida, Regina Celia Cerqueira de
1993-12-31
A space-time finite element finite element formulation for the compressible Euler and Navier-Stokes equations is proposed. The present work develops a stable generalized CAU method which represents shocks and boundary-layers accurately. An h-adaptive remeshing refinement, which takes into account directional stretching and stretching ratio, is used leading to a very good way to indicate and refine the flow regions with singularities. Numerical experiment were conducted for some steady and unsteady problems and the performance of the proposed methods is discussed. (author) 63 refs., 40 figs.
Energy Technology Data Exchange (ETDEWEB)
Almeida, Regina Celia Cerqueira de
1994-12-31
A space-time finite element finite element formulation for the compressible Euler and Navier-Stokes equations is proposed. The present work develops a stable generalized CAU method which represents shocks and boundary-layers accurately. An h-adaptive remeshing refinement, which takes into account directional stretching and stretching ratio, is used leading to a very good way to indicate and refine the flow regions with singularities. Numerical experiment were conducted for some steady and unsteady problems and the performance of the proposed methods is discussed. (author) 63 refs., 40 figs.
International Nuclear Information System (INIS)
Merzari, E.; Ninokata, H.; Baglietto, E.
2008-01-01
Traditional steady-state simulation and turbulence modelling are not always reliable. Even in simple flows, the results can be not accurate when particular conditions occur. Examples are buoyancy, flow oscillations, and turbulent mixing. Often, unsteady simulations are necessary, but they tend to be computationally not affordable. The Unsteady Reynolds Averaged Navier-Stokes (URANS) approach holds promise to be less computational expensive than Large Eddy Simulation (LES) or Direct Numerical Simulation (DNS), reaching a considerable degree of accuracy. Moreover, URANS methodologies do not need complex boundary formulations for the inlet and the outlet like LES or DNS. The Test cases for this methodology will be Fuel Bundles and T-junctions. Tight-Fuel Rod-Bundles present large scale coherent structures than cannot be taken into account by a simple steady-state simulation. T-junctions where a hot fluid and a cold fluid mix present temperature fluctuations and therefore thermal fatigue. For both cases the capacity of the methodology to reproduce the flow field are assessed and it is evaluated that URANS holds promise to be the industrial standard in nuclear engineering applications that do not involve buoyancy. The codes employed are STAR-CD 3.26 and 4.06. (author)
Convergence acceleration of Navier-Stokes equation using adaptive wavelet method
International Nuclear Information System (INIS)
Kang, Hyung Min; Ghafoor, Imran; Lee, Do Hyung
2010-01-01
An efficient adaptive wavelet method is proposed for the enhancement of computational efficiency of the Navier-Stokes equations. The method is based on sparse point representation (SPR), which uses the wavelet decomposition and thresholding to obtain a sparsely distributed dataset. The threshold mechanism is modified in order to maintain the spatial accuracy of a conventional Navier-Stokes solver by adapting the threshold value to the order of spatial truncation error. The computational grid can be dynamically adapted to a transient solution to reflect local changes in the solution. The flux evaluation is then carried out only at the points of the adapted dataset, which reduces the computational effort and memory requirements. A stabilization technique is also implemented to avoid the additional numerical errors introduced by the threshold procedure. The numerical results of the adaptive wavelet method are compared with a conventional solver to validate the enhancement in computational efficiency of Navier-Stokes equations without the degeneration of the numerical accuracy of a conventional solver
An efficient approach to unstructured mesh hydrodynamics on the cell broadband engine (u)
Energy Technology Data Exchange (ETDEWEB)
Ferenbaugh, Charles R [Los Alamos National Laboratory
2010-12-14
Unstructured mesh physics for the Cell Broadband Engine (CBE) has received little or no attention to date, largely because the CBE architecture poses particular challenges for unstructured mesh algorithms. SPU memory management strategies such as data preloading cannot be applied to the irregular memory storage patterns of unstructured meshes; and the SPU vector instruction set does not support the indirect addressing needed by connectivity arrays. This paper presents an approach to unstructured mesh physics that addresses these challenges, by creating a new mesh data structure and reorganizing code to give efficient CBE performance. The approach is demonstrated on the FLAG production hydrodynamics code using standard test problems, and results show an average speedup of more than 5x over the original code.
Moment realizability and the validity of the Navier - Stokes equations for rarefied gas dynamics
International Nuclear Information System (INIS)
Levermore, C.D.; Morokoff, W.J.; Nadiga, B.T.
1998-01-01
We present criteria for monitoring the validity of the Navier - Stokes approximation during the simulation of a rarefied gas. Our approach is based on an underlying kinetic formulation through which one can construct nondimensional non-negative definite matrices from moments of the molecular distribution. We then identify one such 3x3 matrix that can be evaluated intrinsically in the Navier - Stokes approximation. Our criteria are based on deviations of the eigenvalues of this matrix from their equilibrium value of unity. Not being tied to a particular benchmark problem, the resulting criteria are portable and may be applied to any Navier - Stokes simulation. We study its utility here by comparing stationary planar shock profiles computed using the Navier - Stokes equations with those computed using Monte Carlo simulations. copyright 1998 American Institute of Physics
International Nuclear Information System (INIS)
Boukir, K.
1994-06-01
This thesis deals with the extension to higher order in time of two splitting methods for the Navier-Stokes equations: the characteristics method and the projection one. The first consists in decoupling the convection operator from the Stokes one. The second decomposes this latter into a diffusion problem and a pressure-continuity one. Concerning the characteristics method, numerical and theoretical study is developed for the second order scheme together with a finite element spatial discretization. The case of a spectral spatial discretization is also treated and theoretical analysis are given respectively for second and third order schemes. For both spatial discretizations, we obtain good error estimates, unconditionally or under non stringent stability conditions, for both velocity and pressure. Numerical results illustrate the interest of the second order scheme comparing to the first order one. Extensions of the second order scheme to the K-epsilon turbulence model are proposed and tested, in the case of a finite element spatial discretization. Concerning the projection method, we define the order schemes. The theoretical study deals with stability and convergence of first and second order projection schemes, for the incompressible Navier-Stokes equations and with a finite element spatial discretization. The numerical study concerns mainly the second order scheme applied to the Navier-Stokes equations with varying density. (authors). 63 refs., figs
Generalized extended Navier-Stokes theory: Multiscale spin relaxation in molecular fluids
DEFF Research Database (Denmark)
Hansen, Jesper Schmidt
2013-01-01
This paper studies the relaxation of the molecular spin angular velocity in the framework of generalized extended Navier-Stokes theory. Using molecular dynamics simulations, it is shown that for uncharged diatomic molecules the relaxation time decreases with increasing molecular moment of inertia...
Analysis of regularized Navier-Stokes equations, 2
Ou, Yuh-Roung; Sritharan, S. S.
1989-01-01
A practically important regularization of the Navier-Stokes equations was analyzed. As a continuation of the previous work, the structure of the attractors characterizing the solutins was studied. Local as well as global invariant manifolds were found. Regularity properties of these manifolds are analyzed.
International Nuclear Information System (INIS)
Foias, C; Jolly, M S; Kravchenko, R; Titi, E S
2014-01-01
It is shown that the long-time dynamics (the global attractor) of the 2D Navier-Stokes system is embedded in the long-time dynamics of an ordinary differential equation, called a determining form, in a space of trajectories which is isomorphic to C b 1 (R;R N ) for sufficiently large N depending on the physical parameters of the Navier-Stokes equations. A unified approach is presented, based on interpolant operators constructed from various determining parameters for the Navier-Stokes equations, namely, determining nodal values, Fourier modes, finite volume elements, finite elements, and so on. There are two immediate and interesting consequences of this unified approach. The first is that the constructed determining form has a Lyapunov function, and thus its solutions converge to the set of steady states of the determining form as the time goes to infinity. The second is that these steady states of the determining form can be uniquely identified with the trajectories in the global attractor of the Navier-Stokes system. It should be added that this unified approach is general enough that it applies, in an almost straightforward manner, to a whole class of dissipative dynamical systems. Bibliography: 23 titles
A Numerical Study of Mesh Adaptivity in Multiphase Flows with Non-Newtonian Fluids
Percival, James; Pavlidis, Dimitrios; Xie, Zhihua; Alberini, Federico; Simmons, Mark; Pain, Christopher; Matar, Omar
2014-11-01
We present an investigation into the computational efficiency benefits of dynamic mesh adaptivity in the numerical simulation of transient multiphase fluid flow problems involving Non-Newtonian fluids. Such fluids appear in a range of industrial applications, from printing inks to toothpastes and introduce new challenges for mesh adaptivity due to the additional ``memory'' of viscoelastic fluids. Nevertheless, the multiscale nature of these flows implies huge potential benefits for a successful implementation. The study is performed using the open source package Fluidity, which couples an unstructured mesh control volume finite element solver for the multiphase Navier-Stokes equations to a dynamic anisotropic mesh adaptivity algorithm, based on estimated solution interpolation error criteria, and conservative mesh-to-mesh interpolation routine. The code is applied to problems involving rheologies ranging from simple Newtonian to shear-thinning to viscoelastic materials and verified against experimental data for various industrial and microfluidic flows. This work was undertaken as part of the EPSRC MEMPHIS programme grant EP/K003976/1.
Navier-Stokes-Fourier Equations A Rational Asymptotic Modelling Point of View
Zeytounian, Radyadour Kh
2012-01-01
This research monograph deals with a modeling theory of the system of Navier-Stokes-Fourier equations for a Newtonian fluid governing a compressible viscous and heat conducting flows. The main objective is threefold. First , to 'deconstruct' this Navier-Stokes-Fourier system in order to unify the puzzle of the various partial simplified approximate models used in Newtonian Classical Fluid Dynamics and this, first facet, have obviously a challenging approach and a very important pedagogic impact on the university education. The second facet of the main objective is to outline a rational consistent asymptotic/mathematical theory of the of fluid flows modeling on the basis of a typical Navier-Stokes-Fourier initial and boundary value problem. The third facet is devoted to an illustration of our rational asymptotic/mathematical modeling theory for various technological and geophysical stiff problems from: aerodynamics, thermal and thermocapillary convections and also meteofluid dynamics.
A stable penalty method for the compressible Navier-Stokes equations: I. Open boundary conditions
DEFF Research Database (Denmark)
Hesthaven, Jan; Gottlieb, D.
1996-01-01
The purpose of this paper is to present asymptotically stable open boundary conditions for the numerical approximation of the compressible Navier-Stokes equations in three spatial dimensions. The treatment uses the conservation form of the Navier-Stokes equations and utilizes linearization...
Some strange numerical solutions of the non-stationary Navier-Stokes equations in pipes
Energy Technology Data Exchange (ETDEWEB)
Rummler, B.
2001-07-01
A general class of boundary-pressure-driven flows of incompressible Newtonian fluids in three-dimensional pipes with known steady laminar realizations is investigated. Considering the laminar velocity as a 3D-vector-function of the cross-section-circle arguments, we fix the scale for the velocity by the L{sub 2}-norm of the laminar velocity. The usual new variables are introduced to get dimension-free Navier-Stokes equations. The characteristic physical and geometrical quantities are subsumed in the energetic Reynolds number Re and a parameter {psi}, which involves the energetic ratio and the directions of the boundary-driven part and the pressure-driven part of the laminar flow. The solution of non-stationary dimension-free Navier-Stokes equations is sought in the form u=u{sub L}+u, where u{sub L} is the scaled laminar velocity and periodical conditions in center-line-direction are prescribed for u. An autonomous system (S) of ordinary differential equations for the time-dependent coefficients of the spatial Stokes eigenfunction is got by application of the Galerkin-method to the dimension-free Navier-Stokes equations for u. The finite-dimensional approximations u{sub N({lambda}}{sub )} of u are defined in the usual way. (orig.)
MCR2S unstructured mesh capabilities for use in shutdown dose rate analysis
International Nuclear Information System (INIS)
Eade, T.; Stonell, D.; Turner, A.
2015-01-01
Highlights: • Advancements in shutdown dose rate calculations will be needed as fusion moves from experimental reactors to full scale demonstration reactors in order to ensure the safety of personnel. • The MCR2S shutdown dose rate tool has been modified to allow shutdown dose rates calculations using an unstructured mesh. • The unstructured mesh capability of MCR2S was used on three shutdown dose rate models, a simple sphere, the ITER computational benchmark and the DEMO computational benchmark. • The results showed a reasonable agreement between an unstructured mesh approach and the CSG approach and highlighted the need to carefully choose the unstructured mesh resolution. - Abstract: As nuclear fusion progresses towards a sustainable energy source and the power of tokamak devices increases, a greater understanding of the radiation fields will be required. As well as on-load radiation fields, off-load or shutdown radiation field are an important consideration for the safety and economic viability of a commercial fusion reactor. Previously codes such as MCR2S have been written in order to predict the shutdown dose rates within, and in regions surrounding, a fusion reactor. MCR2S utilises a constructive solid geometry (CSG) model and a superimposed structured mesh to calculate 3-D maps of the shutdown dose rate. A new approach to MCR2S calculations is proposed and implemented using a single unstructured mesh to replace both the CSG model and the superimposed structured mesh. This new MCR2S approach has been demonstrated on three models of increasing complexity. These models were: a sphere, the ITER computational shutdown dose rate benchmark and the DEMO computational shutdown dose rate benchmark. In each case the results were compared to MCR2S calculations performed using MCR2S with CSG geometry and a superimposed structured mesh. It was concluded that the results from the unstructured mesh implementation of MCR2S compared well to the CSG structured mesh
Implementation of LDG method for 3D unstructured meshes
Directory of Open Access Journals (Sweden)
Filander A. Sequeira Chavarría
2012-07-01
Full Text Available This paper describes an implementation of the Local Discontinuous Galerkin method (LDG applied to elliptic problems in 3D. The implementation of the major operators is discussed. In particular the use of higher-order approximations and unstructured meshes. Efficient data structures that allow fast assembly of the linear system in the mixed formulation are described in detail. Keywords: Discontinuous finite element methods, high-order approximations, unstructured meshes, object-oriented programming. Mathematics Subject Classification: 65K05, 65N30, 65N55.
Study of Tip-loss Using an Inverse 3D Navier-Stokes Method
DEFF Research Database (Denmark)
Mikkelsen, Robert; Sørensen, Jens Nørkær; Shen, Wen Zhong
2003-01-01
the 3D Navier-Stokes equations combined with the actuator line technique where blade loading is applied using an inverse method. The numerical simulations shows that the method captures the tip-correction when comparing with the theories of Prandtl and Goldstein, however, the accuracy of the obtained...... results reveal that further refinements still is needed. Keywords: Tip-loss; Actuator line; 3D Navier-Stokes methods....
Algebraic mesh generation for large scale viscous-compressible aerodynamic simulation
International Nuclear Information System (INIS)
Smith, R.E.
1984-01-01
Viscous-compressible aerodynamic simulation is the numerical solution of the compressible Navier-Stokes equations and associated boundary conditions. Boundary-fitted coordinate systems are well suited for the application of finite difference techniques to the Navier-Stokes equations. An algebraic approach to boundary-fitted coordinate systems is one where an explicit functional relation describes a mesh on which a solution is obtained. This approach has the advantage of rapid-precise mesh control. The basic mathematical structure of three algebraic mesh generation techniques is described. They are transfinite interpolation, the multi-surface method, and the two-boundary technique. The Navier-Stokes equations are transformed to a computational coordinate system where boundary-fitted coordinates can be applied. Large-scale computation implies that there is a large number of mesh points in the coordinate system. Computation of viscous compressible flow using boundary-fitted coordinate systems and the application of this computational philosophy on a vector computer are presented
International Nuclear Information System (INIS)
Kawashima, S.; Matsumara, A.; Nishida, T.
1979-01-01
The compressible and heat-conductive Navier-Stokes equation obtained as the second approximation of the formal Chapman-Enskog expansion is investigated on its relations to the original nonlinear Boltzmann equation and also to the incompressible Navier-Stokes equation. The solutions of the Boltzmann equation and the incompressible Navier-Stokes equation for small initial data are proved to be asymptotically equivalent (mod decay rate tsup(-5/4)) as t → + infinitely to that of the compressible Navier-Stokes equation for the corresponding initial data. (orig.) 891 HJ/orig. 892 MKO
Energy Technology Data Exchange (ETDEWEB)
Boukir, K
1994-06-01
This thesis deals with the extension to higher order in time of two splitting methods for the Navier-Stokes equations: the characteristics method and the projection one. The first consists in decoupling the convection operator from the Stokes one. The second decomposes this latter into a diffusion problem and a pressure-continuity one. Concerning the characteristics method, numerical and theoretical study is developed for the second order scheme together with a finite element spatial discretization. The case of a spectral spatial discretization is also treated and theoretical analysis are given respectively for second and third order schemes. For both spatial discretizations, we obtain good error estimates, unconditionally or under non stringent stability conditions, for both velocity and pressure. Numerical results illustrate the interest of the second order scheme comparing to the first order one. Extensions of the second order scheme to the K-epsilon turbulence model are proposed and tested, in the case of a finite element spatial discretization. Concerning the projection method, we define the order schemes. The theoretical study deals with stability and convergence of first and second order projection schemes, for the incompressible Navier-Stokes equations and with a finite element spatial discretization. The numerical study concerns mainly the second order scheme applied to the Navier-Stokes equations with varying density. (authors). 63 refs., figs.
Hydrodynamic potentials for the micropolar Navier-Stokes problem
International Nuclear Information System (INIS)
Martynenko, M.D.; Dimian, M.
1995-01-01
An integral representation of linear and angular velocities and pressure for the description of linear stationary flows of micropolar viscous liquid media is obtained, and on its basis hydrodynamic potentials for the micropolar Navier-Stokes problem are introduced
Numerical resolution of Navier-Stokes equations coupled to the heat equation
International Nuclear Information System (INIS)
Zenouda, Jean-Claude
1970-08-01
The author proves a uniqueness theorem for the time dependent Navier-Stokes equations coupled with heat flow in the two-dimensional case. He studies stability and convergence of several finite - difference schemes to solve these equations. Numerical experiments are done in the case of a square domain. (author) [fr
Advances in Spectral Methods for UQ in Incompressible Navier-Stokes Equations
Le Maitre, Olivier
2014-01-06
In this talk, I will present two recent contributions to the development of efficient methodologies for uncertainty propagation in the incompressible Navier-Stokes equations. The first one concerns the reduced basis approximation of stochastic steady solutions, using Proper Generalized Decompositions (PGD). An Arnoldi problem is projected to obtain a low dimensional Galerkin problem. The construction then amounts to the resolution of a sequence of uncoupled deterministic Navier-Stokes like problem and simple quadratic stochastic problems, followed by the resolution of a low-dimensional coupled quadratic stochastic problem, with a resulting complexity which has to be contrasted with the dimension of the whole Galerkin problem for classical spectral approaches. An efficient algorithm for the approximation of the stochastic pressure field is also proposed. Computations are presented for uncertain viscosity and forcing term to demonstrate the effectiveness of the reduced method. The second contribution concerns the computation of stochastic periodic solutions to the Navier-Stokes equations. The objective is to circumvent the well-known limitation of spectral methods for long-time integration. We propose to directly determine the stochastic limit-cycles through the definition of its stochastic period and an initial condition over the cycle. A modified Newton method is constructed to compute iteratively both the period and initial conditions. Owing to the periodic character of the solution, and by introducing an appropriate time-scaling, the solution can be approximated using low-degree polynomial expansions with large computational saving as a result. The methodology is illustrated for the von-Karman flow around a cylinder with stochastic inflow conditions.
Advances in Spectral Methods for UQ in Incompressible Navier-Stokes Equations
Le Maitre, Olivier
2014-01-01
In this talk, I will present two recent contributions to the development of efficient methodologies for uncertainty propagation in the incompressible Navier-Stokes equations. The first one concerns the reduced basis approximation of stochastic steady solutions, using Proper Generalized Decompositions (PGD). An Arnoldi problem is projected to obtain a low dimensional Galerkin problem. The construction then amounts to the resolution of a sequence of uncoupled deterministic Navier-Stokes like problem and simple quadratic stochastic problems, followed by the resolution of a low-dimensional coupled quadratic stochastic problem, with a resulting complexity which has to be contrasted with the dimension of the whole Galerkin problem for classical spectral approaches. An efficient algorithm for the approximation of the stochastic pressure field is also proposed. Computations are presented for uncertain viscosity and forcing term to demonstrate the effectiveness of the reduced method. The second contribution concerns the computation of stochastic periodic solutions to the Navier-Stokes equations. The objective is to circumvent the well-known limitation of spectral methods for long-time integration. We propose to directly determine the stochastic limit-cycles through the definition of its stochastic period and an initial condition over the cycle. A modified Newton method is constructed to compute iteratively both the period and initial conditions. Owing to the periodic character of the solution, and by introducing an appropriate time-scaling, the solution can be approximated using low-degree polynomial expansions with large computational saving as a result. The methodology is illustrated for the von-Karman flow around a cylinder with stochastic inflow conditions.
Investigation of vortex breakdown on a delta wing using Euler and Navier-Stokes equations
Agrawal, S.; Barnett, R. M.; Robinson, B. A.
1991-01-01
A numerical investigation of leading edge vortex breakdown in a delta wing at high angles of attack is presented. The analysis was restricted to low speed flows on a flat plate wing with sharp leading edges. Both Euler and Navier-Stokes equations were used and the results were compared with experimental data. Predictions of vortex breakdown progression with angle of attack with both Euler and Navier-Stokes equations are shown to be consistent with the experimental data. However, the Navier-Stokes predictions show significant improvements in breakdown location at angles of attack where the vortex breakdown approaches the wing apex. The predicted trajectories of the primary vortex are in very good agreement with the test data, the laminar solutions providing the overall best comparison. The Euler shows a small displacement of the primary vortex, relative to experiment, due to the lack of secondary vortices. The turbulent Navier-Stokes, in general, fall between the Euler and laminar solutions.
Pelties, Christian
2012-02-18
Accurate and efficient numerical methods to simulate dynamic earthquake rupture and wave propagation in complex media and complex fault geometries are needed to address fundamental questions in earthquake dynamics, to integrate seismic and geodetic data into emerging approaches for dynamic source inversion, and to generate realistic physics-based earthquake scenarios for hazard assessment. Modeling of spontaneous earthquake rupture and seismic wave propagation by a high-order discontinuous Galerkin (DG) method combined with an arbitrarily high-order derivatives (ADER) time integration method was introduced in two dimensions by de la Puente et al. (2009). The ADER-DG method enables high accuracy in space and time and discretization by unstructured meshes. Here we extend this method to three-dimensional dynamic rupture problems. The high geometrical flexibility provided by the usage of tetrahedral elements and the lack of spurious mesh reflections in the ADER-DG method allows the refinement of the mesh close to the fault to model the rupture dynamics adequately while concentrating computational resources only where needed. Moreover, ADER-DG does not generate spurious high-frequency perturbations on the fault and hence does not require artificial Kelvin-Voigt damping. We verify our three-dimensional implementation by comparing results of the SCEC TPV3 test problem with two well-established numerical methods, finite differences, and spectral boundary integral. Furthermore, a convergence study is presented to demonstrate the systematic consistency of the method. To illustrate the capabilities of the high-order accurate ADER-DG scheme on unstructured meshes, we simulate an earthquake scenario, inspired by the 1992 Landers earthquake, that includes curved faults, fault branches, and surface topography. Copyright 2012 by the American Geophysical Union.
Discretizations in isogeometric analysis of Navier-Stokes flow
DEFF Research Database (Denmark)
Nielsen, Peter Nørtoft; Gersborg, Allan Roulund; Gravesen, Jens
2011-01-01
This paper deals with isogeometric analysis of 2-dimensional, steady state, incompressible Navier-Stokes flow subjected to Dirichlet boundary conditions. We present a detailed description of the numerical method used to solve the boundary value problem. Numerical inf-sup stability tests...
Sigma-convergence of stationary Navier-Stokes type equations
Directory of Open Access Journals (Sweden)
Gabriel Nguetseng
2009-06-01
Full Text Available In the framework of homogenization theory, the Sigma-convergence method is carried out on stationary Navier-Stokes type equations on a fixed domain. Our main tools are the two-scale convergence concept and the so-called homogenization algebras.
DEFF Research Database (Denmark)
Hesthaven, Jan
1997-01-01
This paper presents asymptotically stable schemes for patching of nonoverlapping subdomains when approximating the compressible Navier-Stokes equations given on conservation form. The scheme is a natural extension of a previously proposed scheme for enforcing open boundary conditions and as a res......This paper presents asymptotically stable schemes for patching of nonoverlapping subdomains when approximating the compressible Navier-Stokes equations given on conservation form. The scheme is a natural extension of a previously proposed scheme for enforcing open boundary conditions...... and as a result the patching of subdomains is local in space. The scheme is studied in detail for Burgers's equation and developed for the compressible Navier-Stokes equations in general curvilinear coordinates. The versatility of the proposed scheme for the compressible Navier-Stokes equations is illustrated...
Time-Accurate Simulations of Synthetic Jet-Based Flow Control for An Axisymmetric Spinning Body
National Research Council Canada - National Science Library
Sahu, Jubaraj
2004-01-01
.... A time-accurate Navier-Stokes computational technique has been used to obtain numerical solutions for the unsteady jet-interaction flow field for a spinning projectile at a subsonic speed, Mach...
Symmetry breaking and uniqueness for the incompressible Navier-Stokes equations
International Nuclear Information System (INIS)
Dascaliuc, Radu; Thomann, Enrique; Waymire, Edward C.; Michalowski, Nicholas
2015-01-01
The present article establishes connections between the structure of the deterministic Navier-Stokes equations and the structure of (similarity) equations that govern self-similar solutions as expected values of certain naturally associated stochastic cascades. A principle result is that explosion criteria for the stochastic cascades involved in the probabilistic representations of solutions to the respective equations coincide. While the uniqueness problem itself remains unresolved, these connections provide interesting problems and possible methods for investigating symmetry breaking and the uniqueness problem for Navier-Stokes equations. In particular, new branching Markov chains, including a dilogarithmic branching random walk on the multiplicative group (0, ∞), naturally arise as a result of this investigation
Symmetry breaking and uniqueness for the incompressible Navier-Stokes equations.
Dascaliuc, Radu; Michalowski, Nicholas; Thomann, Enrique; Waymire, Edward C
2015-07-01
The present article establishes connections between the structure of the deterministic Navier-Stokes equations and the structure of (similarity) equations that govern self-similar solutions as expected values of certain naturally associated stochastic cascades. A principle result is that explosion criteria for the stochastic cascades involved in the probabilistic representations of solutions to the respective equations coincide. While the uniqueness problem itself remains unresolved, these connections provide interesting problems and possible methods for investigating symmetry breaking and the uniqueness problem for Navier-Stokes equations. In particular, new branching Markov chains, including a dilogarithmic branching random walk on the multiplicative group (0, ∞), naturally arise as a result of this investigation.
Eulerian derivations of non-inertial Navier-Stokes equations
CSIR Research Space (South Africa)
Combrinck, MA
2014-09-01
Full Text Available The paper presents an Eulerian derivation of the non-inertial Navier-Stokes equations as an alternative to the Lagrangian fluid parcel approach. This work expands on the work of Kageyama and Hyodo [1] who derived the incompressible momentum equation...
Homogenization of the evolutionary Navier-Stokes system
Czech Academy of Sciences Publication Activity Database
Feireisl, Eduard; Namlyeyeva, Yuliya; Nečasová, Šárka
2016-01-01
Roč. 149, č. 1 (2016), s. 251-274 ISSN 0025-2611 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier-Stokes system Subject RIV: BA - General Mathematics Impact factor: 0.607, year: 2016 http://link.springer.com/article/10.1007%2Fs00229-015-0778-y
Partial Averaged Navier-Stokes approach for cavitating flow
International Nuclear Information System (INIS)
Zhang, L; Zhang, Y N
2015-01-01
Partial Averaged Navier Stokes (PANS) is a numerical approach developed for studying practical engineering problems (e.g. cavitating flow inside hydroturbines) with a resonance cost and accuracy. One of the advantages of PANS is that it is suitable for any filter width, leading a bridging method from traditional Reynolds Averaged Navier-Stokes (RANS) to direct numerical simulations by choosing appropriate parameters. Comparing with RANS, the PANS model will inherit many physical nature from parent RANS but further resolve more scales of motion in great details, leading to PANS superior to RANS. As an important step for PANS approach, one need to identify appropriate physical filter-width control parameters e.g. ratios of unresolved-to-total kinetic energy and dissipation. In present paper, recent studies of cavitating flow based on PANS approach are introduced with a focus on the influences of filter-width control parameters on the simulation results
Smooth Bézier surfaces over unstructured quadrilateral meshes
Bercovier, Michel
2017-01-01
Using an elegant mixture of geometry, graph theory and linear analysis, this monograph completely solves a problem lying at the interface of Isogeometric Analysis (IgA) and Finite Element Methods (FEM). The recent explosion of IgA, strongly tying Computer Aided Geometry Design to Analysis, does not easily apply to the rich variety of complex shapes that engineers have to design and analyse. Therefore new developments have studied the extension of IgA to unstructured unions of meshes, similar to those one can find in FEM. The following problem arises: given an unstructured planar quadrilateral mesh, construct a C1-surface, by piecewise Bézier or B-Spline patches defined over this mesh. This problem is solved for C1-surfaces defined over plane bilinear Bézier patches, the corresponding results for B-Splines then being simple consequences. The method can be extended to higher-order quadrilaterals and even to three dimensions, and the most recent developments in this direction are also mentioned here.
ARC2D - EFFICIENT SOLUTION METHODS FOR THE NAVIER-STOKES EQUATIONS (DEC RISC ULTRIX VERSION)
Biyabani, S. R.
1994-01-01
ARC2D is a computational fluid dynamics program developed at the NASA Ames Research Center specifically for airfoil computations. The program uses implicit finite-difference techniques to solve two-dimensional Euler equations and thin layer Navier-Stokes equations. It is based on the Beam and Warming implicit approximate factorization algorithm in generalized coordinates. The methods are either time accurate or accelerated non-time accurate steady state schemes. The evolution of the solution through time is physically realistic; good solution accuracy is dependent on mesh spacing and boundary conditions. The mathematical development of ARC2D begins with the strong conservation law form of the two-dimensional Navier-Stokes equations in Cartesian coordinates, which admits shock capturing. The Navier-Stokes equations can be transformed from Cartesian coordinates to generalized curvilinear coordinates in a manner that permits one computational code to serve a wide variety of physical geometries and grid systems. ARC2D includes an algebraic mixing length model to approximate the effect of turbulence. In cases of high Reynolds number viscous flows, thin layer approximation can be applied. ARC2D allows for a variety of solutions to stability boundaries, such as those encountered in flows with shocks. The user has considerable flexibility in assigning geometry and developing grid patterns, as well as in assigning boundary conditions. However, the ARC2D model is most appropriate for attached and mildly separated boundary layers; no attempt is made to model wake regions and widely separated flows. The techniques have been successfully used for a variety of inviscid and viscous flowfield calculations. The Cray version of ARC2D is written in FORTRAN 77 for use on Cray series computers and requires approximately 5Mb memory. The program is fully vectorized. The tape includes variations for the COS and UNICOS operating systems. Also included is a sample routine for CONVEX
Symmetric approximations of the Navier-Stokes equations
International Nuclear Information System (INIS)
Kobel'kov, G M
2002-01-01
A new method for the symmetric approximation of the non-stationary Navier-Stokes equations by a Cauchy-Kovalevskaya-type system is proposed. Properties of the modified problem are studied. In particular, the convergence as ε→0 of the solutions of the modified problem to the solutions of the original problem on an infinite interval is established
Navier-Stokes equations by the finite element method
International Nuclear Information System (INIS)
Portella, P.E.
1984-01-01
A computer program to solve the Navier-Stokes equations by using the Finite Element Method is implemented. The solutions variables investigated are stream-function/vorticity in the steady case and velocity/pressure in the steady state and transient cases. For steady state flow the equations are solved simultaneously by the Newton-Raphson method. For the time dependent formulation, a fractional step method is employed to discretize in time and artificial viscosity is used to preclude spurious oscilations in the solution. The element used is the three node triangle. Some numerical examples are presented and comparisons are made with applications already existent. (Author) [pt
Inertial algorithms for the stationary Navier-Stokes equations
Hou, Yanren; Mattheij, R.M.M.
2003-01-01
Several kind of new numerical schemes for the stationary Navier-Stokes equations based on the virtue of Inertial Manifold and Approximate Inertial Manifold, which we call them inertial algorithms in this paper, together with their error estimations are presented. All these algorithms are constructed
Navier-Stokes Computations of Sabot Discard Using Chimera Scheme
National Research Council Canada - National Science Library
Ferry, E
1997-01-01
.... Numerical flow field computations have been made for various orientations and locations of sabots using an unsteady, zonal Navier-Stokes code and the Chimera composite grid discretization technique at M = 4.0 and alpha = 0...
Energy Technology Data Exchange (ETDEWEB)
Durand, A
1996-10-10
In this thesis, we are interested in the modeling of the compressible Navier-Stokes equations in 2-D moving domains with hybrid meshes. This work, far from being restricted to these equations, could be generalized to any other convection-diffusion system written in conservative vector form. After having described the mathematical equations and elaborated on finite volume (FV) methods, numerical schemes and various meshes, we have selected the Galerkin FV method. This method consists in locating the unknowns at the mesh nodes, then in solving the convective terms by means of VF method - quasi 1-D by edge approximation - and the diffusive terms by means of the finite element (FE) method - P{sub 1} for the triangular and Q{sub 1} for the quadrilateral. The equivalence between the Galerkin FV method and a mass-lumped FE method for temporal terms allows the construction of a new control volume constructed by means of medians. Then, show its interest in comparison to the classical control volume constructed by means of medians. Then first-order in comparison to the classical control volume constructed bu means of medians. Then, the first-order Roe scheme and its extension to second-order by the MUSCL method are detailed Emphasis is laid on two calculations oF the Gradient integral. Numerous numerical tests as well as the comparison with another code validate the approach. In particular, we show that triangular meshes lead to less precise results compared to quadrilateral meshes in certain cases. Afterward, we switch to the dimensionless Navier-Stokes equations and we describe a simplified (Bubnov)-Galerkin FE method in the case of the quadrilaterals. The newly deduced computer code is validated bu the means of a vortex convection-diffusion for different Reynolds numbers. This test shows that only highly viscous flows give rise to equivalent solutions for both meshes. (author)
A nonperturbative approximation for the moderate Reynolds number Navier-Stokes equations.
Roper, Marcus; Brenner, Michael P
2009-03-03
The nonlinearity of the Navier-Stokes equations makes predicting the flow of fluid around rapidly moving small bodies highly resistant to all approaches save careful experiments or brute force computation. Here, we show how a linearization of the Navier-Stokes equations captures the drag-determining features of the flow and allows simplified or analytical computation of the drag on bodies up to Reynolds number of order 100. We illustrate the utility of this linearization in 2 practical problems that normally can only be tackled with sophisticated numerical methods: understanding flow separation in the flow around a bluff body and finding drag-minimizing shapes.
KNOW-BLADE task-4 report: Navier-Stokes aeroelasticity
DEFF Research Database (Denmark)
Politis, E.S.; Nikolaou, I.G.; Chaviaropoulos, P.K.
2004-01-01
wind turbine blade have been combined with 2D and 3D unsteady Navier-Stokes solvers. The relative disadvantage of the quasi-3D approach (where the elastic solver is coupled with a 2D Navier-Stokes solver) isits inability to model induced flow. The lack of a validation test case did not allow...... the computations for the full blade, 2D computations for the so-called “typical section” have been carried out. The 2D aeroelastic tools resulted in similar aerodynamic damping values. Qualitative agreement was better for the lead-lagmode. The presence of roughness tapes has a small, rather negligible impact...... on aeroelastic stability as depicted by the results of both aeroelastic tools. On the other hand, in conformity to the inability of the adopted computational model to successfullypredict the corresponding test cases under work package 2 of the project, the aeroelastic tools are not capable to predict the correct...
Length scales for the Navier-Stokes equations on a rotating sphere
International Nuclear Information System (INIS)
Kyrychko, Yuliya N.; Bartuccelli, Michele V.
2004-01-01
In this Letter we obtain the dissipative length scale for the Navier-Stokes equations on a two-dimensional rotating sphere S 2 . This system is a fundamental model of the large scale atmospheric dynamics. Using the equations of motion in their vorticity form, we construct the ladder inequalities from which a set of time-averaged length scales is obtained
Tetrahedral-Mesh Simulation of Turbulent Flows with the Space-Time Conservative Schemes
Chang, Chau-Lyan; Venkatachari, Balaji; Cheng, Gary C.
2015-01-01
Direct numerical simulations of turbulent flows are predominantly carried out using structured, hexahedral meshes despite decades of development in unstructured mesh methods. Tetrahedral meshes offer ease of mesh generation around complex geometries and the potential of an orientation free grid that would provide un-biased small-scale dissipation and more accurate intermediate scale solutions. However, due to the lack of consistent multi-dimensional numerical formulations in conventional schemes for triangular and tetrahedral meshes at the cell interfaces, numerical issues exist when flow discontinuities or stagnation regions are present. The space-time conservative conservation element solution element (CESE) method - due to its Riemann-solver-free shock capturing capabilities, non-dissipative baseline schemes, and flux conservation in time as well as space - has the potential to more accurately simulate turbulent flows using unstructured tetrahedral meshes. To pave the way towards accurate simulation of shock/turbulent boundary-layer interaction, a series of wave and shock interaction benchmark problems that increase in complexity, are computed in this paper with triangular/tetrahedral meshes. Preliminary computations for the normal shock/turbulence interactions are carried out with a relatively coarse mesh, by direct numerical simulations standards, in order to assess other effects such as boundary conditions and the necessity of a buffer domain. The results indicate that qualitative agreement with previous studies can be obtained for flows where, strong shocks co-exist along with unsteady waves that display a broad range of scales, with a relatively compact computational domain and less stringent requirements for grid clustering near the shock. With the space-time conservation properties, stable solutions without any spurious wave reflections can be obtained without a need for buffer domains near the outflow/farfield boundaries. Computational results for the
Ameri, Ali; Shyam, Vikram; Rigby, David; Poinsatte, Philip; Thurman, Douglas; Steinthorsson, Erlendur
2014-01-01
Computational fluid dynamics (CFD) analysis using Reynolds-averaged Navier-Stokes (RANS) formulation for turbomachinery-related flows has enabled improved engine component designs. RANS methodology has limitations which are related to its inability to accurately describe the spectrum of flow phenomena encountered in engines. Examples of flows that are difficult to compute accurately with RANS include phenomena such as laminarturbulent transition, turbulent mixing due to mixing of streams, and separated flows. Large eddy simulation (LES) can improve accuracy but at a considerably higher cost. In recent years, hybrid schemes which take advantage of both unsteady RANS and LES have been proposed. This study investigated an alternative scheme, the time-filtered Navier-Stokes (TFNS) method applied to compressible flows. The method developed by Shih and Liu was implemented in the Glenn-HT code and applied to film cooling flows. In this report the method and its implementation is briefly described. The film effectiveness results obtained for film cooling from a row of 30 holes with a pitch of 3.0 diameters emitting air at a nominal density ratio of unity and four blowing ratios of 0.5, 1.0, 1.5 and 2.0 are shown. Flow features under those conditions are also described.
International Nuclear Information System (INIS)
Choi, Hyeon Kyeong; Park, Jong Woon
2013-01-01
In this work, behavior of unsteady and oscillating flow through a typical tube bundle array are analyzed by unsteady computations: 2D unsteady Reynolds averaged Navier-Stokes (URANS) and 3D Large Eddy Simulation (LES) and the results are compared with existing experimental data. In order to confirm appropriateness and limitations of CFD applications in the Korean VHTR design, two types of unsteady computations are performed such as 2D unsteady Reynolds averaged Navier-Stokes (URANS) and 3D Large Eddy Simulation (LES) for the existing tube bundle array. The velocity component profiles are compared with the experimental data and it is concluded that the URANS with the standard k-ω model is reasonably appropriate for cost-effective VHTR lower plenum analysis. Nevertheless, if more accurate results are needed, the LES-Smagorinsky computation is recommended considering limitations in the time averaged RANS in capturing small eddies
Random Attractors for the Stochastic Navier-Stokes Equations on the 2D Unit Sphere
Brzeźniak, Z.; Goldys, B.; Le Gia, Q. T.
2018-03-01
In this paper we prove the existence of random attractors for the Navier-Stokes equations on 2 dimensional sphere under random forcing irregular in space and time. We also deduce the existence of an invariant measure.
The quasidiffusion method for transport problems on unstructured meshes
Wieselquist, William A.
2009-06-01
In this work, we develop a quasidiffusion (QD) method for solving radiation transport problems on unstructured quadrilateral meshes in 2D Cartesian geometry, for example hanging-node meshes from adaptive mesh refinement (AMR) applications or skewed quadrilateral meshes from radiation hydrodynamics with Lagrangian meshing. The main result of the work is a new low-order quasidiffusion (LOQD) discretization on arbitrary quadrilaterals and a strategy for the efficient iterative solution which uses Krylov methods and incomplete LU factorization (ILU) preconditioning. The LOQD equations are a non-symmetric set of first-order PDEs that in second-order form resembles convection- diffusion with a diffusion tensor, with the difference that the LOQD equations contain extra cross-derivative terms. Our finite volume (FV) discretization of the LOQD equations is compared with three LOQD discretizations from literature. We then present a conservative, short characteristics discretization based on subcell balances (SCSB) that uses polynomial exponential moments to achieve robust behavior in various limits (e.g. small cells and voids) and is second- order accurate in space. A linear representation of the isotropic component of the scattering source based on face-average and cell-average scalar fluxes is also proposed and shown to be effective in some problems. In numerical tests, our QD method with linear scattering source representation shows some advantages compared to other transport methods. We conclude with avenues for future research and note that this QD method may easily be extended to arbitrary meshes in 3D Cartesian geometry.
Preconditioned conjugate gradient methods for the Navier-Stokes equations
Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing
1994-01-01
A preconditioned Krylov subspace method (GMRES) is used to solve the linear systems of equations formed at each time-integration step of the unsteady, two-dimensional, compressible Navier-Stokes equations of fluid flow. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux-split formulation. Several preconditioning techniques are investigated to enhance the efficiency and convergence rate of the implicit solver based on the GMRES algorithm. The superiority of the new solver is established by comparisons with a conventional implicit solver, namely line Gauss-Seidel relaxation (LGSR). Computational test results for low-speed (incompressible flow over a backward-facing step at Mach 0.1), transonic flow (trailing edge flow in a transonic turbine cascade), and hypersonic flow (shock-on-shock interactions on a cylindrical leading edge at Mach 6.0) are presented. For the Mach 0.1 case, overall speedup factors of up to 17 (in terms of time-steps) and 15 (in terms of CPU time on a CRAY-YMP/8) are found in favor of the preconditioned GMRES solver, when compared with the LGSR solver. The corresponding speedup factors for the transonic flow case are 17 and 23, respectively. The hypersonic flow case shows slightly lower speedup factors of 9 and 13, respectively. The study of preconditioners conducted in this research reveals that a new LUSGS-type preconditioner is much more efficient than a conventional incomplete LU-type preconditioner.
An unstructured-mesh finite-volume MPDATA for compressible atmospheric dynamics
International Nuclear Information System (INIS)
Kühnlein, Christian; Smolarkiewicz, Piotr K.
2017-01-01
An advancement of the unstructured-mesh finite-volume MPDATA (Multidimensional Positive Definite Advection Transport Algorithm) is presented that formulates the error-compensative pseudo-velocity of the scheme to rely only on face-normal advective fluxes to the dual cells, in contrast to the full vector employed in previous implementations. This is essentially achieved by expressing the temporal truncation error underlying the pseudo-velocity in a form consistent with the flux-divergence of the governing conservation law. The development is especially important for integrating fluid dynamics equations on non-rectilinear meshes whenever face-normal advective mass fluxes are employed for transport compatible with mass continuity—the latter being essential for flux-form schemes. In particular, the proposed formulation enables large-time-step semi-implicit finite-volume integration of the compressible Euler equations using MPDATA on arbitrary hybrid computational meshes. Furthermore, it facilitates multiple error-compensative iterations of the finite-volume MPDATA and improved overall accuracy. The advancement combines straightforwardly with earlier developments, such as the nonoscillatory option, the infinite-gauge variant, and moving curvilinear meshes. A comprehensive description of the scheme is provided for a hybrid horizontally-unstructured vertically-structured computational mesh for efficient global atmospheric flow modelling. The proposed finite-volume MPDATA is verified using selected 3D global atmospheric benchmark simulations, representative of hydrostatic and non-hydrostatic flow regimes. Besides the added capabilities, the scheme retains fully the efficacy of established finite-volume MPDATA formulations.
An unstructured-mesh finite-volume MPDATA for compressible atmospheric dynamics
Energy Technology Data Exchange (ETDEWEB)
Kühnlein, Christian, E-mail: christian.kuehnlein@ecmwf.int; Smolarkiewicz, Piotr K., E-mail: piotr.smolarkiewicz@ecmwf.int
2017-04-01
An advancement of the unstructured-mesh finite-volume MPDATA (Multidimensional Positive Definite Advection Transport Algorithm) is presented that formulates the error-compensative pseudo-velocity of the scheme to rely only on face-normal advective fluxes to the dual cells, in contrast to the full vector employed in previous implementations. This is essentially achieved by expressing the temporal truncation error underlying the pseudo-velocity in a form consistent with the flux-divergence of the governing conservation law. The development is especially important for integrating fluid dynamics equations on non-rectilinear meshes whenever face-normal advective mass fluxes are employed for transport compatible with mass continuity—the latter being essential for flux-form schemes. In particular, the proposed formulation enables large-time-step semi-implicit finite-volume integration of the compressible Euler equations using MPDATA on arbitrary hybrid computational meshes. Furthermore, it facilitates multiple error-compensative iterations of the finite-volume MPDATA and improved overall accuracy. The advancement combines straightforwardly with earlier developments, such as the nonoscillatory option, the infinite-gauge variant, and moving curvilinear meshes. A comprehensive description of the scheme is provided for a hybrid horizontally-unstructured vertically-structured computational mesh for efficient global atmospheric flow modelling. The proposed finite-volume MPDATA is verified using selected 3D global atmospheric benchmark simulations, representative of hydrostatic and non-hydrostatic flow regimes. Besides the added capabilities, the scheme retains fully the efficacy of established finite-volume MPDATA formulations.
Navier-Stokes Calculations of Helicopter Fuselage Flowfield and Loads
DEFF Research Database (Denmark)
M, Costes; Filippone, Antonino; N, Kroll
1999-01-01
This paper describes the theoretically basedactivities conducted during the first year of theBrite/Euram Helifuse Porgramme. These activitiesmainly consisted of the numerical prediction ofhelicopter fuselage flowfields with existing Navier-Stokes solvers on a number of pre-selectedcases, taken out...
Optimization-based Fluid Simulation on Unstructured Meshes
DEFF Research Database (Denmark)
Misztal, Marek Krzysztof; Bridson, Robert; Erleben, Kenny
2010-01-01
for solving the fluid dynamics equations as well as direct access to the interface geometry data, making in- clusion of a new surface energy term feasible. Furthermore, using an unstructured mesh makes it straightforward to handle curved solid boundaries and gives us a possibility to explore several fluid...
Partitioning of unstructured meshes for load balancing
International Nuclear Information System (INIS)
Martin, O.C.; Otto, S.W.
1994-01-01
Many large-scale engineering and scientific calculations involve repeated updating of variables on an unstructured mesh. To do these types of computations on distributed memory parallel computers, it is necessary to partition the mesh among the processors so that the load balance is maximized and inter-processor communication time is minimized. This can be approximated by the problem, of partitioning a graph so as to obtain a minimum cut, a well-studied combinatorial optimization problem. Graph partitioning algorithms are discussed that give good but not necessarily optimum solutions. These algorithms include local search methods recursive spectral bisection, and more general purpose methods such as simulated annealing. It is shown that a general procedure enables to combine simulated annealing with Kernighan-Lin. The resulting algorithm is both very fast and extremely effective. (authors) 23 refs., 3 figs., 1 tab
International Nuclear Information System (INIS)
An, Hongli; Yuen, Manwai
2014-01-01
In this paper, we investigate the analytical solutions of the compressible Navier-Stokes equations with dependent-density viscosity. By using the characteristic method, we successfully obtain a class of drifting solutions with elliptic symmetry for the Navier-Stokes model wherein the velocity components are governed by a generalized Emden dynamical system. In particular, when the viscosity variables are taken the same as Yuen [M. W. Yuen, “Analytical solutions to the Navier-Stokes equations,” J. Math. Phys. 49, 113102 (2008)], our solutions constitute a generalization of that obtained by Yuen. Interestingly, numerical simulations show that the analytical solutions can be used to explain the drifting phenomena of the propagation wave like Tsunamis in oceans
Unstructured Mesh Movement and Viscous Mesh Generation for CFD-Based Design Optimization, Phase II
National Aeronautics and Space Administration — The innovations proposed are twofold: 1) a robust unstructured mesh movement method able to handle isotropic (Euler), anisotropic (viscous), mixed element (hybrid)...
Split-Cell Exponential Characteristic Transport Method for Unstructured Tetrahedral Meshes
International Nuclear Information System (INIS)
Brennan, Charles R.; Miller, Rodney L.; Mathews, Kirk A.
2001-01-01
The nonlinear, exponential characteristic (EC) method is extended to unstructured meshes of tetrahedral cells in three-dimensional Cartesian coordinates. The split-cell approach developed for the linear characteristic (LC) method on such meshes is used. Exponential distributions of the source within a cell and of the inflow flux on upstream faces of the cell are assumed. The coefficients of these distributions are determined by nonlinear root solving so as to match the zeroth and first moments of the source or entering flux. Good conditioning is achieved by casting the formulas for the moments of the source, inflow flux, and solution flux as sums of positive functions and by using accurate and robust algorithms for evaluation of those functions. Various test problems are used to compare the performance of the EC and LC methods. The EC method is somewhat less accurate than the LC method in regions of net out leakage but is strictly positive and retains good accuracy with optically thick cells, as in shielding problems, unlike the LC method. The computational cost per cell is greater for the EC method, but the use of substantially coarser meshes can make the EC method less expensive in total cost. The EC method, unlike the LC method, may fail if negative cross sections or angular quadrature weights are used. It is concluded that the EC and LC methods should be practical, reliable, and complimentary schemes for these meshes
International Nuclear Information System (INIS)
Anderson, C.R.; Reider, M.B.
1994-01-01
The technique of combining solutions of the Prandtl equations with solutions of the Navier--Stokes equations to compute incompressible flow around two-dimensional bodies is investigated herein. Computational evidence is presented which shows that if the ''obvious'' coupling is used to combine the solutions, then the resulting solution is not accurate. An alternate coupling procedure is described which greatly improves the accuracy of the solutions obtained with the combined equation approach. An alternate coupling that can be used to create a more accurate vortex sheet/vortex blob method is then shown
Riding Bare-Back on unstructured meshes for 21. century criticality calculations - 244
International Nuclear Information System (INIS)
Kelley, K.C.; Martz, R.L.; Crane, D.L.
2010-01-01
MCNP has a new capability that permits tracking of neutrons and photons on an unstructured mesh which is embedded as a mesh universe within its legacy geometry capability. The mesh geometry is created through Abaqus/CAE using its solid modeling capabilities. Transport results are calculated for mesh elements through a path length estimator while element to element tracking is performed on the mesh. The results from MCNP can be exported to Abaqus/CAE for visualization or other-physics analysis. The simple Godiva criticality benchmark problem was tested with this new mesh capability. Computer run time is proportional to the number of mesh elements used. Both first and second order polyhedrons are used. Models that used second order polyhedrons produced slightly better results without significantly increasing computer run time. Models that used first order hexahedrons had shorter runtimes than models that used first order tetrahedrons. (authors)
Viscous-inviscid interaction using the parabolized Navier-Stokes equations
DEFF Research Database (Denmark)
Filippone, Antonino; Sørensen, Jens Nørkær
1997-01-01
adaptive grid is used.The interaction is achieved by iterative updatingof the boundary conditions, through the wall transpiration concept. The Navier-Stokes equationsare discretized on a semi-staggered grid.Space-marching integration is performed starting from the stagnation streamline ontwo independent......A numerical model for the calculation of incompressible viscous flows past airfoils andwings has been developed. The approach is based on a strong viscous-inviscid coupling of aboundary element method with the Navier-Stokesequations in vorticity-streamfunction formulation.A semi-adaptive or fully...
Unstructed Navier-Stokes Analysis of Wind-Tunnel Aeroelastic Effects on TCA Model 2
Frink, Neal T.; Allison, Dennis O.; Parikh, Paresh C.
1999-01-01
The aim of this work is to demonstrate a simple technique which accounts for aeroelastic deformations experienced by HSR wind-tunnel models within CFD computations. With improved correlations, CFD can become a more effective tool for augmenting the post-test understanding of experimental data. The present technique involves the loose coupling of a low-level structural representation within the ELAPS code, to an unstructured Navier-Stokes flow solver, USM3Dns. The ELAPS model is initially calibrated against bending characteristics of the wind-tunnel model. The strength of this method is that, with a single point calibration of a simple structural representation, the static aeroelastic effects can be accounted for in CFD calculations across a range of test conditions. No prior knowledge of the model deformation during the wind-on test is required. This approach has been successfully applied to the high aspect-ratio planforms of subsonic transports. The current challenge is to adapt the procedure to low aspect-ratio planforms typical of HSR configurations.
Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.
2015-01-01
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators on unstructured grids are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction/correction procedure via reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.
Scaling Relations and Self-Similarity of 3-Dimensional Reynolds-Averaged Navier-Stokes Equations.
Ercan, Ali; Kavvas, M Levent
2017-07-25
Scaling conditions to achieve self-similar solutions of 3-Dimensional (3D) Reynolds-Averaged Navier-Stokes Equations, as an initial and boundary value problem, are obtained by utilizing Lie Group of Point Scaling Transformations. By means of an open-source Navier-Stokes solver and the derived self-similarity conditions, we demonstrated self-similarity within the time variation of flow dynamics for a rigid-lid cavity problem under both up-scaled and down-scaled domains. The strength of the proposed approach lies in its ability to consider the underlying flow dynamics through not only from the governing equations under consideration but also from the initial and boundary conditions, hence allowing to obtain perfect self-similarity in different time and space scales. The proposed methodology can be a valuable tool in obtaining self-similar flow dynamics under preferred level of detail, which can be represented by initial and boundary value problems under specific assumptions.
Application of the implicit MacCormack scheme to the parabolized Navier-Stokes equations
Lawrence, J. L.; Tannehill, J. C.; Chaussee, D. S.
1984-01-01
MacCormack's implicit finite-difference scheme was used to solve the two-dimensional parabolized Navier-Stokes (PNS) equations. This method for solving the PNS equations does not require the inversion of block tridiagonal systems of algebraic equations and permits the original explicit MacCormack scheme to be employed in those regions where implicit treatment is not needed. The advantages and disadvantages of the present adaptation are discussed in relation to those of the conventional Beam-Warming scheme for a flat plate boundary layer test case. Comparisons are made for accuracy, stability, computer time, computer storage, and ease of implementation. The present method was also applied to a second test case of hypersonic laminar flow over a 15% compression corner. The computed results compare favorably with experiment and a numerical solution of the complete Navier-Stokes equations.
Implementation of compact finite-difference method to parabolized Navier-Stokes equations
International Nuclear Information System (INIS)
Esfahanian, V.; Hejranfar, K.; Darian, H.M.
2005-01-01
The numerical simulation of the Parabolized Navier-Stokes (PNS) equations for supersonic/hypersonic flow field is obtained by using the fourth-order compact finite-difference method. The PNS equations in the general curvilinear coordinates are solved by using the implicit finite-difference algorithm of Beam and Warming. A shock fitting procedure is utilized to obtain the accurate solution in the vicinity of the shock. The computations are performed for hypersonic axisymmetric flow over a blunt cone. The present results for the flow field along with those of the second-order method are presented and accuracy analysis is performed to insure the fourth-order accuracy of the method. (author)
The Navier-Stokes Equations Theory and Numerical Methods
Masuda, Kyûya; Rautmann, Reimund; Solonnikov, Vsevolod
1990-01-01
These proceedings contain original (refereed) research articles by specialists from many countries, on a wide variety of aspects of Navier-Stokes equations. Additionally, 2 survey articles intended for a general readership are included: one surveys the present state of the subject via open problems, and the other deals with the interplay between theory and numerical analysis.
Pipe Flow and Wall Turbulence Using a Modified Navier-Stokes Equation
International Nuclear Information System (INIS)
Jirkovsky, L.; Muriel, A.
2012-01-01
We use a derived incompressible modified Navier-Stokes equation to model pipe flow and wall turbulence. We reproduce the observed flattened paraboloid velocity profiles of turbulence that cannot be obtained directly using standard incompressible Navier-Stokes equation. The solutions found are in harmony with multi-valued velocity fields as a definition of turbulence. Repeating the procedure for the flow of turbulent fluid between two parallel flat plates we find similar flattened velocity profiles. We extend the analysis to the turbulent flow along a single wall and compare the results with experimental data and the established controversial von Karman logarithmic law of the wall. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
Implementation and analysis of a Navier-Stokes algorithm on parallel computers
Fatoohi, Raad A.; Grosch, Chester E.
1988-01-01
The results of the implementation of a Navier-Stokes algorithm on three parallel/vector computers are presented. The object of this research is to determine how well, or poorly, a single numerical algorithm would map onto three different architectures. The algorithm is a compact difference scheme for the solution of the incompressible, two-dimensional, time-dependent Navier-Stokes equations. The computers were chosen so as to encompass a variety of architectures. They are the following: the MPP, an SIMD machine with 16K bit serial processors; Flex/32, an MIMD machine with 20 processors; and Cray/2. The implementation of the algorithm is discussed in relation to these architectures and measures of the performance on each machine are given. The basic comparison is among SIMD instruction parallelism on the MPP, MIMD process parallelism on the Flex/32, and vectorization of a serial code on the Cray/2. Simple performance models are used to describe the performance. These models highlight the bottlenecks and limiting factors for this algorithm on these architectures. Finally, conclusions are presented.
Directory of Open Access Journals (Sweden)
Gao Guo-Ping
2016-01-01
Full Text Available In this article, we investigate the local fractional 3-D compressible Navier-Stokes equation via local fractional derivative. We use the Cantor-type cylindrical co-ordinate method to transfer 3-D compressible Navier-Stokes equation from the Cantorian co-ordinate system to the Cantor-type cylindrical co-ordinate system.
Navier-Stokes-like equations for traffic flow.
Velasco, R M; Marques, W
2005-10-01
The macroscopic traffic flow equations derived from the reduced Paveri-Fontana equation are closed starting with the maximization of the informational entropy. The homogeneous steady state taken as a reference is obtained for a specific model of the desired velocity and a kind of Chapman-Enskog method is developed to calculate the traffic pressure at the Navier-Stokes level. Numerical solution of the macroscopic traffic equations is obtained and its characteristics are analyzed.
Finite elements volumes methods: applications to the Navier-Stokes equations and convergence results
International Nuclear Information System (INIS)
Emonot, P.
1992-01-01
In the first chapter are described the equations modeling incompressible fluid flow and a quick presentation of finite volumes method. The second chapter is an introduction to the finite elements volumes method. The box model is described and a method adapted to Navier-Stokes problems is proposed. The third chapter shows a fault analysis of the finite elements volumes method for the Laplacian problem and some examples in one, two, three dimensional calculations. The fourth chapter is an extension of the error analysis of the method for the Navier-Stokes problem
Multigrid and defect correction for the steady Navier-Stokes equations
Koren, B.
1990-01-01
Theoretical and experimental convergence results are presented for nonlinear multigrid and iterative defect correction applied to finite volume discretizations of the full, steady, 2D, compressible Navier-Stokes equations. Iterative defect correction is introduced for circumventing the difficulty in
Shape Optimization for Navier-Stokes Equations with Algebraic Turbulence Model: Existence Analysis
International Nuclear Information System (INIS)
Bulicek, Miroslav; Haslinger, Jaroslav; Malek, Josef; Stebel, Jan
2009-01-01
We study a shape optimization problem for the paper machine headbox which distributes a mixture of water and wood fibers in the paper making process. The aim is to find a shape which a priori ensures the given velocity profile on the outlet part. The mathematical formulation leads to an optimal control problem in which the control variable is the shape of the domain representing the header, the state problem is represented by a generalized stationary Navier-Stokes system with nontrivial mixed boundary conditions. In this paper we prove the existence of solutions both to the generalized Navier-Stokes system and to the shape optimization problem
A new nonlinear turbulence model based on Partially-Averaged Navier-Stokes Equations
International Nuclear Information System (INIS)
Liu, J T; Wu, Y L; Cai, C; Liu, S H; Wang, L Q
2013-01-01
Partially-averaged Navier-Stokes (PANS) Model was recognized as a Reynolds-averaged Navier-Stokes (RANS) to direct numerical simulation (DNS) bridging method. PANS model was purported for any filter width-from RANS to DNS. PANS method also shared some similarities with the currently popular URANS (unsteady RANS) method. In this paper, a new PANS model was proposed, which was based on RNG k-ε turbulence model. The Standard and RNG k-ε turbulence model were both isotropic models, as well as PANS models. The sheer stress in those PANS models was solved by linear equation. The linear hypothesis was not accurate in the simulation of complex flow, such as stall phenomenon. The sheer stress here was solved by nonlinear method proposed by Ehrhard. Then, the nonlinear PANS model was set up. The pressure coefficient of the suction side of the NACA0015 hydrofoil was predicted. The result of pressure coefficient agrees well with experimental result, which proves that the nonlinear PANS model can capture the high pressure gradient flow. A low specific centrifugal pump was used to verify the capacity of the nonlinear PANS model. The comparison between the simulation results of the centrifugal pump and Particle Image Velocimetry (PIV) results proves that the nonlinear PANS model can be used in the prediction of complex flow field
Introducing a distributed unstructured mesh into gyrokinetic particle-in-cell code, XGC
Yoon, Eisung; Shephard, Mark; Seol, E. Seegyoung; Kalyanaraman, Kaushik
2017-10-01
XGC has shown good scalability for large leadership supercomputers. The current production version uses a copy of the entire unstructured finite element mesh on every MPI rank. Although an obvious scalability issue if the mesh sizes are to be dramatically increased, the current approach is also not optimal with respect to data locality of particles and mesh information. To address these issues we have initiated the development of a distributed mesh PIC method. This approach directly addresses the base scalability issue with respect to mesh size and, through the use of a mesh entity centric view of the particle mesh relationship, provides opportunities to address data locality needs of many core and GPU supported heterogeneous systems. The parallel mesh PIC capabilities are being built on the Parallel Unstructured Mesh Infrastructure (PUMI). The presentation will first overview the form of mesh distribution used and indicate the structures and functions used to support the mesh, the particles and their interaction. Attention will then focus on the node-level optimizations being carried out to ensure performant operation of all PIC operations on the distributed mesh. Partnership for Edge Physics Simulation (EPSI) Grant No. DE-SC0008449 and Center for Extended Magnetohydrodynamic Modeling (CEMM) Grant No. DE-SC0006618.
An Algorithm for Parallel Sn Sweeps on Unstructured Meshes
International Nuclear Information System (INIS)
Pautz, Shawn D.
2002-01-01
A new algorithm for performing parallel S n sweeps on unstructured meshes is developed. The algorithm uses a low-complexity list ordering heuristic to determine a sweep ordering on any partitioned mesh. For typical problems and with 'normal' mesh partitionings, nearly linear speedups on up to 126 processors are observed. This is an important and desirable result, since although analyses of structured meshes indicate that parallel sweeps will not scale with normal partitioning approaches, no severe asymptotic degradation in the parallel efficiency is observed with modest (≤100) levels of parallelism. This result is a fundamental step in the development of efficient parallel S n methods
Implicit methods for the Navier-Stokes equations
Yoon, S.; Kwak, D.
1990-01-01
Numerical solutions of the Navier-Stokes equations using explicit schemes can be obtained at the expense of efficiency. Conventional implicit methods which often achieve fast convergence rates suffer high cost per iteration. A new implicit scheme based on lower-upper factorization and symmetric Gauss-Seidel relaxation offers very low cost per iteration as well as fast convergence. High efficiency is achieved by accomplishing the complete vectorizability of the algorithm on oblique planes of sweep in three dimensions.
Modeling Vortex Generators in a Navier-Stokes Code
Dudek, Julianne C.
2011-01-01
A source-term model that simulates the effects of vortex generators was implemented into the Wind-US Navier-Stokes code. The source term added to the Navier-Stokes equations simulates the lift force that would result from a vane-type vortex generator in the flowfield. The implementation is user-friendly, requiring the user to specify only three quantities for each desired vortex generator: the range of grid points over which the force is to be applied and the planform area and angle of incidence of the physical vane. The model behavior was evaluated for subsonic flow in a rectangular duct with a single vane vortex generator, subsonic flow in an S-duct with 22 corotating vortex generators, and supersonic flow in a rectangular duct with a counter-rotating vortex-generator pair. The model was also used to successfully simulate microramps in supersonic flow by treating each microramp as a pair of vanes with opposite angles of incidence. The validation results indicate that the source-term vortex-generator model provides a useful tool for screening vortex-generator configurations and gives comparable results to solutions computed using gridded vanes.
Grid adaptation using chimera composite overlapping meshes
Kao, Kai-Hsiung; Liou, Meng-Sing; Chow, Chuen-Yen
1994-01-01
The objective of this paper is to perform grid adaptation using composite overlapping meshes in regions of large gradient to accurately capture the salient features during computation. The chimera grid scheme, a multiple overset mesh technique, is used in combination with a Navier-Stokes solver. The numerical solution is first converged to a steady state based on an initial coarse mesh. Solution-adaptive enhancement is then performed by using a secondary fine grid system which oversets on top of the base grid in the high-gradient region, but without requiring the mesh boundaries to join in any special way. Communications through boundary interfaces between those separated grids are carried out using trilinear interpolation. Application to the Euler equations for shock reflections and to shock wave/boundary layer interaction problem are tested. With the present method, the salient features are well-resolved.
Ameri, Ali; Shyam, Vikram; Rigby, David; Poinsatte, Phillip; Thurman, Douglas; Steinthorsson, Erlendur
2014-01-01
Computational fluid dynamics (CFD) analysis using Reynolds-averaged Navier-Stokes (RANS) formulation for turbomachinery-related flows has enabled improved engine component designs. RANS methodology has limitations that are related to its inability to accurately describe the spectrum of flow phenomena encountered in engines. Examples of flows that are difficult to compute accurately with RANS include phenomena such as laminar/turbulent transition, turbulent mixing due to mixing of streams, and separated flows. Large eddy simulation (LES) can improve accuracy but at a considerably higher cost. In recent years, hybrid schemes that take advantage of both unsteady RANS and LES have been proposed. This study investigated an alternative scheme, the time-filtered Navier-Stokes (TFNS) method applied to compressible flows. The method developed by Shih and Liu was implemented in the Glenn-Heat-Transfer (Glenn-HT) code and applied to film-cooling flows. In this report the method and its implementation is briefly described. The film effectiveness results obtained for film cooling from a row of 30deg holes with a pitch of 3.0 diameters emitting air at a nominal density ratio of unity and two blowing ratios of 0.5 and 1.0 are shown. Flow features under those conditions are also described.
Ameri, Ali A.; Shyam, Vikram; Rigby, David; Poinsatte, Phillip; Thurman, Douglas; Steinthorsson, Erlendur
2014-01-01
Computational fluid dynamics (CFD) analysis using Reynolds-averaged Navier-Stokes (RANS) formulation for turbomachinery-related flows has enabled improved engine component designs. RANS methodology has limitations that are related to its inability to accurately describe the spectrum of flow phenomena encountered in engines. Examples of flows that are difficult to compute accurately with RANS include phenomena such as laminar/turbulent transition, turbulent mixing due to mixing of streams, and separated flows. Large eddy simulation (LES) can improve accuracy but at a considerably higher cost. In recent years, hybrid schemes that take advantage of both unsteady RANS and LES have been proposed. This study investigated an alternative scheme, the time-filtered Navier-Stokes (TFNS) method applied to compressible flows. The method developed by Shih and Liu was implemented in the Glenn-Heat-Transfer (Glenn-HT) code and applied to film-cooling flows. In this report the method and its implementation is briefly described. The film effectiveness results obtained for film cooling from a row of 30deg holes with a pitch of 3.0 diameters emitting air at a nominal density ratio of unity and two blowing ratios of 0.5 and 1.0 are shown. Flow features under those conditions are also described.
Parallel computation of Euler and Navier-Stokes flows
International Nuclear Information System (INIS)
Swisshelm, J.M.; Johnson, G.M.; Kumar, S.P.
1986-01-01
A multigrid technique useful for accelerating the convergence of Euler and Navier-Stokes flow computations has been restructured to improve its performance on both SIMD and MIMD computers. The new algorithm allows both the construction of longer coarse-grid vectors and the multitasking of entire grids. Computational results are presented for the CDC Cyber 205, Cray X-MP, and Denelcor HEP I. 15 references
New representation of Navier-Stokes equations governing self-similar homogeneous turbulence
International Nuclear Information System (INIS)
Foias, C.; Manley, O.P.; Temam, R.
1983-01-01
A new form of the Navier-Stokes equation resulting from a change of variables is presented. The new form has several advantages: It yields a new asymptotic behavior of the flow for long times and vanishingly small viscosity. In addition an interpretation of the new equation in terms of a simple random walk yields immediately not only the Kolmogorov (2/3)-power law but also an intermittency exponent well within the experimental uncertainty
Verschaeve, Joris C G
2011-06-13
By means of the continuity equation of the incompressible Navier-Stokes equations, additional physical arguments for the derivation of a formulation of the no-slip boundary condition for the lattice Boltzmann method for straight walls at rest are obtained. This leads to a boundary condition that is second-order accurate with respect to the grid spacing and conserves mass. In addition, the boundary condition is stable for relaxation frequencies close to two.
Modeling shock waves in an ideal gas: Going beyond the Navier-Stokes level
International Nuclear Information System (INIS)
Holian, B.L.; Patterson, C.W.; Mareschal, M.; Salomons, E.
1993-01-01
We model a shock wave in an ideal gas by solving a modified version of the compressible Navier-Stokes equations of hydrodynamics, where, following an earlier conjecture by Holian [Phys. Rev. A 37, 2562 (1988)], we use the temperature in the direction of shock propagation T xx , rather than the average temperature T=(T xx +T yy +T zz )/3, in the evaluation of the linear transport coefficients. The results are found to agree much better with the molecular-dynamics simulations of Salomons and Mareschal [Phys. Rev. Lett. 69, 269 (1992)] than standard Navier-Stokes theory
Discretization of the Joule heating term for plasma discharge fluid models in unstructured meshes
International Nuclear Information System (INIS)
Deconinck, T.; Mahadevan, S.; Raja, L.L.
2009-01-01
The fluid (continuum) approach is commonly used for simulation of plasma phenomena in electrical discharges at moderate to high pressures (>10's mTorr). The description comprises governing equations for charged and neutral species transport and energy equations for electrons and the heavy species, coupled to equations for the electromagnetic fields. The coupling of energy from the electrostatic field to the plasma species is modeled by the Joule heating term which appears in the electron and heavy species (ion) energy equations. Proper numerical discretization of this term is necessary for accurate description of discharge energetics; however, discretization of this term poses a special problem in the case of unstructured meshes owing to the arbitrary orientation of the faces enclosing each cell. We propose a method for the numerical discretization of the Joule heating term using a cell-centered finite volume approach on unstructured meshes with closed convex cells. The Joule heating term is computed by evaluating both the electric field and the species flux at the cell center. The dot product of these two vector quantities is computed to obtain the Joule heating source term. We compare two methods to evaluate the species flux at the cell center. One is based on reconstructing the fluxes at the cell centers from the fluxes at the face centers. The other recomputes the flux at the cell center using the common drift-diffusion approximation. The reconstructed flux scheme is the most stable method and yields reasonably accurate results on coarse meshes.
Modified Einstein and Navier-Stokes Equations
Bulyzhenkov, I. É.
2018-05-01
The appearance of inertial rest mass-energy is associated with the kinematic slowing-down of time and with the vortex state of the elementary massive space with zero integral of its kinetic and potential energies. An analog of the Einstein equation is found for moving densities of a non-empty metric space in the concept of the Einstein-Infeld material field. The vector consequences of this tensor equation for a metric medium of overlapping elementary carriers of continuous mass-energies allow us to modify the Navier-Stokes equation under inertial motion of the matter of the nonlocal field in the nonrelativistic limit. The nonlocality of massenergy generates kinematic accelerations of feedback to Newtonian acceleration, which impedes asymptotic divergence of energy fluxes. Stabilization of inertial media by dynamic Bernoulli pressure corresponds to nonlocal self-organization of Einstein-Infeld non-empty space and invalidates Newtonian localization of masses in empty space.
Incompressible Navier-Stokes equation from Einstein-Maxwell and Gauss-Bonnet-Maxwell theories
International Nuclear Information System (INIS)
Niu Chao; Tian Yu; Wu Xiaoning; Ling Yi
2012-01-01
The dual fluid description for a general cutoff surface at radius r=r c outside the horizon in the charged AdS black brane bulk space-time is investigated, first in the Einstein-Maxwell theory. Under the non-relativistic long-wavelength expansion with parameter ε, the coupled Einstein-Maxwell equations are solved up to O(ε 2 ). The incompressible Navier-Stokes equation with external force density is obtained as the constraint equation at the cutoff surface. For non-extremal black brane, the viscosity of the dual fluid is determined by the regularity of the metric fluctuation at the horizon, whose ratio to entropy density η/s is independent of both the cutoff r c and the black brane charge. Then, we extend our discussion to the Gauss-Bonnet-Maxwell case, where the incompressible Navier-Stokes equation with external force density is also obtained at a general cutoff surface. In this case, it turns out that the ratio η/s is independent of the cutoff r c but dependent on the charge density of the black brane.
Smooth solutions of the Navier-Stokes equations
International Nuclear Information System (INIS)
Pokhozhaev, S I
2014-01-01
We consider smooth solutions of the Cauchy problem for the Navier-Stokes equations on the scale of smooth functions which are periodic with respect to x∈R 3 . We obtain existence theorems for global (with respect to t>0) and local solutions of the Cauchy problem. The statements of these depend on the smoothness and the norm of the initial vector function. Upper bounds for the behaviour of solutions in both classes, which depend on t, are also obtained. Bibliography: 10 titles
Turbine Internal and Film Cooling Modeling For 3D Navier-Stokes Codes
DeWitt, Kenneth; Garg Vijay; Ameri, Ali
2005-01-01
The aim of this research project is to make use of NASA Glenn on-site computational facilities in order to develop, validate and apply aerodynamic, heat transfer, and turbine cooling models for use in advanced 3D Navier-Stokes Computational Fluid Dynamics (CFD) codes such as the Glenn-" code. Specific areas of effort include: Application of the Glenn-HT code to specific configurations made available under Turbine Based Combined Cycle (TBCC), and Ultra Efficient Engine Technology (UEET) projects. Validating the use of a multi-block code for the time accurate computation of the detailed flow and heat transfer of cooled turbine airfoils. The goal of the current research is to improve the predictive ability of the Glenn-HT code. This will enable one to design more efficient turbine components for both aviation and power generation. The models will be tested against specific configurations provided by NASA Glenn.
Spectral/hp least-squares finite element formulation for the Navier-Stokes equations
International Nuclear Information System (INIS)
Pontaza, J.P.; Reddy, J.N.
2003-01-01
We consider the application of least-squares finite element models combined with spectral/hp methods for the numerical solution of viscous flow problems. The paper presents the formulation, validation, and application of a spectral/hp algorithm to the numerical solution of the Navier-Stokes equations governing two- and three-dimensional stationary incompressible and low-speed compressible flows. The Navier-Stokes equations are expressed as an equivalent set of first-order equations by introducing vorticity or velocity gradients as additional independent variables and the least-squares method is used to develop the finite element model. High-order element expansions are used to construct the discrete model. The discrete model thus obtained is linearized by Newton's method, resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method. Spectral convergence of the L 2 least-squares functional and L 2 error norms is verified using smooth solutions to the two-dimensional stationary Poisson and incompressible Navier-Stokes equations. Numerical results for flow over a backward-facing step, steady flow past a circular cylinder, three-dimensional lid-driven cavity flow, and compressible buoyant flow inside a square enclosure are presented to demonstrate the predictive capability and robustness of the proposed formulation
DEFF Research Database (Denmark)
N., Kroll; P., Renzoni; M., Amato
1998-01-01
The purpose of this paper is to describe the influence of different Navier-Stokes solvers and grids on the prediction of the global coefficients for a simplified geometry of a helicopter fuselage.......The purpose of this paper is to describe the influence of different Navier-Stokes solvers and grids on the prediction of the global coefficients for a simplified geometry of a helicopter fuselage....
Asgharzadeh, Hafez; Borazjani, Iman
2014-11-01
Time step-size restrictions and low convergence rates are major bottle necks for implicit solution of the Navier-Stokes in simulations involving complex geometries with moving boundaries. Newton-Krylov method (NKM) is a combination of a Newton-type method for super-linearly convergent solution of nonlinear equations and Krylov subspace methods for solving the Newton correction equations, which can theoretically address both bottle necks. The efficiency of this method vastly depends on the Jacobian forming scheme e.g. automatic differentiation is very expensive and Jacobian-free methods slow down as the mesh is refined. A novel, computationally efficient analytical Jacobian for NKM was developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered curvilinear grids with immersed boundaries. The NKM was validated and verified against Taylor-Green vortex and pulsatile flow in a 90 degree bend and efficiently handles complex geometries such as an intracranial aneurysm with multiple overset grids, pulsatile inlet flow and immersed boundaries. The NKM method is shown to be more efficient than the semi-implicit Runge-Kutta methods and Jabobian-free Newton-Krylov methods. We believe NKM can be applied to many CFD techniques to decrease the computational cost. This work was supported partly by the NIH Grant R03EB014860, and the computational resources were partly provided by Center for Computational Research (CCR) at University at Buffalo.
Continuum Navier-Stokes modelling of water ow past fullerene molecules
DEFF Research Database (Denmark)
Walther, J. H.; Popadic, A.; Koumoutsakos, P.
We present continuum simulations of water flow past fullerene molecules. The governing Navier-Stokes equations are complemented with the Navier slip boundary condition with a slip length that is extracted from related molecular dynamics simulations. We find that several quantities of interest...... as computed by the present model are in good agreement with results from atomistic and atomistic-continuum simulations at a fraction of the computational cost. We simulate the flow past a single fullerene and an array of fullerenes and demonstrate that such nanoscale flows can be computed efficiently...
Continuum Navier-Stokes modelling of water flow past fullerene molecules
DEFF Research Database (Denmark)
Walther, J. H.; Popadic, A.; Koumoutsakos, P.
We present continuum simulations of water flow past fullerene molecules. The governing Navier-Stokes equations are complemented with the Navier slip boundary condition with a slip length that is extracted from related molecular dynamics simulations. We find that several quantities of interest...... as computed by the present model are in good agreement with results from atomistic and atomistic-continuum simulations at a fraction of the computational cost. We simulate the flow past a single fullerene and an array of fullerenes and demonstrate that such nanoscale flows can be computed efficiently...
An Equal-Order DG Method for the Incompressible Navier-Stokes Equations
Cockburn, Bernardo; Kanschat, Guido; Schö tzau, Dominik
2008-01-01
We introduce and analyze a discontinuous Galerkin method for the incompressible Navier-Stokes equations that is based on finite element spaces of the same polynomial order for the approximation of the velocity and the pressure. Stability
Bilyeu, David
This dissertation presents an extension of the Conservation Element Solution Element (CESE) method from second- to higher-order accuracy. The new method retains the favorable characteristics of the original second-order CESE scheme, including (i) the use of the space-time integral equation for conservation laws, (ii) a compact mesh stencil, (iii) the scheme will remain stable up to a CFL number of unity, (iv) a fully explicit, time-marching integration scheme, (v) true multidimensionality without using directional splitting, and (vi) the ability to handle two- and three-dimensional geometries by using unstructured meshes. This algorithm has been thoroughly tested in one, two and three spatial dimensions and has been shown to obtain the desired order of accuracy for solving both linear and non-linear hyperbolic partial differential equations. The scheme has also shown its ability to accurately resolve discontinuities in the solutions. Higher order unstructured methods such as the Discontinuous Galerkin (DG) method and the Spectral Volume (SV) methods have been developed for one-, two- and three-dimensional application. Although these schemes have seen extensive development and use, certain drawbacks of these methods have been well documented. For example, the explicit versions of these two methods have very stringent stability criteria. This stability criteria requires that the time step be reduced as the order of the solver increases, for a given simulation on a given mesh. The research presented in this dissertation builds upon the work of Chang, who developed a fourth-order CESE scheme to solve a scalar one-dimensional hyperbolic partial differential equation. The completed research has resulted in two key deliverables. The first is a detailed derivation of a high-order CESE methods on unstructured meshes for solving the conservation laws in two- and three-dimensional spaces. The second is the code implementation of these numerical methods in a computer code. For
Five-dimensional truncation of the plane incompressible navier-stokes equations
Energy Technology Data Exchange (ETDEWEB)
Boldrighini, C [Camerino Univ. (Italy). Istituto di Matematica; Franceschini, V [Modena Univ. (Italy). Istituto Matematico
1979-01-01
A five-modes truncation of the Navier-Stokes equations for a two dimensional incompressible fluid on a torus is considered. A computer analysis shows that for a certain range of the Reynolds number the system exhibits a stochastic behaviour, approached through an involved sequence of bifurcations.
Piatkowski, Marian; Müthing, Steffen; Bastian, Peter
2018-03-01
In this paper we consider discontinuous Galerkin (DG) methods for the incompressible Navier-Stokes equations in the framework of projection methods. In particular we employ symmetric interior penalty DG methods within the second-order rotational incremental pressure correction scheme. The major focus of the paper is threefold: i) We propose a modified upwind scheme based on the Vijayasundaram numerical flux that has favourable properties in the context of DG. ii) We present a novel postprocessing technique in the Helmholtz projection step based on H (div) reconstruction of the pressure correction that is computed locally, is a projection in the discrete setting and ensures that the projected velocity satisfies the discrete continuity equation exactly. As a consequence it also provides local mass conservation of the projected velocity. iii) Numerical results demonstrate the properties of the scheme for different polynomial degrees applied to two-dimensional problems with known solution as well as large-scale three-dimensional problems. In particular we address second-order convergence in time of the splitting scheme as well as its long-time stability.
Prandtl boundary layer expansions of steady Navier-Stokes flows over a moving plate
Guo, Yan; Nguyen, Toan T.
2014-01-01
This paper concerns the validity of the Prandtl boundary layer theory in the inviscid limit for steady incompressible Navier-Stokes flows. The stationary flows, with small viscosity, are considered on $[0,L]\\times \\mathbb{R}_{+}$, assuming a no-slip boundary condition over a moving plate at $y=0$. We establish the validity of the Prandtl boundary layer expansion and its error estimates.
Grid adaption using Chimera composite overlapping meshes
Kao, Kai-Hsiung; Liou, Meng-Sing; Chow, Chuen-Yen
1993-01-01
The objective of this paper is to perform grid adaptation using composite over-lapping meshes in regions of large gradient to capture the salient features accurately during computation. The Chimera grid scheme, a multiple overset mesh technique, is used in combination with a Navier-Stokes solver. The numerical solution is first converged to a steady state based on an initial coarse mesh. Solution-adaptive enhancement is then performed by using a secondary fine grid system which oversets on top of the base grid in the high-gradient region, but without requiring the mesh boundaries to join in any special way. Communications through boundary interfaces between those separated grids are carried out using tri-linear interpolation. Applications to the Euler equations for shock reflections and to a shock wave/boundary layer interaction problem are tested. With the present method, the salient features are well resolved.
Kierkegaard, Axel; Boij, Susann; Efraimsson, Gunilla
2010-02-01
Acoustic wave propagation in flow ducts is commonly modeled with time-domain non-linear Navier-Stokes equation methodologies. To reduce computational effort, investigations of a linearized approach in frequency domain are carried out. Calculations of sound wave propagation in a straight duct are presented with an orifice plate and a mean flow present. Results of transmission and reflections at the orifice are presented on a two-port scattering matrix form and are compared to measurements with good agreement. The wave propagation is modeled with a frequency domain linearized Navier-Stokes equation methodology. This methodology is found to be efficient for cases where the acoustic field does not alter the mean flow field, i.e., when whistling does not occur.
Large Deviations for Stochastic Tamed 3D Navier-Stokes Equations
International Nuclear Information System (INIS)
Roeckner, Michael; Zhang, Tusheng; Zhang Xicheng
2010-01-01
In this paper, using weak convergence method, we prove a large deviation principle of Freidlin-Wentzell type for the stochastic tamed 3D Navier-Stokes equations driven by multiplicative noise, which was investigated in (Roeckner and Zhang in Probab. Theory Relat. Fields 145(1-2), 211-267, 2009).
Directory of Open Access Journals (Sweden)
Qijun ZHAO
2018-02-01
Full Text Available A robust unsteady rotor flowfield solver CLORNS code is established to predict the complex unsteady aerodynamic characteristics of rotor flowfield. In order to handle the difficult problem about grid generation around rotor with complex aerodynamic shape in this CFD code, a parameterized grid generated method is established, and the moving-embedded grids are constructed by several proposed universal methods. In this work, the unsteady Reynolds-Averaged Navier-Stokes (RANS equations with Spalart-Allmaras are selected as the governing equations to predict the unsteady flowfield of helicopter rotor. The discretization of convective fluxes is accomplished by employing the second-order central difference scheme, third-order MUSCL-Roe scheme, and fifth-order WENO-Roe scheme. Aimed at simulating the unsteady aerodynamic characteristics of helicopter rotor, the dual-time scheme with implicit LU-SGS scheme is employed to accomplish the temporal discretization. In order to improve the computational efficiency of hole-cells and donor elements searching of the moving-embedded grid technology, the “disturbance diffraction method” and “minimum distance scheme of donor elements method” are established in this work. To improve the computational efficiency, Message Passing Interface (MPI parallel method based on subdivision of grid, local preconditioning method and Full Approximation Storage (FAS multi-grid method are combined in this code. By comparison of the numerical results simulated by CLORNS code with test data, it is illustrated that the present code could simulate the aerodynamic loads and aerodynamic noise characteristics of helicopter rotor accurately. Keywords: Aerodynamic characteristics, Helicopter rotor, Moving-embedded grid, Navier-Stokes equations, Upwind schemes
Directory of Open Access Journals (Sweden)
Meng Zhi-Jun
2016-01-01
Full Text Available This paper addresses the systems of the incompressible Navier-Stokes equations on Cantor sets without the external force involving the fractal heat-conduction problem vial local fractional derivative. The spherical Cantor type co-ordinate method is used to transfer the incompressible Navier-Stokes equation from the Cantorian co-ordinate system into the spherical Cantor type co-ordinate system.
A matrix-free implicit treatment for all speed flows on unstructured grids
International Nuclear Information System (INIS)
Kloczko, Th.
2006-03-01
The aim of this research work is the development of an efficient implicit scheme for computing compressible and low-speed flows on unstructured meshes. The first part is devoted to the review and analysis of some standard block-implicit treatments for the two-dimensional Euler and Navier-Stokes equations with a view to identify the best candidate for a fair comparison with the matrix-free treatment. The second part forms the main original contribution of this research work. It describes and analyses a matrix-free treatment that can be applied to any type of flow (inviscid/viscous, low Mach/highly compressible, steady/unsteady). The third part deals with the implementation of this treatment within the CAST3M code, and the demonstration of its advantages over existing techniques for computing applications of interest for the CEA: low-Mach number steady and unsteady flows in a Tee junction for example
A software platform for continuum modeling of ion channels based on unstructured mesh
International Nuclear Information System (INIS)
Tu, B; Bai, S Y; Xie, Y; Zhang, L B; Lu, B Z; Chen, M X
2014-01-01
Most traditional continuum molecular modeling adopted finite difference or finite volume methods which were based on a structured mesh (grid). Unstructured meshes were only occasionally used, but an increased number of applications emerge in molecular simulations. To facilitate the continuum modeling of biomolecular systems based on unstructured meshes, we are developing a software platform with tools which are particularly beneficial to those approaches. This work describes the software system specifically for the simulation of a typical, complex molecular procedure: ion transport through a three-dimensional channel system that consists of a protein and a membrane. The platform contains three parts: a meshing tool chain for ion channel systems, a parallel finite element solver for the Poisson–Nernst–Planck equations describing the electrodiffusion process of ion transport, and a visualization program for continuum molecular modeling. The meshing tool chain in the platform, which consists of a set of mesh generation tools, is able to generate high-quality surface and volume meshes for ion channel systems. The parallel finite element solver in our platform is based on the parallel adaptive finite element package PHG which wass developed by one of the authors [1]. As a featured component of the platform, a new visualization program, VCMM, has specifically been developed for continuum molecular modeling with an emphasis on providing useful facilities for unstructured mesh-based methods and for their output analysis and visualization. VCMM provides a graphic user interface and consists of three modules: a molecular module, a meshing module and a numerical module. A demonstration of the platform is provided with a study of two real proteins, the connexin 26 and hemolysin ion channels. (paper)
Stability result for Navier-Stokes equations with entropy transport
Czech Academy of Sciences Publication Activity Database
Michálek, Martin
2015-01-01
Roč. 17, č. 2 (2015), s. 279-285 ISSN 1422-6928 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : compressible Navier-Stokes system * entropy transport * effective viscous flux Subject RIV: BA - General Mathematics Impact factor: 1.023, year: 2015 http://link.springer.com/article/10.1007%2Fs00021-015-0205-x
Peng, NaiFu; Guan, Hui; Wu, ChuiJie
2016-04-01
In this paper, the theory of constructing optimal dynamical systems based on weighted residual presented by Wu & Sha is applied to three-dimensional Navier-Stokes equations, and the optimal dynamical system modeling equations are derived. Then the multiscale global optimization method based on coarse graining analysis is presented, by which a set of approximate global optimal bases is directly obtained from Navier-Stokes equations and the construction of optimal dynamical systems is realized. The optimal bases show good properties, such as showing the physical properties of complex flows and the turbulent vortex structures, being intrinsic to real physical problem and dynamical systems, and having scaling symmetry in mathematics, etc.. In conclusion, using fewer terms of optimal bases will approach the exact solutions of Navier-Stokes equations, and the dynamical systems based on them show the most optimal behavior.
An Interpreted Language and System for the Visualization of Unstructured Meshes
Moran, Patrick J.; Gerald-Yamasaki, Michael (Technical Monitor)
1998-01-01
We present an interpreted language and system supporting the visualization of unstructured meshes and the manipulation of shapes defined in terms of mesh subsets. The language features primitives inspired by geometric modeling, mathematical morphology and algebraic topology. The adaptation of the topology ideas to an interpreted environment, along with support for programming constructs such, as user function definition, provide a flexible system for analyzing a mesh and for calculating with shapes defined in terms of the mesh. We present results demonstrating some of the capabilities of the language, based on an implementation called the Shape Calculator, for tetrahedral meshes in R^3.
Newton-like methods for Navier-Stokes solution
Qin, N.; Xu, X.; Richards, B. E.
1992-12-01
The paper reports on Newton-like methods called SFDN-alpha-GMRES and SQN-alpha-GMRES methods that have been devised and proven as powerful schemes for large nonlinear problems typical of viscous compressible Navier-Stokes solutions. They can be applied using a partially converged solution from a conventional explicit or approximate implicit method. Developments have included the efficient parallelization of the schemes on a distributed memory parallel computer. The methods are illustrated using a RISC workstation and a transputer parallel system respectively to solve a hypersonic vortical flow.
Numerical experiments on unstructured PIC stability.
Energy Technology Data Exchange (ETDEWEB)
Day, David Minot
2011-04-01
Particle-In-Cell (PIC) is a method for plasmas simulation. Particles are pushed with Verlet time integration. Fields are modeled using finite differences on a tensor product mesh (cells). The Unstructured PIC methods studied here use instead finite element discretizations on unstructured (simplicial) meshes. PIC is constrained by stability limits (upper bounds) on mesh and time step sizes. Numerical evidence (2D) and analysis will be presented showing that similar bounds constrain unstructured PIC.
Li, Jichun
2014-12-02
For decades, the widely used finite difference method on staggered grids, also known as the marker and cell (MAC) method, has been one of the simplest and most effective numerical schemes for solving the Stokes equations and Navier–Stokes equations. Its superconvergence on uniform meshes has been observed by Nicolaides (SIAM J Numer Anal 29(6):1579–1591, 1992), but the rigorous proof is never given. Its behavior on non-uniform grids is not well studied, since most publications only consider uniform grids. In this work, we develop the MAC scheme on non-uniform rectangular meshes, and for the first time we theoretically prove that the superconvergence phenomenon (i.e., second order convergence in the (Formula presented.) norm for both velocity and pressure) holds true for the MAC method on non-uniform rectangular meshes. With a careful and accurate analysis of various sources of errors, we observe that even though the local truncation errors are only first order in terms of mesh size, the global errors after summation are second order due to the amazing cancellation of local errors. This observation leads to the elegant superconvergence analysis even with non-uniform meshes. Numerical results are given to verify our theoretical analysis.
Generalized extended Navier-Stokes theory
DEFF Research Database (Denmark)
Hansen, J. S.; Daivis, Peter J.; Dyre, Jeppe C.
2013-01-01
in molecular fluids. To discuss these phenomena in detail, molecular dynamics simulations of molecular chlorine are performed for three different state points. In general, the theory captures the behavior for small wavevector and frequencies as expected. For example, in the hydrodynamic regime......The extended Navier-Stokes theory accounts for the coupling between the translational and rotational molecular degrees of freedom. In this paper, we generalize this theory to non-zero frequencies and wavevectors, which enables a new study of spatio-temporal correlation phenomena present...... and for molecular fluids with small moment of inertia like chlorine, the theory predicts that the longitudinal and transverse intrinsic angular velocity correlation functions are almost identical, which is also seen in the molecular dynamics simulations. However, the theory fails at large wavevector and frequencies...
Navier-Stokes and Comprehensive Analysis Performance Predictions of the NREL Phase VI Experiment
Duque, Earl P. N.; Burklund, Michael D.; Johnson, Wayne
2003-01-01
A vortex lattice code, CAMRAD II, and a Reynolds-Averaged Navier-Stoke code, OVERFLOW-D2, were used to predict the aerodynamic performance of a two-bladed horizontal axis wind turbine. All computations were compared with experimental data that was collected at the NASA Ames Research Center 80- by 120-Foot Wind Tunnel. Computations were performed for both axial as well as yawed operating conditions. Various stall delay models and dynamics stall models were used by the CAMRAD II code. Comparisons between the experimental data and computed aerodynamic loads show that the OVERFLOW-D2 code can accurately predict the power and spanwise loading of a wind turbine rotor.
Ge, Liang; Sotiropoulos, Fotis
2007-08-01
A novel numerical method is developed that integrates boundary-conforming grids with a sharp interface, immersed boundary methodology. The method is intended for simulating internal flows containing complex, moving immersed boundaries such as those encountered in several cardiovascular applications. The background domain (e.g. the empty aorta) is discretized efficiently with a curvilinear boundary-fitted mesh while the complex moving immersed boundary (say a prosthetic heart valve) is treated with the sharp-interface, hybrid Cartesian/immersed-boundary approach of Gilmanov and Sotiropoulos [A. Gilmanov, F. Sotiropoulos, A hybrid cartesian/immersed boundary method for simulating flows with 3d, geometrically complex, moving bodies, Journal of Computational Physics 207 (2005) 457-492.]. To facilitate the implementation of this novel modeling paradigm in complex flow simulations, an accurate and efficient numerical method is developed for solving the unsteady, incompressible Navier-Stokes equations in generalized curvilinear coordinates. The method employs a novel, fully-curvilinear staggered grid discretization approach, which does not require either the explicit evaluation of the Christoffel symbols or the discretization of all three momentum equations at cell interfaces as done in previous formulations. The equations are integrated in time using an efficient, second-order accurate fractional step methodology coupled with a Jacobian-free, Newton-Krylov solver for the momentum equations and a GMRES solver enhanced with multigrid as preconditioner for the Poisson equation. Several numerical experiments are carried out on fine computational meshes to demonstrate the accuracy and efficiency of the proposed method for standard benchmark problems as well as for unsteady, pulsatile flow through a curved, pipe bend. To demonstrate the ability of the method to simulate flows with complex, moving immersed boundaries we apply it to calculate pulsatile, physiological flow
Navier-Stokes-Voigt Equations with Memory in 3D Lacking Instantaneous Kinematic Viscosity
Di Plinio, Francesco; Giorgini, Andrea; Pata, Vittorino; Temam, Roger
2018-04-01
We consider a Navier-Stokes-Voigt fluid model where the instantaneous kinematic viscosity has been completely replaced by a memory term incorporating hereditary effects, in presence of Ekman damping. Unlike the classical Navier-Stokes-Voigt system, the energy balance involves the spatial gradient of the past history of the velocity rather than providing an instantaneous control on the high modes. In spite of this difficulty, we show that our system is dissipative in the dynamical systems sense and even possesses regular global and exponential attractors of finite fractal dimension. Such features of asymptotic well-posedness in absence of instantaneous high modes dissipation appear to be unique within the realm of dynamical systems arising from fluid models.
Exact solutions of the Navier-Stokes equations generalized for flow in porous media
Daly, Edoardo; Basser, Hossein; Rudman, Murray
2018-05-01
Flow of Newtonian fluids in porous media is often modelled using a generalized version of the full non-linear Navier-Stokes equations that include additional terms describing the resistance to flow due to the porous matrix. Because this formulation is becoming increasingly popular in numerical models, exact solutions are required as a benchmark of numerical codes. The contribution of this study is to provide a number of non-trivial exact solutions of the generalized form of the Navier-Stokes equations for parallel flow in porous media. Steady-state solutions are derived in the case of flows in a medium with constant permeability along the main direction of flow and a constant cross-stream velocity in the case of both linear and non-linear drag. Solutions are also presented for cases in which the permeability changes in the direction normal to the main flow. An unsteady solution for a flow with velocity driven by a time-periodic pressure gradient is also derived. These solutions form a basis for validating computational models across a wide range of Reynolds and Darcy numbers.
Euler and Navier-Stokes equations on the hyperbolic plane.
Khesin, Boris; Misiolek, Gerard
2012-11-06
We show that nonuniqueness of the Leray-Hopf solutions of the Navier-Stokes equation on the hyperbolic plane (2) observed by Chan and Czubak is a consequence of the Hodge decomposition. We show that this phenomenon does not occur on (n) whenever n ≥ 3. We also describe the corresponding general Hamiltonian framework of hydrodynamics on complete Riemannian manifolds, which includes the hyperbolic setting.
Cellular neural networks, the Navier-Stokes equation, and microarray image reconstruction.
Zineddin, Bachar; Wang, Zidong; Liu, Xiaohui
2011-11-01
Although the last decade has witnessed a great deal of improvements achieved for the microarray technology, many major developments in all the main stages of this technology, including image processing, are still needed. Some hardware implementations of microarray image processing have been proposed in the literature and proved to be promising alternatives to the currently available software systems. However, the main drawback of those proposed approaches is the unsuitable addressing of the quantification of the gene spot in a realistic way without any assumption about the image surface. Our aim in this paper is to present a new image-reconstruction algorithm using the cellular neural network that solves the Navier-Stokes equation. This algorithm offers a robust method for estimating the background signal within the gene-spot region. The MATCNN toolbox for Matlab is used to test the proposed method. Quantitative comparisons are carried out, i.e., in terms of objective criteria, between our approach and some other available methods. It is shown that the proposed algorithm gives highly accurate and realistic measurements in a fully automated manner within a remarkably efficient time.
Shock-wave structure based on the Navier-Stokes-Fourier equations
Uribe, F. J.; Velasco, R. M.
2018-04-01
We use the Navier-Stokes-Fourier constitutive equations to study plane shock waves in dilute gases. It is shown that the experimental information on the normalized density profiles can be fit by using the so-called soft sphere model, in which the viscosity and thermal conductivity are proportional to a power of the temperature.
Robustness of strong solutions to the compressible Navier-Stokes system
Czech Academy of Sciences Publication Activity Database
Bella, P.; Feireisl, Eduard; Jin, B.J.; Novotný, A.
2015-01-01
Roč. 362, 1-2 (2015), s. 281-303 ISSN 0025-5831 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : compressible Navier-Stokes system * smooth solution * stability Subject RIV: BA - General Mathematics Impact factor: 1.366, year: 2015 http://link.springer.com/article/10.1007%2Fs00208-014-1119-2
A convergent numerical method for the Navier-Stokes-Fourier system
Czech Academy of Sciences Publication Activity Database
Feireisl, Eduard; Karper, T.; Novotný, A.
2016-01-01
Roč. 36, č. 4 (2016), s. 1477-1535 ISSN 0272-4979 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : Navier-Stokes-Fourier system * Crouzeix-Raviart finite element method * finite volume method Subject RIV: BA - General Mathematics Impact factor: 1.703, year: 2016 http://imajna.oxfordjournals.org/content/36/4/1477
Modelling of arc jet plasma flow in transitional regime by Navier Stokes and state-to-state coupling
International Nuclear Information System (INIS)
Alexandrova, T.; Izrar, B.; Lino da Silva, M.; Dudeck, M.
2005-01-01
The combination of 2D Navier-Stokes and state-to-state approaches has been used to describe the air plasma flow in an arc-jet. The gas dynamic parameters were calculated in Navier-Stokes approximation in a steady state description without chemical reaction and vibrational exchanges. And then, the set of equations of vibrational level densities and atomic species densities was locally solved. Experimental validations have been performed
International Nuclear Information System (INIS)
Constantin, P.; Wu, J.
1997-01-01
Using the methods of Foias [Sem. Math. Univ. Padova 48, 219 endash 343 (1972); 49, 9 endash 123 (1973)] and Vishik endash Fursikov [Mathematical Problems of Statistical Hydromechanics (Kluwer, Dordrecht, 1988)], we prove the existence and uniqueness of both spatial and space endash time statistical solutions of the Navier endash Stokes equations on the phase space of vorticity. Here the initial vorticity is in Yudovich space and the initial measure has finite mean enstrophy. We show under further assumptions on the initial vorticity that the statistical solutions of the Navier endash Stokes equations converge weakly and the inviscid limits are the corresponding statistical solutions of the Euler equations. copyright 1997 American Institute of Physics
Lee, Byungjoon; Min, Chohong
2018-05-01
We introduce a stable method for solving the incompressible Navier-Stokes equations with variable density and viscosity. Our method is stable in the sense that it does not increase the total energy of dynamics that is the sum of kinetic energy and potential energy. Instead of velocity, a new state variable is taken so that the kinetic energy is formulated by the L2 norm of the new variable. Navier-Stokes equations are rephrased with respect to the new variable, and a stable time discretization for the rephrased equations is presented. Taking into consideration the incompressibility in the Marker-And-Cell (MAC) grid, we present a modified Lax-Friedrich method that is L2 stable. Utilizing the discrete integration-by-parts in MAC grid and the modified Lax-Friedrich method, the time discretization is fully discretized. An explicit CFL condition for the stability of the full discretization is given and mathematically proved.
Ha, Sanghyun; Park, Junshin; You, Donghyun
2017-11-01
Utility of the computational power of modern Graphics Processing Units (GPUs) is elaborated for solutions of incompressible Navier-Stokes equations which are integrated using a semi-implicit fractional-step method. Due to its serial and bandwidth-bound nature, the present choice of numerical methods is considered to be a good candidate for evaluating the potential of GPUs for solving Navier-Stokes equations using non-explicit time integration. An efficient algorithm is presented for GPU acceleration of the Alternating Direction Implicit (ADI) and the Fourier-transform-based direct solution method used in the semi-implicit fractional-step method. OpenMP is employed for concurrent collection of turbulence statistics on a CPU while Navier-Stokes equations are computed on a GPU. Extension to multiple NVIDIA GPUs is implemented using NVLink supported by the Pascal architecture. Performance of the present method is experimented on multiple Tesla P100 GPUs compared with a single-core Xeon E5-2650 v4 CPU in simulations of boundary-layer flow over a flat plate. Supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (Ministry of Science, ICT and Future Planning NRF-2016R1E1A2A01939553, NRF-2014R1A2A1A11049599, and Ministry of Trade, Industry and Energy 201611101000230).
Falling paper: Navier-Stokes solutions, model of fluid forces, and center of mass elevation.
Pesavento, Umberto; Wang, Z Jane
2004-10-01
We investigate the problem of falling paper by solving the two dimensional Navier-Stokes equations subject to the motion of a free-falling body at Reynolds numbers around 10(3). The aerodynamic lift on a tumbling plate is found to be dominated by the product of linear and angular velocities rather than velocity squared, as appropriate for an airfoil. This coupling between translation and rotation provides a mechanism for a brief elevation of center of mass near the cusplike turning points. The Navier-Stokes solutions further provide the missing quantity in the classical theory of lift, the instantaneous circulation, and suggest a revised model for the fluid forces.
Edwards, Jack R.; Mcrae, D. S.
1993-01-01
An efficient implicit method for the computation of steady, three-dimensional, compressible Navier-Stokes flowfields is presented. A nonlinear iteration strategy based on planar Gauss-Seidel sweeps is used to drive the solution toward a steady state, with approximate factorization errors within a crossflow plane reduced by the application of a quasi-Newton technique. A hybrid discretization approach is employed, with flux-vector splitting utilized in the streamwise direction and central differences with artificial dissipation used for the transverse fluxes. Convergence histories and comparisons with experimental data are presented for several 3-D shock-boundary layer interactions. Both laminar and turbulent cases are considered, with turbulent closure provided by a modification of the Baldwin-Barth one-equation model. For the problems considered (175,000-325,000 mesh points), the algorithm provides steady-state convergence in 900-2000 CPU seconds on a single processor of a Cray Y-MP.
Local strong solutions to the stochastic compressible Navier-Stokes system
Czech Academy of Sciences Publication Activity Database
Breit, D.; Feireisl, Eduard; Hofmanová, M.
2018-01-01
Roč. 43, č. 2 (2018), s. 313-345 ISSN 0360-5302 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : compressible fluids * local strong solutions * Navier-Stokes system Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.608, year: 2016 https://www.tandfonline.com/doi/full/10.1080/03605302.2018.1442476
Inviscid incompressible limits of the full Navier-Stokes-Fourier system
Czech Academy of Sciences Publication Activity Database
Feireisl, Eduard; Novotný, A.
2013-01-01
Roč. 321, č. 3 (2013), s. 605-628 ISSN 0010-3616 R&D Projects: GA ČR GA201/09/0917 Institutional support: RVO:67985840 Keywords : Navier-Stokes-Fourier system * inviscid limit * incompressible limit Subject RIV: BA - General Mathematics Impact factor: 1.901, year: 2013 http://link.springer.com/article/10.1007%2Fs00220-013-1691-4
Regularity of the 3D Navier-Stokes equations with viewpoint of 2D flow
Bae, Hyeong-Ohk
2018-04-01
The regularity of 2D Navier-Stokes flow is well known. In this article we study the relationship of 3D and 2D flow, and the regularity of the 3D Naiver-Stokes equations with viewpoint of 2D equations. We consider the problem in the Cartesian and in the cylindrical coordinates.
An introduction to the mathematical theory of the Navier-Stokes equations
Galdi, Giovanni P
1994-01-01
Undoubtedly, the Navier-Stokes equations are of basic importance within the context of modern theory of partial differential equations. Although the range of their applicability to concrete problems has now been clearly recognised to be limited, as my dear friend and bright colleague K.R. Ra jagopal has showed me by several examples during the past six years, the mathematical questions that remain open are of such a fascinating and challenging nature that analysts and applied mathematicians cannot help being attracted by them and trying to contribute to their resolution. Thus, it is not a coincidence that over the past ten years more than seventy sig nificant research papers have appeared concerning the well-posedness of boundary and initial-boundary value problems. In this monograph I shall perform a systematic and up-to-date investiga tion of the fundamental properties of the Navier-Stokes equations, including existence, uniqueness, and regularity of solutions and, whenever the region of flow is unbou...
Boltzmann equation and hydrodynamics beyond Navier-Stokes.
Bobylev, A V
2018-04-28
We consider in this paper the problem of derivation and regularization of higher (in Knudsen number) equations of hydrodynamics. The author's approach based on successive changes of hydrodynamic variables is presented in more detail for the Burnett level. The complete theory is briefly discussed for the linearized Boltzmann equation. It is shown that the best results in this case can be obtained by using the 'diagonal' equations of hydrodynamics. Rigorous estimates of accuracy of the Navier-Stokes and Burnett approximations are also presented.This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).
Czech Academy of Sciences Publication Activity Database
Neustupa, Jiří; Al Baba, Hind
2018-01-01
Roč. 463, č. 1 (2018), s. 222-234 ISSN 0022-247X R&D Projects: GA ČR(CZ) GA17-01747S Institutional support: RVO:67985840 Keywords : Navier-Stokes equation * Navier-type boundary conditions * interior regularity Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.064, year: 2016 https://www.sciencedirect.com/science/article/pii/S0022247X18302233?via%3Dihub
Directory of Open Access Journals (Sweden)
Miryam Lucía Guerra-Mazo
2016-05-01
Full Text Available Presenta los resultados de la comparación entre las ecuaciones de Stokes y de Navier-Stokes para la simulación del flujo de agua líquida, a condiciones atmosféricas, a través de una placa orificio concéntrica. A partir de los datos experimentales que fueron tomados en el banco de fluidos, se evaluaron las simulaciones de ambas ecuaciones, usando el software libre Freefem++cs, que se basa en el método de los elementos finitos; las variables evaluadas son velocidad y presión en un intervalo de tiempo. Al analizar los resultados obtenidos con las simulaciones y comparar con los datos experimentales se encontró que las ecuaciones de Navier-Stokes representan mejor el sistema que la ecuación de Stokes.
Application of an upwind Navier-Stokes code to two-dimensional transonic airfoil flow
International Nuclear Information System (INIS)
Rumsey, C.L.; Thomas, J.L.; Anderson, W.K.; Taylor, S.L.
1987-01-01
An upwind-biased implicit approximate factorization Navier-Stokes algorithm is applied to a variety of steady transonic airfoil cases, using the NACA 0012, RAE 2822, and Jones supercritical airfoils. The thin-layer form of the compressible Navier-Stokes equations is used. Both the CYBER 205 and CRAY 2 supercomputers are utilized, with average computational speeds of about 18 and 16 microsec/gridpoint/iteration, respectively. Lift curves, drag polars, and variations in drag coefficient with Mach number are determined for the NACA 0012 and Jones supercritical airfoils. Also, several cases are computed for comparison with experiment. The effect of grid density and grid extent on a typical turbulent airfoil solution is shown. An algebraic eddy-viscosity turbulence model is used for all of the computations. 10 references
Dynamics of three-tori in a periodically forced navier-stokes flow
Lopez; Marques
2000-07-31
Three-tori solutions of the Navier-Stokes equations and their dynamics are elucidated by use of a global Poincare map. The flow is contained in a finite annular gap between two concentric cylinders, driven by the steady rotation and axial harmonic oscillations of the inner cylinder. The three-tori solutions undergo global bifurcations, including a new gluing bifurcation, associated with homoclinic and heteroclinic connections to unstable solutions (two-tori). These unstable two-tori act as organizing centers for the three-tori dynamics. A discrete space-time symmetry influences the dynamics.
Ha, Sanghyun; Park, Junshin; You, Donghyun
2018-01-01
Utility of the computational power of Graphics Processing Units (GPUs) is elaborated for solutions of incompressible Navier-Stokes equations which are integrated using a semi-implicit fractional-step method. The Alternating Direction Implicit (ADI) and the Fourier-transform-based direct solution methods used in the semi-implicit fractional-step method take advantage of multiple tridiagonal matrices whose inversion is known as the major bottleneck for acceleration on a typical multi-core machine. A novel implementation of the semi-implicit fractional-step method designed for GPU acceleration of the incompressible Navier-Stokes equations is presented. Aspects of the programing model of Compute Unified Device Architecture (CUDA), which are critical to the bandwidth-bound nature of the present method are discussed in detail. A data layout for efficient use of CUDA libraries is proposed for acceleration of tridiagonal matrix inversion and fast Fourier transform. OpenMP is employed for concurrent collection of turbulence statistics on a CPU while the Navier-Stokes equations are computed on a GPU. Performance of the present method using CUDA is assessed by comparing the speed of solving three tridiagonal matrices using ADI with the speed of solving one heptadiagonal matrix using a conjugate gradient method. An overall speedup of 20 times is achieved using a Tesla K40 GPU in comparison with a single-core Xeon E5-2660 v3 CPU in simulations of turbulent boundary-layer flow over a flat plate conducted on over 134 million grids. Enhanced performance of 48 times speedup is reached for the same problem using a Tesla P100 GPU.
International Nuclear Information System (INIS)
Hayder, M.E.
1988-01-01
A new scientific supercomputer, known as the Navier-Stokes Computer (NSC), has been designed. The NSC is a multi-purpose machine, and for applications in the field of computational fluid dynamics (CFD), this supercomputer is expected to yield a computational speed far exceeding that of the present-day super computers. This computer has a few very powerful processors (known as nodes) connected by an internodal network. There are three versions of the NSC nodes: micro-, mini- and full-node. The micro-node was developed to prove, to demonstrate and to refine the key architectural features of the NSC. Architectures of the two recent versions of the NSC nodes are presented, with the main focus on the full-node. At a clock speed of 20 MHz, the mini- and the full-node have peak computational speeds of 200 and 640 MFLOPS, respectively. The full-node is the final version for the NSC nodes and an NSC is expected to have 128 full-nodes. To test the suitability of different algorithms on the NSC architecture, an NSC simulator was developed. Some of the existing computational fluid dynamics codes were placed on this simulator to determine important and relevant issues relating to the efficient use of the NSC architecture
Czech Academy of Sciences Publication Activity Database
Neustupa, Jiří; Al Baba, Hind
2018-01-01
Roč. 463, č. 1 (2018), s. 222-234 ISSN 0022-247X R&D Projects: GA ČR(CZ) GA17-01747S Institutional support: RVO:67985840 Keywords : Navier-Stokes equation * Navier-type boundary conditions * interior regularity Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.064, year: 2016 https://www. science direct.com/ science /article/pii/S0022247X18302233?via%3Dihub
KNOW-BLADE task-4 report. Navier-Stokes aeroelasticity
Energy Technology Data Exchange (ETDEWEB)
Politis, E.S.; Nikolaou, I.G.; Chaviaropoulos, P.K.; Bertagnolio, F.; Soerensen, N.N.; Johansen, J.
2005-01-01
The problem of the aeroelastic stability of wind turbine blades is addressed in this report by advancing the aerodynamic modelling in the beam element type codes from the engineering-type empirical models to unsteady, 2D or 3D, Navier-Stokes solvers. In this project, structural models for the full wind turbine blade have been combined with 2D and 3D unsteady Navier-Stokes solvers. The relative disadvantage of the quasi-3D approach (where the elastic solver is coupled with a 2D Navier-Stokes solver) is its inability to model induced flow. The lack of a validation test case did not allow for quantitative comparisons with experimental data to be carried out; instead the results of the advanced aeroelastic tools are qualitatively cross-compared. All investigated methods predicted qualitatively similar results. They all resulted in positive aerodynamic damping values for the flap mode, in a decrease in damping with the increase of wind speeds and in a minimum value for the damping for wind speed around 15{approx}m/s. The eigenvalue analyses resulted in steeper distributions for this mode. The agreement in aerodynamic damping decrease with the increase of wind speed is also observed in the distributions for the lead-lag mode. In perspective, the uncoupled, linear method results in higher values of aerodynamic damping compared to the 3D aeroelastic tool. The quasi-3D tool results in lower aerodynamic damping values in the higher wind speeds and in lower damping values in the lower wind speed regime. Apart from the computations for the full blade, 2D computations for the so-called 'typical section' have been carried out. The 2D aeroelastic tools resulted in similar aerodynamic damping values. Qualitative agreement was better for the lead-lag mode. The presence of roughness tapes has a small, rather negligible impact on aeroelastic stability as depicted by the results of both aeroelastic tools. On the other hand, in conformity to the inability of the adopted
A Modular Approach to Model Oscillating Control Surfaces Using Navier Stokes Equations
Guruswamy, Guru P.; Lee, Henry
2014-01-01
The use of active controls for rotorcraft is becoming more important for modern aerospace configurations. Efforts to reduce the vibrations of helicopter blades with use of active-controls are in progress. Modeling oscillating control surfaces using the linear aerodynamics theory is well established. However, higher-fidelity methods are needed to account for nonlinear effects, such as those that occur in transonic flow. The aeroelastic responses of a wing with an oscillating control surface, computed using the transonic small perturbation (TSP) theory, have been shown to cause important transonic flow effects such as a reversal of control surface effectiveness that occurs as the shock wave crosses the hinge line. In order to account for flow complexities such as blade-vortex interactions of rotor blades higher-fidelity methods based on the Navier-Stokes equations are used. Reference 6 presents a procedure that uses the Navier-Stokes equations with moving-sheared grids and demonstrates up to 8 degrees of control-surface amplitude, using a single grid. Later, this procedure was extended to accommodate larger amplitudes, based on sliding grid zones. The sheared grid method implemented in EulerlNavier-Stokes-based aeroelastic code ENS AERO was successfully applied to active control design by industry. Recently there are several papers that present results for oscillating control surface using Reynolds Averaged Navier-Stokes (RANS) equations. References 9 and 10 report 2-D cases by filling gaps with overset grids. Reference 9 compares integrated forces with the experiment at low oscillating frequencies whereas Ref. 10 reports parametric studies but with no validation. Reference II reports results for a 3D case by modeling the gap region with a deformed grid and compares force results with the experiment only at the mid-span of flap. In Ref. II grid is deformed to match the control surface deflections at the section where the measurements are made. However, there is no
SALE-3D, 3-D Fluid Flow, Navier Stokes Equation Using Lagrangian or Eulerian Method
International Nuclear Information System (INIS)
Amsden, A.A.; Ruppel, H.M.
1991-01-01
1 - Description of problem or function: SALE-3D calculates three- dimensional fluid flows at all speeds, from the incompressible limit to highly supersonic. An implicit treatment of the pressure calculation similar to that in the Implicit Continuous-fluid Eulerian (ICE) technique provides this flow speed flexibility. In addition, the computing mesh may move with the fluid in a typical Lagrangian fashion, be held fixed in an Eulerian manner, or move in some arbitrarily specified way to provide a continuous rezoning capability. This latitude results from use of an Arbitrary Lagrangian-Eulerian (ALE) treatment of the mesh. The partial differential equations solved are the Navier-Stokes equations and the mass and internal energy equations. The fluid pressure is determined from an equation of state and supplemented with an artificial viscous pressure for the computation of shock waves. The computing mesh consists of a three-dimensional network of arbitrarily shaped, six-sided deformable cells, and a variety of user-selectable boundary conditions are provided in the program. 2 - Method of solution: SALE3D uses an ICED-ALE technique, which combines the ICE method of treating flow speeds and the ALE mesh treatment to calculate three-dimensional fluid flow. The finite- difference approximations to the conservation of mass, momentum, and specific internal energy differential equations are solved in a sequence of time steps on a network of deformable computational cells. The basic hydrodynamic part of each cycle is divided into three phases: (1) an explicit solution of the Lagrangian equations of motion updating the velocity field by the effects of all forces, (2) an implicit calculation using Newton-Raphson iterative scheme that provides time-advanced pressures and velocities, and (3) the addition of advective contributions for runs that are Eulerian or contain some relative motion of grid and fluid. A powerful feature of this three-phases approach is the ease with which
Decay Properties of Axially Symmetric D-Solutions to the Steady Navier-Stokes Equations
Weng, Shangkun
2018-03-01
We investigate the decay properties of smooth axially symmetric D-solutions to the steady Navier-Stokes equations. The achievements of this paper are two folds. One is improved decay rates of u_{θ } and \
Berselli, Luigi C.; Spirito, Stefano
2018-06-01
Obtaining reliable numerical simulations of turbulent fluids is a challenging problem in computational fluid mechanics. The large eddy simulation (LES) models are efficient tools to approximate turbulent fluids, and an important step in the validation of these models is the ability to reproduce relevant properties of the flow. In this paper, we consider a fully discrete approximation of the Navier-Stokes-Voigt model by an implicit Euler algorithm (with respect to the time variable) and a Fourier-Galerkin method (in the space variables). We prove the convergence to weak solutions of the incompressible Navier-Stokes equations satisfying the natural local entropy condition, hence selecting the so-called physically relevant solutions.
Navier-Stokes calculations on multi-element airfoils using a chimera-based solver
Jasper, Donald W.; Agrawal, Shreekant; Robinson, Brian A.
1993-01-01
A study of Navier-Stokes calculations of flows about multielement airfoils using a chimera grid approach is presented. The chimera approach utilizes structured, overlapped grids which allow great flexibility of grid arrangement and simplifies grid generation. Calculations are made for two-, three-, and four-element airfoils, and modeling of the effect of gap distance between elements is demonstrated for a two element case. Solutions are obtained using the thin-layer form of the Reynolds averaged Navier-Stokes equations with turbulence closure provided by the Baldwin-Lomax algebraic model or the Baldwin-Barth one equation model. The Baldwin-Barth turbulence model is shown to provide better agreement with experimental data and to dramatically improve convergence rates for some cases. Recently developed, improved farfield boundary conditions are incorporated into the solver for greater efficiency. Computed results show good comparison with experimental data which include aerodynamic forces, surface pressures, and boundary layer velocity profiles.
The Actuator Surface Model: A New Navier-Stokes Based Model for Rotor Computations
DEFF Research Database (Denmark)
Shen, Wen Zhong; Zhang, J.H.; Sørensen, Jens Nørkær
2009-01-01
This paper presents a new numerical technique for simulating two-dimensional wind turbine flow. The method, denoted as the 2D actuator surface technique, consists of a two-dimensional Navier-Stokes solver in which the pressure distribution is represented by body forces that are distributed along ....... In the last part, the actuator surface technique is applied to compute the flow past a two-bladed vertical axis wind turbine equipped with NACA 0012 airfoils. Comparisons with experimental data show an encouraging performance of the method.......This paper presents a new numerical technique for simulating two-dimensional wind turbine flow. The method, denoted as the 2D actuator surface technique, consists of a two-dimensional Navier-Stokes solver in which the pressure distribution is represented by body forces that are distributed along...
Generalized conjugate-gradient methods for the Navier-Stokes equations
Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing
1991-01-01
A generalized conjugate-gradient method is used to solve the two-dimensional, compressible Navier-Stokes equations of fluid flow. The equations are discretized with an implicit, upwind finite-volume formulation. Preconditioning techniques are incorporated into the new solver to accelerate convergence of the overall iterative method. The superiority of the new solver is demonstrated by comparisons with a conventional line Gauss-Siedel Relaxation solver. Computational test results for transonic flow (trailing edge flow in a transonic turbine cascade) and hypersonic flow (M = 6.0 shock-on-shock phenoena on a cylindrical leading edge) are presented. When applied to the transonic cascade case, the new solver is 4.4 times faster in terms of number of iterations and 3.1 times faster in terms of CPU time than the Relaxation solver. For the hypersonic shock case, the new solver is 3.0 times faster in terms of number of iterations and 2.2 times faster in terms of CPU time than the Relaxation solver.
Turbomachinery Heat Transfer and Loss Modeling for 3D Navier-Stokes Codes
DeWitt, Kenneth; Ameri, Ali
2005-01-01
This report's contents focus on making use of NASA Glenn on-site computational facilities,to develop, validate, and apply models for use in advanced 3D Navier-Stokes Computational Fluid Dynamics (CFD) codes to enhance the capability to compute heat transfer and losses in turbomachiney.
On Stationary Navier-Stokes Flows Around a Rotating Obstacle in Two-Dimensions
Higaki, Mitsuo; Maekawa, Yasunori; Nakahara, Yuu
2018-05-01
We study the two-dimensional stationary Navier-Stokes equations describing the flows around a rotating obstacle. The unique existence of solutions and their asymptotic behavior at spatial infinity are established when the rotation speed of the obstacle and the given exterior force are sufficiently small.
Aland, Sebastian; Lowengrub, John; Voigt, Axel
2012-10-01
Colloid particles that are partially wetted by two immiscible fluids can become confined to fluid-fluid interfaces. At sufficiently high volume fractions, the colloids may jam and the interface may crystallize. The fluids together with the interfacial colloids form an emulsion with interesting material properties and offer an important route to new soft materials. A promising approach to simulate these emulsions was presented in Aland et al. [Phys. Fluids 23, 062103 (2011)], where a Navier-Stokes-Cahn-Hilliard model for the macroscopic two-phase fluid system was combined with a surface phase-field-crystal model for the microscopic colloidal particles along the interface. Unfortunately this model leads to spurious velocities which require very fine spatial and temporal resolutions to accurately and stably simulate. In this paper we develop an improved Navier-Stokes-Cahn-Hilliard-surface phase-field-crystal model based on the principles of mass conservation and thermodynamic consistency. To validate our approach, we derive a sharp interface model and show agreement with the improved diffuse interface model. Using simple flow configurations, we show that the new model has much better properties and does not lead to spurious velocities. Finally, we demonstrate the solid-like behavior of the crystallized interface by simulating the fall of a solid ball through a colloid-laden multiphase fluid.
International Nuclear Information System (INIS)
Koleshko, S.B.
1989-01-01
A three-parametric set of difference schemes is suggested to solve Navier-Stokes equations with the use of the relaxation form of the continuity equation. The initial equations are stated for time increments. Use is made of splitting the operator into one-dimensional forms that reduce calculations to scalar factorizations. Calculated results for steady- and unsteady-state flows in a cavity are presented
Richter, Christiane; Kotz, Frederik; Giselbrecht, Stefan; Helmer, Dorothea; Rapp, Bastian E
2016-06-01
The fluid mechanics of microfluidics is distinctively simpler than the fluid mechanics of macroscopic systems. In macroscopic systems effects such as non-laminar flow, convection, gravity etc. need to be accounted for all of which can usually be neglected in microfluidic systems. Still, there exists only a very limited selection of channel cross-sections for which the Navier-Stokes equation for pressure-driven Poiseuille flow can be solved analytically. From these equations, velocity profiles as well as flow rates can be calculated. However, whenever a cross-section is not highly symmetric (rectangular, elliptical or circular) the Navier-Stokes equation can usually not be solved analytically. In all of these cases, numerical methods are required. However, in many instances it is not necessary to turn to complex numerical solver packages for deriving, e.g., the velocity profile of a more complex microfluidic channel cross-section. In this paper, a simple spreadsheet analysis tool (here: Microsoft Excel) will be used to implement a simple numerical scheme which allows solving the Navier-Stokes equation for arbitrary channel cross-sections.
A quasi-Lagrangian finite element method for the Navier-Stokes equations in a time-dependent domain
Lozovskiy, Alexander; Olshanskii, Maxim A.; Vassilevski, Yuri V.
2018-05-01
The paper develops a finite element method for the Navier-Stokes equations of incompressible viscous fluid in a time-dependent domain. The method builds on a quasi-Lagrangian formulation of the problem. The paper provides stability and convergence analysis of the fully discrete (finite-difference in time and finite-element in space) method. The analysis does not assume any CFL time-step restriction, it rather needs mild conditions of the form $\\Delta t\\le C$, where $C$ depends only on problem data, and $h^{2m_u+2}\\le c\\,\\Delta t$, $m_u$ is polynomial degree of velocity finite element space. Both conditions result from a numerical treatment of practically important non-homogeneous boundary conditions. The theoretically predicted convergence rate is confirmed by a set of numerical experiments. Further we apply the method to simulate a flow in a simplified model of the left ventricle of a human heart, where the ventricle wall dynamics is reconstructed from a sequence of contrast enhanced Computed Tomography images.
Mathematical geophysics an introduction to rotating fluids and the Navier-Stokes equations
Chemin, Jean-Yves; Gallagher, Isabelle; Grenier, Emmanuel
2006-01-01
Aimed at graduate students and researchers in mathematics, engineering, oceanography, meteorology and mechanics, this text provides a detailed introduction to the physical theory of rotating fluids, a significant part of geophysical fluid dynamics. The Navier-Stokes equations are examined in both incompressible and rapidly rotating forms.
Mesh Generation and Adaption for High Reynolds Number RANS Computations, Phase I
National Aeronautics and Space Administration — This proposal offers to provide NASA with an automatic mesh generator for the simulation of aerodynamic flows using Reynolds-Averages Navier-Stokes (RANS) models....
Mesh Generation and Adaption for High Reynolds Number RANS Computations, Phase II
National Aeronautics and Space Administration — This proposal offers to provide NASA with an automatic mesh generator for the simulation of aerodynamic flows using Reynolds-Averages Navier-Stokes (RANS) models....
Reliability enhancement of Navier-Stokes codes through convergence acceleration
Merkle, Charles L.; Dulikravich, George S.
1995-01-01
Methods for enhancing the reliability of Navier-Stokes computer codes through improving convergence characteristics are presented. The improving of these characteristics decreases the likelihood of code unreliability and user interventions in a design environment. The problem referred to as a 'stiffness' in the governing equations for propulsion-related flowfields is investigated, particularly in regard to common sources of equation stiffness that lead to convergence degradation of CFD algorithms. Von Neumann stability theory is employed as a tool to study the convergence difficulties involved. Based on the stability results, improved algorithms are devised to ensure efficient convergence in different situations. A number of test cases are considered to confirm a correlation between stability theory and numerical convergence. The examples of turbulent and reacting flow are presented, and a generalized form of the preconditioning matrix is derived to handle these problems, i.e., the problems involving additional differential equations for describing the transport of turbulent kinetic energy, dissipation rate and chemical species. Algorithms for unsteady computations are considered. The extension of the preconditioning techniques and algorithms derived for Navier-Stokes computations to three-dimensional flow problems is discussed. New methods to accelerate the convergence of iterative schemes for the numerical integration of systems of partial differential equtions are developed, with a special emphasis on the acceleration of convergence on highly clustered grids.
On a model for the Navier-Stokes equations using magnetization variables
Pooley, Benjamin C.
2018-04-01
It is known that in a classical setting, the Navier-Stokes equations can be reformulated in terms of so-called magnetization variables w that satisfy Our main focus is the proof of global well-posedness in H 1 / 2 for a new variant of (1), where Pw is replaced by w in the second nonlinear term:
Numerical Solution of Stokes Flow in a Circular Cavity Using Mesh-free Local RBF-DQ
DEFF Research Database (Denmark)
Kutanaai, S Soleimani; Roshan, Naeem; Vosoughi, A
2012-01-01
This work reports the results of a numerical investigation of Stokes flow problem in a circular cavity as an irregular geometry using mesh-free local radial basis function-based differential quadrature (RBF-DQ) method. This method is the combination of differential quadrature approximation of der...... in solution of partial differential equations (PDEs).......This work reports the results of a numerical investigation of Stokes flow problem in a circular cavity as an irregular geometry using mesh-free local radial basis function-based differential quadrature (RBF-DQ) method. This method is the combination of differential quadrature approximation...... is applied on a two-dimensional geometry. The obtained results from the numerical simulations are compared with those gained by previous works. Outcomes prove that the current technique is in very good agreement with previous investigations and this fact that RBF-DQ method is an accurate and flexible method...
Directory of Open Access Journals (Sweden)
Juergen Saal
2007-02-01
Full Text Available It is proved under mild regularity assumptions on the data that the Navier-Stokes equations in bounded and unbounded noncylindrical regions admit a unique local-in-time strong solution. The result is based on maximal regularity estimates for the in spatial regions with a moving boundary obtained in [16] and the contraction mapping principle.
Li, Zhilin; Xiao, Li; Cai, Qin; Zhao, Hongkai; Luo, Ray
2015-08-15
In this paper, a new Navier-Stokes solver based on a finite difference approximation is proposed to solve incompressible flows on irregular domains with open, traction, and free boundary conditions, which can be applied to simulations of fluid structure interaction, implicit solvent model for biomolecular applications and other free boundary or interface problems. For some problems of this type, the projection method and the augmented immersed interface method (IIM) do not work well or does not work at all. The proposed new Navier-Stokes solver is based on the local pressure boundary method, and a semi-implicit augmented IIM. A fast Poisson solver can be used in our algorithm which gives us the potential for developing fast overall solvers in the future. The time discretization is based on a second order multi-step method. Numerical tests with exact solutions are presented to validate the accuracy of the method. Application to fluid structure interaction between an incompressible fluid and a compressible gas bubble is also presented.
Multigrid and defect correction for the steady Navier-Stokes equations : application to aerodynamics
Koren, B.
1991-01-01
Theoretical and expcrimental convergence results are presented for nonlinear multigrid and iterative defect correction applied to finite volume discretizations of the full, steady, 2D, compressible NavierStokes equations. lterative defect correction is introduced for circumventing the difficulty in
Farquharson, C.; Long, J.; Lu, X.; Lelievre, P. G.
2017-12-01
Real-life geology is complex, and so, even when allowing for the diffusive, low resolution nature of geophysical electromagnetic methods, we need Earth models that can accurately represent this complexity when modelling and inverting electromagnetic data. This is particularly the case for the scales, detail and conductivity contrasts involved in mineral and hydrocarbon exploration and development, but also for the larger scale of lithospheric studies. Unstructured tetrahedral meshes provide a flexible means of discretizing a general, arbitrary Earth model. This is important when wanting to integrate a geophysical Earth model with a geological Earth model parameterized in terms of surfaces. Finite-element and finite-volume methods can be derived for computing the electric and magnetic fields in a model parameterized using an unstructured tetrahedral mesh. A number of such variants have been proposed and have proven successful. However, the efficiency and accuracy of these methods can be affected by the "quality" of the tetrahedral discretization, that is, how many of the tetrahedral cells in the mesh are long, narrow and pointy. This is particularly the case if one wants to use an iterative technique to solve the resulting linear system of equations. One approach to deal with this issue is to develop sophisticated model and mesh building and manipulation capabilities in order to ensure that any mesh built from geological information is of sufficient quality for the electromagnetic modelling. Another approach is to investigate other methods of synthesizing the electromagnetic fields. One such example is a "meshfree" approach in which the electromagnetic fields are synthesized using a mesh that is distinct from the mesh used to parameterized the Earth model. There are then two meshes, one describing the Earth model and one used for the numerical mathematics of computing the fields. This means that there are no longer any quality requirements on the model mesh, which
Incomplete augmented Lagrangian preconditioner for steady incompressible Navier-Stokes equations.
Tan, Ning-Bo; Huang, Ting-Zhu; Hu, Ze-Jun
2013-01-01
An incomplete augmented Lagrangian preconditioner, for the steady incompressible Navier-Stokes equations discretized by stable finite elements, is proposed. The eigenvalues of the preconditioned matrix are analyzed. Numerical experiments show that the incomplete augmented Lagrangian-based preconditioner proposed is very robust and performs quite well by the Picard linearization or the Newton linearization over a wide range of values of the viscosity on both uniform and stretched grids.
Chaos Synchronization in Navier-Stokes Turbulence
Lalescu, Cristian; Meneveau, Charles; Eyink, Gregory
2013-03-01
Chaos synchronization (CS) has been studied for some time now (Pecora & Carroll 1990), for systems with only a few degrees of freedom as well as for systems described by partial differential equations (Boccaletti et al 2002). CS in general is said to be present in coupled dynamical systems when a specific property of each system has the same time evolution for all, even though the evolution itself is chaotic. The Navier-Stokes (NS) equations describe the velocity for a wide range of fluids, and their solutions are usually called turbulent if fluctuation amplitudes decrease as a power of their wavenumber. There have been some studies of CS for continuous systems (Kocarev et al 1997), but CS for NS turbulence seems not to have been investigated so far. We focus on the synchronization of the small scales of a turbulent flow for which the time history of large scales is prescribed. Our DNS results show that high-wavenumbers in turbulence are fully slaved to modes with wavenumbers up to a critical fraction of the Kolmogorov dissipation wavenumber. The motivation for our work is to study deeply sub-Kolmogorov scales in fully developed turbulence (Schumacher 2007), which we found to be recoverable even at very high Reynolds number from simulations with moderate resolutions. This work is supported by the National Science Foundation's CDI-II program, project CMMI-0941530
Identification of severe wind conditions using a Reynolds averaged Navier-Stokes solver
DEFF Research Database (Denmark)
Sørensen, Niels N.; Bechmann, Andreas; Johansen, Jeppe
2007-01-01
The present paper describes the application of a Navier-Stokes solver to predict the presence of severe flow conditions in complex terrain, capturing conditions that may be critical to the siting of wind turbines in the terrain. First it is documented that the flow solver is capable of predicting...
Fluctuating Navier-Stokes equations for inelastic hard spheres or disks.
Brey, J Javier; Maynar, P; de Soria, M I García
2011-04-01
Starting from the fluctuating Boltzmann equation for smooth inelastic hard spheres or disks, closed equations for the fluctuating hydrodynamic fields to Navier-Stokes order are derived. This requires deriving constitutive relations for both the fluctuating fluxes and the correlations of the random forces. The former are identified as having the same form as the macroscopic average fluxes and involving the same transport coefficients. On the other hand, the random force terms exhibit two peculiarities as compared with their elastic limit for molecular systems. First, they are not white but have some finite relaxation time. Second, their amplitude is not determined by the macroscopic transport coefficients but involves new coefficients. ©2011 American Physical Society
International Nuclear Information System (INIS)
Hammouch, Z.
2012-01-01
The 'anelastic' approximation allows us to filter the acoustic waves thanks to an asymptotic development of the Navier-Stokes equations, so increasing the averaged time step, during the numerical simulation of hydrodynamic instabilities development. So, the anelastic equations for a two fluid mixture in case of Rayleigh-Taylor instability are established.The linear stability of Rayleigh-Taylor flow is studied, for the first time, for perfect fluids in the anelastic approximation. We define the Stokes problem resulting from Navier-Stokes equations without the non linear terms (a part of the buoyancy is considered); the ellipticity is demonstrated, the Eigenmodes and the invariance related to the pressure are detailed. The Uzawa's method is extended to the anelastic approximation and shows the decoupling speeds in 3D, the particular case k = 0 and the spurious modes of pressure. Passing to multi-domain allowed to establish the transmission conditions.The algorithms and the implementation in the existing program are validated by comparing the Uzawa's operator in Fortran and Mathematica languages, to an experiment with incompressible fluids and results from anelastic and compressible numerical simulations. The study of the influence of the initial stratification of both fluids on the development of the Rayleigh-Taylor instability is initiated. (author) [fr
Directory of Open Access Journals (Sweden)
Neng Wan
2014-01-01
Full Text Available In terms of the poor geometric adaptability of spline element method, a geometric precision spline method, which uses the rational Bezier patches to indicate the solution domain, is proposed for two-dimensional viscous uncompressed Navier-Stokes equation. Besides fewer pending unknowns, higher accuracy, and computation efficiency, it possesses such advantages as accurate representation of isogeometric analysis for object boundary and the unity of geometry and analysis modeling. Meanwhile, the selection of B-spline basis functions and the grid definition is studied and a stable discretization format satisfying inf-sup conditions is proposed. The degree of spline functions approaching the velocity field is one order higher than that approaching pressure field, and these functions are defined on one-time refined grid. The Dirichlet boundary conditions are imposed through the Nitsche variational principle in weak form due to the lack of interpolation properties of the B-splines functions. Finally, the validity of the proposed method is verified with some examples.
Actuator Line/Navier-Stokes Computations for Flows past the Yawed MEXICO Rotor
DEFF Research Database (Denmark)
Shen, Wen Zhong; Sørensen, Jens Nørkær; Yang, H.
2011-01-01
In the paper the Actuator Line/Navier-Stokes model has been used to simulate flows past the yawed MEXICO rotor. The computed loads as well as the velocity field behind the yawed rotor are compared to detailed pressure and PIV measurements which were carried out in the EU funded MEXICO project...
Status for the two-dimensional Navier-Stokes solver EllipSys2D
DEFF Research Database (Denmark)
Bertagnolio, F.; Sørensen, Niels N.; Johansen, J.
2001-01-01
This report sets up an evaluation of the two-dimensional Navier-Stokes solver EllipSys2D in its present state. This code is used for blade aerodynamics simulations in the Aeroelastic Design group at Risø. Two airfoils are investigated by computing theflow at several angles of attack ranging from...
Existence of weak solutions for compressible Navier-Stokes equations with entropy transport
Czech Academy of Sciences Publication Activity Database
Maltese, D.; Michálek, Martin; Mucha, P.; Novotný, A.; Pokorný, M.; Zatorska, E.
2016-01-01
Roč. 261, č. 8 (2016), s. 4448-4485 ISSN 0022-0396 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier-Stokes equations Subject RIV: BA - General Mathematics Impact factor: 1.988, year: 2016 http://www.sciencedirect.com/science/article/pii/S0022039616301656
On the Critical One Component Regularity for 3-D Navier-Stokes System: General Case
Chemin, Jean-Yves; Zhang, Ping; Zhang, Zhifei
2017-06-01
Let us consider initial data {v_0} for the homogeneous incompressible 3D Navier-Stokes equation with vorticity belonging to {L^{3/2}\\cap L^2}. We prove that if the solution associated with {v_0} blows up at a finite time {T^\\star}, then for any p in {]4,∞[}, and any unit vector e of {R^3}, the L p norm in time with value in \\dot{H}^{1/2 + 2/p } of {(v|e)_{R^3}} blows up at {T^\\star}.
The Navier-Stokes-Fourier system: From weak solutions to numerical analysis
Czech Academy of Sciences Publication Activity Database
Feireisl, Eduard
2015-01-01
Roč. 35, č. 3 (2015), s. 185-193 ISSN 0174-4747 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier-Stokes-Fourier system * weak solution * mixed finite-volume finite-element numerical scheme Subject RIV: BA - General Mathematics http://www.degruyter.com/view/j/anly.2015.35.issue-3/anly-2014-1300/anly-2014-1300. xml
Investigation of vortex breakdown on delta wings using Navier-Stokes equations
Hsu, C.-H.; Liu, C. H.
1992-01-01
An efficient finite-difference scheme solving for the three-dimensional incompressible Navier-Stokes equations is described. Numerical simulations of vortex breakdown are then carried out for a sharp-edged delta wing and a round-edged double-delta wing at high Reynolds numbers. Computed results show that several major features of vortex breakdown are qualitatively in agreement with observations made in experiments.
EXPONENTIAL ERGODICITY FOR STOCHASTIC BURGERS AND 2D NAVIER-STOKES EQUATIONS
Goldys, B
2004-01-01
It is shown that transition measures of the stochastic Navier-Stokes equation in dimension 2 converge exponentially fast to the corresponding invariant measures in the distance of total variation. As a corollary we obtain the existence of spectral gap for a related semigroup obtained by a sort of ground state trasformation. Analogous results are proved for the stochastic Burgers equation.
Gkioulekas, Eleftherios
2016-09-01
Using the fusion-rules hypothesis for three-dimensional and two-dimensional Navier-Stokes turbulence, we generalize a previous nonperturbative locality proof to multiple applications of the nonlinear interactions operator on generalized structure functions of velocity differences. We call this generalization of nonperturbative locality to multiple applications of the nonlinear interactions operator "multilocality." The resulting cross terms pose a new challenge requiring a new argument and the introduction of a new fusion rule that takes advantage of rotational symmetry. Our main result is that the fusion-rules hypothesis implies both locality and multilocality in both the IR and UV limits for the downscale energy cascade of three-dimensional Navier-Stokes turbulence and the downscale enstrophy cascade and inverse energy cascade of two-dimensional Navier-Stokes turbulence. We stress that these claims relate to nonperturbative locality of generalized structure functions on all orders and not the term-by-term perturbative locality of diagrammatic theories or closure models that involve only two-point correlation and response functions.
Coupling Navier-stokes and Cahn-hilliard Equations in a Two-dimensional Annular flow Configuration
Vignal, Philippe; Sarmiento, Adel; Cortes, Adriano Mauricio; Dalcin, Lisandro; Calo, Victor M.
2015-01-01
In this work, we present a novel isogeometric analysis discretization for the Navier-Stokes- Cahn-Hilliard equation, which uses divergence-conforming spaces. Basis functions generated with this method can have higher-order continuity, and allow
Large-Eddy / Reynolds-Averaged Navier-Stokes Simulations of a Dual-Mode Scramjet Combustor
Fulton, Jesse A.; Edwards, Jack R.; Hassan, Hassan A.; Rockwell, Robert; Goyne, Christopher; McDaniel, James; Smith, Chad; Cutler, Andrew; Johansen, Craig; Danehy, Paul M.;
2012-01-01
Numerical simulations of reacting and non-reacting flows within a scramjet combustor configuration experimentally mapped at the University of Virginia s Scramjet Combustion Facility (operating with Configuration A ) are described in this paper. Reynolds-Averaged Navier-Stokes (RANS) and hybrid Large Eddy Simulation / Reynolds-Averaged Navier-Stokes (LES / RANS) methods are utilized, with the intent of comparing essentially blind predictions with results from non-intrusive flow-field measurement methods including coherent anti-Stokes Raman spectroscopy (CARS), hydroxyl radical planar laser-induced fluorescence (OH-PLIF), stereoscopic particle image velocimetry (SPIV), wavelength modulation spectroscopy (WMS), and focusing Schlieren. NC State's REACTMB solver was used both for RANS and LES / RANS, along with a 9-species, 19- reaction H2-air kinetics mechanism by Jachimowski. Inviscid fluxes were evaluated using Edwards LDFSS flux-splitting scheme, and the Menter BSL turbulence model was utilized in both full-domain RANS simulations and as the unsteady RANS portion of the LES / RANS closure. Simulations were executed and compared with experiment at two equivalence ratios, PHI = 0.17 and PHI = 0.34. Results show that the PHI = 0.17 flame is hotter near the injector while the PHI = 0.34 flame is displaced further downstream in the combustor, though it is still anchored to the injector. Reactant mixing was predicted to be much better at the lower equivalence ratio. The LES / RANS model appears to predict lower overall heat release compared to RANS (at least for PHI = 0.17), and its capability to capture the direct effects of larger turbulent eddies leads to much better predictions of reactant mixing and combustion in the flame stabilization region downstream of the fuel injector. Numerical results from the LES/RANS model also show very good agreement with OH-PLIF and SPIV measurements. An un-damped long-wave oscillation of the pre-combustion shock train, which caused
Investigation of Navier-Stokes Code Verification and Design Optimization
Vaidyanathan, Rajkumar
2004-01-01
With rapid progress made in employing computational techniques for various complex Navier-Stokes fluid flow problems, design optimization problems traditionally based on empirical formulations and experiments are now being addressed with the aid of computational fluid dynamics (CFD). To be able to carry out an effective CFD-based optimization study, it is essential that the uncertainty and appropriate confidence limits of the CFD solutions be quantified over the chosen design space. The present dissertation investigates the issues related to code verification, surrogate model-based optimization and sensitivity evaluation. For Navier-Stokes (NS) CFD code verification a least square extrapolation (LSE) method is assessed. This method projects numerically computed NS solutions from multiple, coarser base grids onto a freer grid and improves solution accuracy by minimizing the residual of the discretized NS equations over the projected grid. In this dissertation, the finite volume (FV) formulation is focused on. The interplay between the xi concepts and the outcome of LSE, and the effects of solution gradients and singularities, nonlinear physics, and coupling of flow variables on the effectiveness of LSE are investigated. A CFD-based design optimization of a single element liquid rocket injector is conducted with surrogate models developed using response surface methodology (RSM) based on CFD solutions. The computational model consists of the NS equations, finite rate chemistry, and the k-6 turbulence closure. With the aid of these surrogate models, sensitivity and trade-off analyses are carried out for the injector design whose geometry (hydrogen flow angle, hydrogen and oxygen flow areas and oxygen post tip thickness) is optimized to attain desirable goals in performance (combustion length) and life/survivability (the maximum temperatures on the oxidizer post tip and injector face and a combustion chamber wall temperature). A preliminary multi-objective optimization
Computation of 3D steady Navier-Stokes flow with free-surface gravity waves
Lewis, M.R.; Koren, B.; Raven, H.C.; Armfield, S.; Morgan, P.; Srinivas, K,
2003-01-01
In this paper an iterative method for the computation of stationary gravity-wave solutions is investigated, using a novel formulation of the free-surface (FS) boundary-value problem. This method requires the solution of a sequence of stationary Reynolds-Averaged Navier-Stokes subproblems employing
Computation of 3D steady Navier-Stokes flow with free-surface gravity waves
M.R. Lewis; B. Koren (Barry); H.C. Raven
2003-01-01
textabstractIn this paper an iterative method for the computation of stationary gravity-wave solutions is investigated, using a novel formulation of the free-surface (FS) boundary-value problem. This method requires the solution of a sequence of stationary Reynolds-Averaged Navier-Stokes subproblems
Quasiconservation laws for compressible three-dimensional Navier-Stokes flow.
Gibbon, J D; Holm, D D
2012-10-01
We formulate the quasi-Lagrangian fluid transport dynamics of mass density ρ and the projection q=ω·∇ρ of the vorticity ω onto the density gradient, as determined by the three-dimensional compressible Navier-Stokes equations for an ideal gas, although the results apply for an arbitrary equation of state. It turns out that the quasi-Lagrangian transport of q cannot cross a level set of ρ. That is, in this formulation, level sets of ρ (isopycnals) are impermeable to the transport of the projection q.
Possible and impossible solutions of the Navier-Stokes equations
International Nuclear Information System (INIS)
Irmay, S.
1998-01-01
Flow of isochoric constant-viscosity fluids obeys continuity and the Navier-Stokes equations. They are difficult to solve being nonlinear with a nonslip boundary condition at solid walls. Berker presented many solutions, but some of them, e.g. irrotational velocity, contradict the repulsion condition. Radial flow, possible between two nonparallel planes, is shown to be impossible in a cone, though an approximate solution exists. Parallel (equidistant) streamlines are possible only if rectilinear, concentric or coaxial circles, or helices of equal inclination on coaxial cylinders. Two-way flows resemble ideal and Stokes flows. The author presents some spatial jets impacting on a fixed or parallelly moving boundary. A general unsteady spatial solution near a plane boundary is expressed as power series of z, distance from the wall, which shows most boundary layer solutions to be valid only up to z 2 terms. Uniform steady-state flow at a constant piezo metric gradient in the x-direction, between nonparallel planes, has a definite solution only up to second-order terms in (y,z), due to undefined boundary condition at ∞. Acceleration averaged over time gives insight into the properties of pseudoturbulent or chaotic (turbulent) flows. Turbulent shear is redefined and Reynolds (turbulent) stresses loose their meaning
Upwind algorithm for the parabolized Navier-Stokes equations
Lawrence, Scott L.; Tannehill, John C.; Chausee, Denny S.
1989-01-01
A new upwind algorithm based on Roe's scheme has been developed to solve the two-dimensional parabolized Navier-Stokes equations. This method does not require the addition of user-specified smoothing terms for the capture of discontinuities such as shock waves. Thus, the method is easy to use and can be applied without modification to a wide variety of supersonic flowfields. The advantages and disadvantages of this adaptation are discussed in relation to those of the conventional Beam-Warming (1978) scheme in terms of accuracy, stability, computer time and storage requirements, and programming effort. The new algorithm has been validated by applying it to three laminar test cases, including flat-plate boundary-layer flow, hypersonic flow past a 15-deg compression corner, and hypersonic flow into a converging inlet. The computed results compare well with experiment and show a dramatic improvement in the resolution of flowfield details when compared with results obtained using the conventional Beam-Warming algorithm.
Chen, Y. K.; Henline, W. D.
1993-01-01
The general boundary conditions including mass and energy balances of chemically equilibrated or nonequilibrated gas adjacent to ablating surfaces have been derived. A computer procedure based on these conditions was developed and interfaced with the Navier-Stokes solver for predictions of the flow field, surface temperature, and surface ablation rates over re-entry space vehicles with ablating Thermal Protection Systems (TPS). The Navier-Stokes solver with general surface thermochemistry boundary conditions can predict more realistic solutions and provide useful information for the design of TPS. A test case with a proposed hypersonic test vehicle configuration and associated free stream conditions was developed. Solutions with various surface boundary conditions were obtained, and the effect of nonequilibrium gas as well as surface chemistry on surface heating and ablation rate were examined. The solutions of the GASP code with complete ablating surface conditions were compared with those of the ASC code. The direction of future work is also discussed.
Capillary-gravity waves and the Navier-Stokes equation
International Nuclear Information System (INIS)
Behroozi, F.; Podolefsky, N.
2001-01-01
Water waves are a source of great fascination for undergraduates and thus provide an excellent context for introducing some important topics in fluid dynamics. In this paper we introduce the potential theory for incompressible and inviscid flow and derive the differential equation that governs the behaviour of the velocity potential. Next we obtain the harmonic solutions of the velocity potential by a very general argument. These solutions in turn yield the equations for the velocity and displacement of a water element under the action of a harmonic wave. Finally we obtain the dispersion relation for surface waves by requiring that the harmonic solutions satisfy the Navier-Stokes equation. (author)
Anomalous scaling of a passive vector advected by the Navier-Stokes velocity field
International Nuclear Information System (INIS)
Jurcisinova, E; Jurcisin, M; Remecky, R
2009-01-01
Using the field theoretic renormalization group and the operator-product expansion, the model of a passive vector field (a weak magnetic field in the framework of the kinematic MHD) advected by the velocity field which is governed by the stochastic Navier-Stokes equation with the Gaussian random stirring force δ-correlated in time and with the correlator proportional to k 4-d-2ε is investigated to the first order in ε (one-loop approximation). It is shown that the single-time correlation functions of the advected vector field have anomalous scaling behavior and the corresponding exponents are calculated in the isotropic case, as well as in the case with the presence of large-scale anisotropy. The hierarchy of the anisotropic critical dimensions is briefly discussed and the persistence of the anisotropy inside the inertial range is demonstrated on the behavior of the skewness and hyperskewness (dimensionless ratios of correlation functions) as functions of the Reynolds number Re. It is shown that even though the present model of a passive vector field advected by the realistic velocity field is mathematically more complicated than, on one hand, the corresponding models of a passive vector field advected by 'synthetic' Gaussian velocity fields and, on the other hand, than the corresponding model of a passive scalar quantity advected by the velocity field driven by the stochastic Navier-Stokes equation, the final one-loop approximate asymptotic scaling behavior of the single-time correlation or structure functions of the advected fields of all models are defined by the same anomalous dimensions (up to normalization)
Energy Technology Data Exchange (ETDEWEB)
Simmons, Daniel, E-mail: daniel.simmons@nottingham.ac.uk; Cools, Kristof; Sewell, Phillip
2016-11-01
Time domain electromagnetic simulation tools have the ability to model transient, wide-band applications, and non-linear problems. The Boundary Element Method (BEM) and the Transmission Line Modeling (TLM) method are both well established numerical techniques for simulating time-varying electromagnetic fields. The former surface based method can accurately describe outwardly radiating fields from piecewise uniform objects and efficiently deals with large domains filled with homogeneous media. The latter volume based method can describe inhomogeneous and non-linear media and has been proven to be unconditionally stable. Furthermore, the Unstructured TLM (UTLM) enables modelling of geometrically complex objects by using triangular meshes which removes staircasing and unnecessary extensions of the simulation domain. The hybridization of BEM and UTLM which is described in this paper is named the Boundary Element Unstructured Transmission-line (BEUT) method. It incorporates the advantages of both methods. The theory and derivation of the 2D BEUT method is described in this paper, along with any relevant implementation details. The method is corroborated by studying its correctness and efficiency compared to the traditional UTLM method when applied to complex problems such as the transmission through a system of Luneburg lenses and the modelling of antenna radomes for use in wireless communications. - Graphical abstract:.
Navier-Stokes Simulation of a Heavy Lift Slowed-Rotor Compound Helicopter Configuration
Allan, Brian G.; Jenkins, Luther N.; Yao, Chung-Sheng; Bartram, Scott M.; Hallissy, Jim B.; Harris, Jerome; Noonan, Kevin W.; Wong, Oliver D.; Jones, Henry E.; Malovrh, Brendon D.;
2009-01-01
Time accurate numerical simulations were performed using the Reynolds-averaged Navier-Stokes (RANS) flow solver OVERFLOW for a heavy lift, slowed-rotor, compound helicopter configuration, tested at the NASA Langley 14- by 22-Foot Subsonic Tunnel. The primary purpose of these simulations is to provide support for the development of a large field of view Particle Imaging Velocimetry (PIV) flow measurement technique supported by the Subsonic Rotary Wing (SRW) project under the NASA Fundamental Aeronautics program. These simulations provide a better understanding of the rotor and body wake flows and helped to define PIV measurement locations as well as requirements for validation of flow solver codes. The large field PIV system can measure the three-dimensional velocity flow field in a 0.914m by 1.83m plane. PIV measurements were performed upstream and downstream of the vertical tail section and are compared to simulation results. The simulations are also used to better understand the tunnel wall and body/rotor support effects by comparing simulations with and without tunnel floor/ceiling walls and supports. Comparisons are also made to the experimental force and moment data for the body and rotor.
On the equivalence between particular types of Navier-Stokes and non-linear Schroedinger equations
International Nuclear Information System (INIS)
Dietrich, K.; Vautherin, D.
1985-01-01
We derive a Schroedinger equation equivalent to the Navier-Stokes equation in the special case of constant kinematic viscosities. This equation contains a non-linear term similar to that proposed by Kostin for a quantum description of friction [fr
International Nuclear Information System (INIS)
Sonnendrucker, E.; Ambrosiano, J.; Brandon, S.
1993-01-01
The Darwin model for electromagnetic simulation is a reduced form of the Maxwell-Vlasov system that retains all essential physical processes except the propagation of light waves. It is useful in modeling systems for which the light-transit timescales are less important than Alfven wave propagation, or quasistatic effects. The Darwin model is elliptic rather than hyperbolic as are the full set of Maxwell's equations. Appropriate boundary conditions must be chosen for the problems to be well-posed. Using finite element techniques to apply this method for unstructured triangular meshes, a mesh made up of unstructured triangles allows realistic device geometries to be modeled without the necessity of using a large number of mesh points. Analyzing the dispersion relation allows us to validate the code as well as the Darwin approximation
The solutions of Navier-Stokes equations in squeezing flow between parallel plates
Czech Academy of Sciences Publication Activity Database
Petrov, A. G.; Kharlamova, Irina
2014-01-01
Roč. 48, November–December (2014), s. 40-48 ISSN 0997-7546 Grant - others:Russian Foundation for Basic Research(RU) 14-01- 00818; Russian Foundation for Basic Research(RU) 14-01-00892 Institutional support: RVO:67985874 Keywords : closed form solution * Navier-Stokes equations * squeezing flow between plates * counterflow Subject RIV: BK - Fluid Dynamics Impact factor: 1.656, year: 2014
Runge-Kutta discontinuous Galerkin method using a new type of WENO limiters on unstructured meshes
Zhu, Jun; Zhong, Xinghui; Shu, Chi-Wang; Qiu, Jianxian
2013-09-01
In this paper we generalize a new type of limiters based on the weighted essentially non-oscillatory (WENO) finite volume methodology for the Runge-Kutta discontinuous Galerkin (RKDG) methods solving nonlinear hyperbolic conservation laws, which were recently developed in [32] for structured meshes, to two-dimensional unstructured triangular meshes. The key idea of such limiters is to use the entire polynomials of the DG solutions from the troubled cell and its immediate neighboring cells, and then apply the classical WENO procedure to form a convex combination of these polynomials based on smoothness indicators and nonlinear weights, with suitable adjustments to guarantee conservation. The main advantage of this new limiter is its simplicity in implementation, especially for the unstructured meshes considered in this paper, as only information from immediate neighbors is needed and the usage of complicated geometric information of the meshes is largely avoided. Numerical results for both scalar equations and Euler systems of compressible gas dynamics are provided to illustrate the good performance of this procedure.
Aeroacoustic Calculations of Wind Turbine Noise with the Actuator Line/ Navier-Stokes Technique
DEFF Research Database (Denmark)
Debertshäuser, Harald; Shen, Wen Zhong; Zhu, Wei Jun
2016-01-01
technique where the wind turbine flow is calculated by using the in-house actuator line/LES/Navier-Stokes technique and the acoustics is obtained by solving the acoustic perturbation equations. In the flow solver, the wind turbine blades are modelled by rotating lines with body forces determined according...
Development and acceleration of unstructured mesh-based cfd solver
Emelyanov, V.; Karpenko, A.; Volkov, K.
2017-06-01
The study was undertaken as part of a larger effort to establish a common computational fluid dynamics (CFD) code for simulation of internal and external flows and involves some basic validation studies. The governing equations are solved with ¦nite volume code on unstructured meshes. The computational procedure involves reconstruction of the solution in each control volume and extrapolation of the unknowns to find the flow variables on the faces of control volume, solution of Riemann problem for each face of the control volume, and evolution of the time step. The nonlinear CFD solver works in an explicit time-marching fashion, based on a three-step Runge-Kutta stepping procedure. Convergence to a steady state is accelerated by the use of geometric technique and by the application of Jacobi preconditioning for high-speed flows, with a separate low Mach number preconditioning method for use with low-speed flows. The CFD code is implemented on graphics processing units (GPUs). Speedup of solution on GPUs with respect to solution on central processing units (CPU) is compared with the use of different meshes and different methods of distribution of input data into blocks. The results obtained provide promising perspective for designing a GPU-based software framework for applications in CFD.
Viswanathan, T M; Viswanathan, G M
2011-01-28
Strong global solvability is difficult to prove for high-dimensional hydrodynamic systems because of the complex interplay between nonlinearity and scale invariance. We define the Ladyzhenskaya-Lions exponent α(L)(n)=(2+n)/4 for Navier-Stokes equations with dissipation -(-Δ)(α) in R(n), for all n≥2. We review the proof of strong global solvability when α≥α(L)(n), given smooth initial data. If the corresponding Euler equations for n>2 were to allow uncontrolled growth of the enstrophy (1/2)∥∇u∥(L²)(2), then no globally controlled coercive quantity is currently known to exist that can regularize solutions of the Navier-Stokes equations for α<α(L)(n). The energy is critical under scale transformations only for α=α(L)(n).
International Nuclear Information System (INIS)
Besse, Nicolas
2003-01-01
This work is dedicated to the mathematical and numerical studies of the Vlasov equation on phase-space unstructured meshes. In the first part, new semi-Lagrangian methods are developed to solve the Vlasov equation on unstructured meshes of phase space. As the Vlasov equation describes multi-scale phenomena, we also propose original methods based on a wavelet multi-resolution analysis. The resulting algorithm leads to an adaptive mesh-refinement strategy. The new massively-parallel computers allow to use these methods with several phase-space dimensions. Particularly, these numerical schemes are applied to plasma physics and charged particle beams in the case of two-, three-, and four-dimensional Vlasov-Poisson systems. In the second part we prove the convergence and give error estimates for several numerical schemes applied to the Vlasov-Poisson system when strong and classical solutions are considered. First we show the convergence of a semi-Lagrangian scheme on an unstructured mesh of phase space, when the regularity hypotheses for the initial data are minimal. Then we demonstrate the convergence of classes of high-order semi-Lagrangian schemes in the framework of the regular classical solution. In order to reconstruct the distribution function, we consider symmetrical Lagrange polynomials, B-Splines and wavelets bases. Finally we prove the convergence of a semi-Lagrangian scheme with propagation of gradients yielding a high-order and stable reconstruction of the solution. (author) [fr
A point-centered diffusion differencing for unstructured meshes in 3-D
International Nuclear Information System (INIS)
Palmer, T.S.
1994-01-01
We describe a point-centered diffusion discretization for 3-D unstructured meshes of polyhedra. The method has several attractive qualities, including second-order accuracy and preservation of linear solutions. A potential drawback to the scheme is that the diffusion matrix is asymmetric, in general. Results of numerical test problems illustrate the behavior of the scheme
Toward a CFD nose-to-tail capability - Hypersonic unsteady Navier-Stokes code validation
Edwards, Thomas A.; Flores, Jolen
1989-01-01
Computational fluid dynamics (CFD) research for hypersonic flows presents new problems in code validation because of the added complexity of the physical models. This paper surveys code validation procedures applicable to hypersonic flow models that include real gas effects. The current status of hypersonic CFD flow analysis is assessed with the Compressible Navier-Stokes (CNS) code as a case study. The methods of code validation discussed to beyond comparison with experimental data to include comparisons with other codes and formulations, component analyses, and estimation of numerical errors. Current results indicate that predicting hypersonic flows of perfect gases and equilibrium air are well in hand. Pressure, shock location, and integrated quantities are relatively easy to predict accurately, while surface quantities such as heat transfer are more sensitive to the solution procedure. Modeling transition to turbulence needs refinement, though preliminary results are promising.
On the Dynamic Programming Approach for the 3D Navier-Stokes Equations
International Nuclear Information System (INIS)
Manca, Luigi
2008-01-01
The dynamic programming approach for the control of a 3D flow governed by the stochastic Navier-Stokes equations for incompressible fluid in a bounded domain is studied. By a compactness argument, existence of solutions for the associated Hamilton-Jacobi-Bellman equation is proved. Finally, existence of an optimal control through the feedback formula and of an optimal state is discussed
Group-theoretical model of developed turbulence and renormalization of the Navier-Stokes equation.
Saveliev, V L; Gorokhovski, M A
2005-07-01
On the basis of the Euler equation and its symmetry properties, this paper proposes a model of stationary homogeneous developed turbulence. A regularized averaging formula for the product of two fields is obtained. An equation for the averaged turbulent velocity field is derived from the Navier-Stokes equation by renormalization-group transformation.
Navier-Stokes Dynamics by a Discrete Boltzmann Model
Rubinstein, Robet
2010-01-01
This work investigates the possibility of particle-based algorithms for the Navier-Stokes equations and higher order continuum approximations of the Boltzmann equation; such algorithms would generalize the well-known Pullin scheme for the Euler equations. One such method is proposed in the context of a discrete velocity model of the Boltzmann equation. Preliminary results on shock structure are consistent with the expectation that the shock should be much broader than the near discontinuity predicted by the Pullin scheme, yet narrower than the prediction of the Boltzmann equation. We discuss the extension of this essentially deterministic method to a stochastic particle method that, like DSMC, samples the distribution function rather than resolving it completely.
A rigorous justification of the Euler and Navier-Stokes equations with geometric effects
Czech Academy of Sciences Publication Activity Database
Bella, P.; Feireisl, Eduard; Lewicka, M.; Novotný, A.
2016-01-01
Roč. 48, č. 6 (2016), s. 3907-3930 ISSN 0036-1410 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : isentropic Navier-Stokes system * isentropic Euler system * inviscid limit Subject RIV: BA - General Mathematics Impact factor: 1.648, year: 2016 http://epubs.siam.org/doi/10.1137/15M1048963
Stability of Planar Rarefaction Wave to 3D Full Compressible Navier-Stokes Equations
Li, Lin-an; Wang, Teng; Wang, Yi
2018-05-01
We prove time-asymptotic stability toward the planar rarefaction wave for the three-dimensional full, compressible Navier-Stokes equations with the heat-conductivities in an infinite long flat nozzle domain {R × T^2} . Compared with one-dimensional case, the proof here is based on our new observations on the cancellations on the flux terms and viscous terms due to the underlying wave structures, which are crucial for overcoming the difficulties due to the wave propagation in the transverse directions x 2 and x 3 and its interactions with the planar rarefaction wave in x 1 direction.
Large Scale Flutter Data for Design of Rotating Blades Using Navier-Stokes Equations
Guruswamy, Guru P.
2012-01-01
A procedure to compute flutter boundaries of rotating blades is presented; a) Navier-Stokes equations. b) Frequency domain method compatible with industry practice. Procedure is initially validated: a) Unsteady loads with flapping wing experiment. b) Flutter boundary with fixed wing experiment. Large scale flutter computation is demonstrated for rotating blade: a) Single job submission script. b) Flutter boundary in 24 hour wall clock time with 100 cores. c) Linearly scalable with number of cores. Tested with 1000 cores that produced data in 25 hrs for 10 flutter boundaries. Further wall-clock speed-up is possible by performing parallel computations within each case.
Some results on the well-posedness of Euler-Voigt and Navier-Stokes-Voigt models
Berselli, Luigi C.; Bisconti, Luca
2010-01-01
We consider the Euler-Voigt equations and the Navier-Stokes-Voigt equations, which are obtained by an inviscid alpha-regularization from the corresponding equations. The main result we show is the structural stability of the system in term of the variations of both viscosity of regularization parameters.
Li, Q; He, Y L; Wang, Y; Tao, W Q
2007-11-01
A coupled double-distribution-function lattice Boltzmann method is developed for the compressible Navier-Stokes equations. Different from existing thermal lattice Boltzmann methods, this method can recover the compressible Navier-Stokes equations with a flexible specific-heat ratio and Prandtl number. In the method, a density distribution function based on a multispeed lattice is used to recover the compressible continuity and momentum equations, while the compressible energy equation is recovered by an energy distribution function. The energy distribution function is then coupled to the density distribution function via the thermal equation of state. In order to obtain an adjustable specific-heat ratio, a constant related to the specific-heat ratio is introduced into the equilibrium energy distribution function. Two different coupled double-distribution-function lattice Boltzmann models are also proposed in the paper. Numerical simulations are performed for the Riemann problem, the double-Mach-reflection problem, and the Couette flow with a range of specific-heat ratios and Prandtl numbers. The numerical results are found to be in excellent agreement with analytical and/or other solutions.
Analysis of spurious oscillation modes for the shallow water and Navier-Stokes equations
Walters, R.A.; Carey, G.F.
1983-01-01
The origin and nature of spurious oscillation modes that appear in mixed finite element methods are examined. In particular, the shallow water equations are considered and a modal analysis for the one-dimensional problem is developed. From the resulting dispersion relations we find that the spurious modes in elevation are associated with zero frequency and large wave number (wavelengths of the order of the nodal spacing) and consequently are zero-velocity modes. The spurious modal behavior is the result of the finite spatial discretization. By means of an artificial compressibility and limiting argument we are able to resolve the similar problem for the Navier-Stokes equations. The relationship of this simpler analysis to alternative consistency arguments is explained. This modal approach provides an explanation of the phenomenon in question and permits us to deduce the cause of the very complex behavior of spurious modes observed in numerical experiments with the shallow water equations and Navier-Stokes equations. Furthermore, this analysis is not limited to finite element formulations, but is also applicable to finite difference formulations. ?? 1983.
Parameter investigation with line-implicit lower-upper symmetric Gauss-Seidel on 3D stretched grids
Otero, Evelyn; Eliasson, Peter
2015-03-01
An implicit lower-upper symmetric Gauss-Seidel (LU-SGS) solver has been implemented as a multigrid smoother combined with a line-implicit method as an acceleration technique for Reynolds-averaged Navier-Stokes (RANS) simulation on stretched meshes. The computational fluid dynamics code concerned is Edge, an edge-based finite volume Navier-Stokes flow solver for structured and unstructured grids. The paper focuses on the investigation of the parameters related to our novel line-implicit LU-SGS solver for convergence acceleration on 3D RANS meshes. The LU-SGS parameters are defined as the Courant-Friedrichs-Lewy number, the left-hand side dissipation, and the convergence of iterative solution of the linear problem arising from the linearisation of the implicit scheme. The influence of these parameters on the overall convergence is presented and default values are defined for maximum convergence acceleration. The optimised settings are applied to 3D RANS computations for comparison with explicit and line-implicit Runge-Kutta smoothing. For most of the cases, a computing time acceleration of the order of 2 is found depending on the mesh type, namely the boundary layer and the magnitude of residual reduction.
One problem of the Navier type for the Stokes system in planar domains
Czech Academy of Sciences Publication Activity Database
Medková, Dagmar
2016-01-01
Roč. 261, č. 10 (2016), s. 5670-5689 ISSN 0022-0396 R&D Projects: GA ČR GA16-03230S Institutional support: RVO:67985840 Keywords : Stokes system * Navier type problem * regularity of a solution Subject RIV: BA - General Mathematics Impact factor: 1.988, year: 2016 http://www.sciencedirect.com/science/article/pii/S0022039616302121
Ergodicity for the Randomly Forced 2D Navier-Stokes Equations
International Nuclear Information System (INIS)
Kuksin, Sergei; Shirikyan, Armen
2001-01-01
We study space-periodic 2D Navier-Stokes equations perturbed by an unbounded random kick-force. It is assumed that Fourier coefficients of the kicks are independent random variables all of whose moments are bounded and that the distributions of the first N 0 coefficients (where N 0 is a sufficiently large integer) have positive densities against the Lebesgue measure. We treat the equation as a random dynamical system in the space of square integrable divergence-free vector fields. We prove that this dynamical system has a unique stationary measure and study its ergodic properties
A study of plunging breaker mechanics by PIV measurements and a Navier-Stokes solver
DEFF Research Database (Denmark)
Emarat, Narumon; Forehand, David I. M.; Christensen, Erik Damgaard
2000-01-01
The mechanics of a surf-zone plunging breaker are studied from Particle Image Velocimetry (PIV) measurements and a numerical model based on the Navier-Stokes equations, using a Volume of Fluid (VOF) method. An additional numerical model using a Boundary-Integral Method (BIM) is also used in order...
International Nuclear Information System (INIS)
Doster, J.M.; Sills, E.D.
1986-01-01
Current efforts are under way to develop and evaluate numerical algorithms for the parallel solution of the large sparse matrix equations associated with the finite difference representation of the macroscopic Navier-Stokes equations. Previous work has shown that these equations can be cast into smaller coupled matrix equations suitable for solution utilizing multiple computer processors operating in parallel. The individual processors themselves may exhibit parallelism through the use of vector pipelines. This wor, has concentrated on the one-dimensional drift flux form of the Navier-Stokes equations. Direct and iterative algorithms that may be suitable for implementation on parallel computer architectures are evaluated in terms of accuracy and overall execution speed. This work has application to engineering and training simulations, on-line process control systems, and engineering workstations where increased computational speeds are required
SIERRA/Aero Theory Manual Version 4.44
Energy Technology Data Exchange (ETDEWEB)
Sierra Thermal/Fluid Team
2017-04-01
SIERRA/Aero is a two and three dimensional, node-centered, edge-based finite volume code that approximates the compressible Navier-Stokes equations on unstructured meshes. It is applicable to inviscid and high Reynolds number laminar and turbulent flows. Currently, two classes of turbulence models are provided: Reynolds Averaged Navier-Stokes (RANS) and hybrid methods such as Detached Eddy Simulation (DES). Large Eddy Simulation (LES) models are currently under development. The gas may be modeled either as ideal, or as a non-equilibrium, chemically reacting mixture of ideal gases. This document describes the mathematical models contained in the code, as well as certain implementation details. First, the governing equations are presented, followed by a description of the spatial discretization. Next, the time discretization is described, and finally the boundary conditions. Throughout the document, SIERRA/ Aero is referred to simply as Aero for brevity.
SIERRA/Aero Theory Manual Version 4.46.
Energy Technology Data Exchange (ETDEWEB)
Sierra Thermal/Fluid Team
2017-09-01
SIERRA/Aero is a two and three dimensional, node-centered, edge-based finite volume code that approximates the compressible Navier-Stokes equations on unstructured meshes. It is applicable to inviscid and high Reynolds number laminar and turbulent flows. Currently, two classes of turbulence models are provided: Reynolds Averaged Navier-Stokes (RANS) and hybrid methods such as Detached Eddy Simulation (DES). Large Eddy Simulation (LES) models are currently under development. The gas may be modeled either as ideal, or as a non-equilibrium, chemically reacting mixture of ideal gases. This document describes the mathematical models contained in the code, as well as certain implementation details. First, the governing equations are presented, followed by a description of the spatial discretization. Next, the time discretization is described, and finally the boundary conditions. Throughout the document, SIERRA/ Aero is referred to simply as Aero for brevity.
An upwind algorithm for the parabolized Navier-Stokes equations
Lawrence, S. L.; Tannehill, J. C.; Chaussee, D. S.
1986-01-01
A new upwind algorithm based on Roe's scheme has been developed to solve the two-dimensional parabolized Navier-Stokes (PNS) equations. This method does not require the addition of user specified smoothing terms for the capture of discontinuities such as shock waves. Thus, the method is easy to use and can be applied without modification to a wide variety of supersonic flowfields. The advantages and disadvantages of this adaptation are discussed in relation to those of the conventional Beam-Warming scheme in terms of accuracy, stability, computer time and storage, and programming effort. The new algorithm has been validated by applying it to three laminar test cases including flat plate boundary-layer flow, hypersonic flow past a 15 deg compression corner, and hypersonic flow into a converging inlet. The computed results compare well with experiment and show a dramatic improvement in the resolution of flowfield details when compared with the results obtained using the conventional Beam-Warming algorithm.
Wang, Zhiheng; Huang, Zhu; Zhang, Wei; Xi, Guang
2014-01-01
main advantages of the method. One is that the unstructured nodes generation in the computational domain is quite simple, without much concern about the mesh quality; the other is that the localization of the obtained collocations for the discretization
Formal solution of the Navier-Stokes initial- and boundary-value problem for incompressible fluids
International Nuclear Information System (INIS)
Alankus, T.
1984-01-01
A general formal solution of the integral equivalent of Navier-Stokes equation for incompressible viscous fluids is presented through a linear operator acting on the functionals of solenoidal vector fields. This solution operator is completely determined by the Green functions of Laplace and diffusion equations corresponding to the flow region
Exponential decay rate of the power spectrum for solutions of the Navier--Stokes equations
International Nuclear Information System (INIS)
Doering, C.R.; Titi, E.S.
1995-01-01
Using a method developed by Foias and Temam [J. Funct. Anal. 87, 359 (1989)], exponential decay of the spatial Fourier power spectrum for solutions of the incompressible Navier--Stokes equations is established and explicit rigorous lower bounds on a small length scale defined by the exponential decay rate are obtained
Bao, Kai
2012-10-01
In this paper, a semi-implicit finite element method is presented for the coupled Cahn-Hilliard and Navier-Stokes equations with the generalized Navier boundary condition for the moving contact line problems. In our method, the system is solved in a decoupled way. For the Cahn-Hilliard equations, a convex splitting scheme is used along with a P1-P1 finite element discretization. The scheme is unconditionally stable. A linearized semi-implicit P2-P0 mixed finite element method is employed to solve the Navier-Stokes equations. With our method, the generalized Navier boundary condition is extended to handle the moving contact line problems with complex boundary in a very natural way. The efficiency and capacity of the present method are well demonstrated with several numerical examples. © 2012 Elsevier Inc..
Bao, Kai; Shi, Yi; Sun, Shuyu; Wang, Xiaoping
2012-01-01
In this paper, a semi-implicit finite element method is presented for the coupled Cahn-Hilliard and Navier-Stokes equations with the generalized Navier boundary condition for the moving contact line problems. In our method, the system is solved in a decoupled way. For the Cahn-Hilliard equations, a convex splitting scheme is used along with a P1-P1 finite element discretization. The scheme is unconditionally stable. A linearized semi-implicit P2-P0 mixed finite element method is employed to solve the Navier-Stokes equations. With our method, the generalized Navier boundary condition is extended to handle the moving contact line problems with complex boundary in a very natural way. The efficiency and capacity of the present method are well demonstrated with several numerical examples. © 2012 Elsevier Inc..
Czech Academy of Sciences Publication Activity Database
Bellout, H.; Neustupa, Jiří; Penel, P.
2010-01-01
Roč. 27, č. 4 (2010), s. 1353-1373 ISSN 1078-0947 R&D Projects: GA AV ČR IAA100190905 Institutional research plan: CEZ:AV0Z10190503 Keywords : Euler equations * Navier-Stokes equations * zero viscosity limit Subject RIV: BA - General Mathematics Impact factor: 0.986, year: 2010 http://www.aimsciences.org/journals/displayArticles.jsp?paperID=5028
Numerical solution of the Navier--Stokes equations at high Reynolds numbers
International Nuclear Information System (INIS)
Shestakov, A.I.
1974-01-01
A numerical method is presented which is designed to solve the Navier-Stokes equations for two-dimensional, incompressible flow. The method is intended for use on problems with high Reynolds numbers for which calculations via finite difference methods have been unattainable or unreliable. The proposed scheme is a hybrid utilizing a time-splitting finite difference method in areas away from the boundaries. In areas neighboring the boundaries, the equations of motion are solved by the newly proposed vortex method by Chorin. The major accomplishment of the new scheme is that it contains a simple way for merging the two methods at the interface of the two subdomains. The proposed algorithm is designed for use on the time-dependent equations but can be used on steady state problems as well. The method is tested on the popular, time-independent, square cavity problem, an example of a separated flow with closed streamlines. Numerical results are presented for a Reynolds number of 10 3 . (auth)
Hypersonic Navier Stokes Comparisons to Orbiter Flight Data
Campbell, Charles H.; Nompelis, Ioannis; Candler, Graham; Barnhart, Michael; Yoon, Seokkwan
2009-01-01
Hypersonic chemical nonequilibrium simulations of low earth orbit entry flow fields are becoming increasingly commonplace as software and computational capabilities become more capable. However, development of robust and accurate software to model these environments will always encounter a significant barrier in developing a suite of high quality calibration cases. The US3D hypersonic nonequilibrium Navier Stokes analysis capability has been favorably compared to a number of wind tunnel test cases. Extension of the calibration basis for this software to Orbiter flight conditions will provide an incremental increase in confidence. As part of the Orbiter Boundary Layer Transition Flight Experiment and the Hypersonic Thermodynamic Infrared Measurements project, NASA is performing entry flight testing on the Orbiter to provide valuable aerothermodynamic heating data. An increase in interest related to orbiter entry environments is resulting from this activity. With the advent of this new data, comparisons of the US3D software to the new flight testing data is warranted. This paper will provide information regarding the framework of analyses that will be applied with the US3D analysis tool. In addition, comparisons will be made to entry flight testing data provided by the Orbiter BLT Flight Experiment and HYTHIRM projects. If data from digital scans of the Orbiter windward surface become available, simulations will also be performed to characterize the difference in surface heating between the CAD reference OML and the digitized surface provided by the surface scans.
A mimetic finite difference method for the Stokes problem with elected edge bubbles
Energy Technology Data Exchange (ETDEWEB)
Lipnikov, K [Los Alamos National Laboratory; Berirao, L [DIPARTMENTO DI MATERMATICA
2009-01-01
A new mimetic finite difference method for the Stokes problem is proposed and analyzed. The unstable P{sub 1}-P{sub 0} discretization is stabilized by adding a small number of bubble functions to selected mesh edges. A simple strategy for selecting such edges is proposed and verified with numerical experiments. The discretizations schemes for Stokes and Navier-Stokes equations must satisfy the celebrated inf-sup (or the LBB) stability condition. The stability condition implies a balance between discrete spaces for velocity and pressure. In finite elements, this balance is frequently achieved by adding bubble functions to the velocity space. The goal of this article is to show that the stabilizing edge bubble functions can be added only to a small set of mesh edges. This results in a smaller algebraic system and potentially in a faster calculations. We employ the mimetic finite difference (MFD) discretization technique that works for general polyhedral meshes and can accomodate non-uniform distribution of stabilizing bubbles.
Czech Academy of Sciences Publication Activity Database
Šístek, Jakub; Cirak, F.
2015-01-01
Roč. 122, 20 November (2015), s. 165-183 ISSN 0045-7930 R&D Projects: GA ČR GA14-02067S Institutional support: RVO:67985840 Keywords : Navier-Stokes * incompressible flow * Krylov subspace methods Subject RIV: BA - General Mathematics Impact factor: 1.891, year: 2015 http://www.sciencedirect.com/science/article/pii/S0045793015003023
A Navier-Stokes phase-field crystal model for colloidal suspensions.
Praetorius, Simon; Voigt, Axel
2015-04-21
We develop a fully continuous model for colloidal suspensions with hydrodynamic interactions. The Navier-Stokes Phase-Field Crystal model combines ideas of dynamic density functional theory with particulate flow approaches and is derived in detail and related to other dynamic density functional theory approaches with hydrodynamic interactions. The derived system is numerically solved using adaptive finite elements and is used to analyze colloidal crystallization in flowing environments demonstrating a strong coupling in both directions between the crystal shape and the flow field. We further validate the model against other computational approaches for particulate flow systems for various colloidal sedimentation problems.
International Nuclear Information System (INIS)
Curchitser, E.N.; Pelz, R.B.; Marconi, F.
1992-01-01
The Euler and Navier-Stokes equations are solved for the steady, two-dimensional flow over a NACA 0012 airfoil using a 1024 node nCUBE/2 multiprocessor. Second-order, upwind-discretized difference equations are solved implicitly using ADI factorization. Parallel cyclic reduction is employed to solve the block tridiagonal systems. For realistic problems, communication times are negligible compared to calculation times. The processors are tightly synchronized, and their loads are well balanced. When the flux Jacobians flux are frozen, the wall-clock time for one implicit timestep is about equal to that of a multistage explicit scheme. 10 refs
Tamellini, L.; Le Maî tre, O.; Nouy, A.
2014-01-01
In this paper we consider a proper generalized decomposition method to solve the steady incompressible Navier-Stokes equations with random Reynolds number and forcing term. The aim of such a technique is to compute a low-cost reduced basis approximation of the full stochastic Galerkin solution of the problem at hand. A particular algorithm, inspired by the Arnoldi method for solving eigenproblems, is proposed for an efficient greedy construction of a deterministic reduced basis approximation. This algorithm decouples the computation of the deterministic and stochastic components of the solution, thus allowing reuse of preexisting deterministic Navier-Stokes solvers. It has the remarkable property of only requiring the solution of m uncoupled deterministic problems for the construction of an m-dimensional reduced basis rather than M coupled problems of the full stochastic Galerkin approximation space, with m l M (up to one order of magnitudefor the problem at hand in this work). © 2014 Society for Industrial and Applied Mathematics.
Sharma, Ati S; Moarref, Rashad; McKeon, Beverley J; Park, Jae Sung; Graham, Michael D; Willis, Ashley P
2016-02-01
We report that many exact invariant solutions of the Navier-Stokes equations for both pipe and channel flows are well represented by just a few modes of the model of McKeon and Sharma [J. Fluid Mech. 658, 336 (2010)]. This model provides modes that act as a basis to decompose the velocity field, ordered by their amplitude of response to forcing arising from the interaction between scales. The model was originally derived from the Navier-Stokes equations to represent turbulent flows and has been used to explain coherent structure and to predict turbulent statistics. This establishes a surprising new link between the two distinct approaches to understanding turbulence.
Strong solutions for an incompressible Navier-Stokes/Allen-Cahn system with different densities
Li, Yinghua; Huang, Mingxia
2018-06-01
In this paper, we investigate a coupled Navier-Stokes/Allen-Cahn system describing a diffuse interface model for two-phase flow of viscous incompressible fluids with different densities in a bounded domain Ω \\subset R^N(N=2,3). We prove the existence and uniqueness of local strong solutions to the initial boundary value problem when the initial density function ρ _0 has a positive lower bound.
Sheng, Chunhua; Hyams, Daniel G.; Sreenivas, Kidambi; Gaither, J. Adam; Marcum, David L.; Whitfield, David L.
2000-01-01
A multiblock unstructured grid approach is presented for solving three-dimensional incompressible inviscid and viscous turbulent flows about complete configurations. The artificial compressibility form of the governing equations is solved by a node-based, finite volume implicit scheme which uses a backward Euler time discretization. Point Gauss-Seidel relaxations are used to solve the linear system of equations at each time step. This work employs a multiblock strategy to the solution procedure, which greatly improves the efficiency of the algorithm by significantly reducing the memory requirements by a factor of 5 over the single-grid algorithm while maintaining a similar convergence behavior. The numerical accuracy of solutions is assessed by comparing with the experimental data for a submarine with stem appendages and a high-lift configuration.
Convergence of a numerical method for the compressible Navier-Stokes system on general domains
Czech Academy of Sciences Publication Activity Database
Feireisl, Eduard; Karper, T.; Michálek, Martin
2016-01-01
Roč. 134, č. 4 (2016), s. 667-704 ISSN 0029-599X R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : numerical methods * Navier-Stokes system Subject RIV: BA - General Mathematics Impact factor: 2.152, year: 2016 http://link.springer.com/article/10.1007%2Fs00211-015-0786-6
Czech Academy of Sciences Publication Activity Database
Šístek, Jakub; Cirak, F.
2015-01-01
Roč. 122, 20 November (2015), s. 165-183 ISSN 0045-7930 R&D Projects: GA ČR GA14-02067S Institutional support: RVO:67985840 Keywords : Navier-Stokes * incompressible flow * Krylov subspace method s Subject RIV: BA - General Mathematics Impact factor: 1.891, year: 2015 http://www. science direct.com/ science /article/pii/S0045793015003023
Lower Bounds for Possible Singular Solutions for the Navier-Stokes and Euler Equations Revisited
Cortissoz, Jean C.; Montero, Julio A.
2018-03-01
In this paper we give optimal lower bounds for the blow-up rate of the \\dot{H}s( T^3) -norm, 1/2Navier-Stokes equations, and we also present an elementary proof for a lower bound on blow-up rate of the Sobolev norms of possible singular solutions to the Euler equations when s>5/2.
Convergence of a numerical method for the compressible Navier-Stokes system on general domains
Czech Academy of Sciences Publication Activity Database
Feireisl, Eduard; Karper, T.; Michálek, Martin
2016-01-01
Roč. 134, č. 4 (2016), s. 667-704 ISSN 0029-599X R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : numerical methods * Navier - Stokes system Subject RIV: BA - General Mathematics Impact factor: 2.152, year: 2016 http://link.springer.com/article/10.1007%2Fs00211-015-0786-6
Czech Academy of Sciences Publication Activity Database
Ciuperca, I. S.; Feireisl, Eduard; Jai, M.; Petrov, A.
2018-01-01
Roč. 28, č. 4 (2018), s. 697-732 ISSN 0218-2025 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : compressible fluids * stationary Navier-Stokes equations * thin films Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 2.860, year: 2016 https://www.worldscientific.com/doi/abs/10.1142/S0218202518500185
Augmented Lagrangian methods to solve Navier-Stokes equations for a Bingham fluid flow
International Nuclear Information System (INIS)
Boscardin, Laetitia
1999-01-01
The objective of this research thesis is to develop one or more methods for the numerical resolution of equations of movement obtained for a Bingham fluid. The resolution of Navier-Stokes equations is processed by splitting elliptic and hyperbolic operators (Galerkin transport). In this purpose, the author first studied the Stokes problem, and then addressed issues of stability and consistency of the global scheme. The variational formulation of the Stokes problem can be expressed under the form of a minimisation problem under the constraint of non linear and non differentiable functions. Then, the author proposes a discretization of the Stokes problem based on a hybrid finite element method. Then he extends the demonstrations of stability and consistency of the Galerkin-transport scheme which have been established for a Newtonian fluid, to the case of a Bingham fluid. A relaxation algorithm and a Newton-GMRES algorithm are developed to solve the problem, and their convergence is studied. To ensure this convergence, some constraints must be verified. In order to do so, a specific speed element has been developed [fr
3D unstructured mesh discontinuous finite element hydro
International Nuclear Information System (INIS)
Prasad, M.K.; Kershaw, D.S.; Shaw, M.J.
1995-01-01
The authors present detailed features of the ICF3D hydrodynamics code used for inertial fusion simulations. This code is intended to be a state-of-the-art upgrade of the well-known fluid code, LASNEX. ICF3D employs discontinuous finite elements on a discrete unstructured mesh consisting of a variety of 3D polyhedra including tetrahedra, prisms, and hexahedra. The authors discussed details of how the ROE-averaged second-order convection was applied on the discrete elements, and how the C++ coding interface has helped to simplify implementing the many physics and numerics modules within the code package. The author emphasized the virtues of object-oriented design in large scale projects such as ICF3D
Carpenter, Mark H.; Fisher, Travis C.; Nielsen, Eric J.; Frankel, Steven H.
2013-01-01
Nonlinear entropy stability and a summation-by-parts framework are used to derive provably stable, polynomial-based spectral collocation methods of arbitrary order. The new methods are closely related to discontinuous Galerkin spectral collocation methods commonly known as DGFEM, but exhibit a more general entropy stability property. Although the new schemes are applicable to a broad class of linear and nonlinear conservation laws, emphasis herein is placed on the entropy stability of the compressible Navier-Stokes equations.
Batina, John T.
1990-01-01
Improved algorithm for the solution of the time-dependent Euler equations are presented for unsteady aerodynamic analysis involving unstructured dynamic meshes. The improvements were developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux-split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves an implicit time-integration scheme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. For example, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady and unsteady flow results are presented for the NACA 0012 airfoil to demonstrate applications of the new Euler solvers. The unsteady results were obtained for the airfoil pitching harmonically about the quarter chord. The resulting instantaneous pressure distributions and lift and moment coefficients during a cycle of motion compare well with experimental data. A description of the Euler solvers is presented along with results and comparisons which assess the capability.
Modeling digital pulse waveforms by solving one-dimensional Navier-stokes equations.
Fedotov, Aleksandr A; Akulova, Anna S; Akulov, Sergey A
2016-08-01
Mathematical modeling for composition distal arterial pulse wave in the blood vessels of the upper limbs was considered. Formation of distal arterial pulse wave is represented as a composition of forward and reflected pulse waves propagating along the arterial vessels. The formal analogy between pulse waves propagation along the human arterial system and the propagation of electrical oscillations in electrical transmission lines with distributed parameters was proposed. Dependencies of pulse wave propagation along the human arterial system were obtained by solving the one-dimensional Navier-Stokes equations for a few special cases.
Note on the fast decay property of steady Navier-Stokes flows in the whole space
Czech Academy of Sciences Publication Activity Database
Nakatsuka, Tomoyuki
2018-01-01
Roč. 38, č. 2 (2018), s. 81-89 ISSN 0174-4747 Institutional support: RVO:67985840 Keywords : stationary Navier-Stokes equation * asymptotic behavior Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics https://www.degruyter.com/view/j/anly.2018.38.issue-2/anly-2017-0016/anly-2017-0016.xml
The Oberbeck-Boussinesq approximation as a singular limit of the full Navier-Stokes-Fourier system
Czech Academy of Sciences Publication Activity Database
Feireisl, Eduard; Novotný, A.
2009-01-01
Roč. 11, č. 2 (2009), s. 274-302 ISSN 1422-6928 R&D Projects: GA ČR GA201/05/0164 Institutional research plan: CEZ:AV0Z10190503 Keywords : singular limit * Navier-Stokes-Fourier system * Oberbeck -Boussinesq approximation Subject RIV: BA - General Mathematics Impact factor: 1.214, year: 2009
Parallel unstructured mesh optimisation for 3D radiation transport and fluids modelling
International Nuclear Information System (INIS)
Gorman, G.J.; Pain, Ch. C.; Oliveira, C.R.E. de; Umpleby, A.P.; Goddard, A.J.H.
2003-01-01
In this paper we describe the theory and application of a parallel mesh optimisation procedure to obtain self-adapting finite element solutions on unstructured tetrahedral grids. The optimisation procedure adapts the tetrahedral mesh to the solution of a radiation transport or fluid flow problem without sacrificing the integrity of the boundary (geometry), or internal boundaries (regions) of the domain. The objective is to obtain a mesh which has both a uniform interpolation error in any direction and the element shapes are of good quality. This is accomplished with use of a non-Euclidean (anisotropic) metric which is related to the Hessian of the solution field. Appropriate scaling of the metric enables the resolution of multi-scale phenomena as encountered in transient incompressible fluids and multigroup transport calculations. The resulting metric is used to calculate element size and shape quality. The mesh optimisation method is based on a series of mesh connectivity and node position searches of the landscape defining mesh quality which is gauged by a functional. The mesh modification thus fits the solution field(s) in an optimal manner. The parallel mesh optimisation/adaptivity procedure presented in this paper is of general applicability. We illustrate this by applying it to a transient CFD (computational fluid dynamics) problem. Incompressible flow past a cylinder at moderate Reynolds numbers is modelled to demonstrate that the mesh can follow transient flow features. (authors)
Effects of friction on forced two-dimensional Navier-Stokes turbulence.
Blackbourn, Luke A K; Tran, Chuong V
2011-10-01
Large-scale dissipation mechanisms have been routinely employed in numerical simulations of two-dimensional turbulence to absorb energy at large scales, presumably mimicking the quasisteady picture of Kraichnan in an unbounded fluid. Here, "side effects" of such a mechanism--mechanical friction--on the small-scale dynamics of forced two-dimensional Navier-Stokes turbulence are elaborated by both theoretical and numerical analysis. Given a positive friction coefficient α, viscous dissipation of enstrophy has been known to vanish in the inviscid limit ν→0. This effectively renders the scale-neutral friction the only mechanism responsible for enstrophy dissipation in that limit. The resulting dynamical picture is that the classical enstrophy inertial range becomes a dissipation range in which the dissipation of enstrophy by friction mainly occurs. For each α>0, there exists a critical viscosity ν(c), which depends on physical parameters, separating the regimes of predominant viscous and frictional dissipation of enstrophy. It is found that ν(c)=[η'(1/3)/(Ck(f)(2))]exp[-η'(1/3)/(Cα)], where η' is half the enstrophy injection rate, k(f) is the forcing wave number, and C is a nondimensional constant (the Kraichnan-Batchelor constant). The present results have important theoretical and practical implications. Apparently, mechanical friction is a poor choice in numerical attempts to address fundamental issues concerning the direct enstrophy transfer in two-dimensional Navier-Stokes turbulence. Furthermore, as relatively strong friction naturally occurs on the surfaces and at lateral boundaries of experimental fluids as well as at the interfaces of shallow layers in geophysical fluid models, the frictional effects discussed in this study are crucial in understanding the dynamics of these systems.
Boundary Layers for the Navier-Stokes Equations Linearized Around a Stationary Euler Flow
Gie, Gung-Min; Kelliher, James P.; Mazzucato, Anna L.
2018-03-01
We study the viscous boundary layer that forms at small viscosity near a rigid wall for the solution to the Navier-Stokes equations linearized around a smooth and stationary Euler flow (LNSE for short) in a smooth bounded domain Ω \\subset R^3 under no-slip boundary conditions. LNSE is supplemented with smooth initial data and smooth external forcing, assumed ill-prepared, that is, not compatible with the no-slip boundary condition. We construct an approximate solution to LNSE on the time interval [0, T], 0Math J 45(3):863-916, 1996), Xin and Yanagisawa (Commun Pure Appl Math 52(4):479-541, 1999), and Gie (Commun Math Sci 12(2):383-400, 2014).
Czech Academy of Sciences Publication Activity Database
Skalák, Zdeněk
2016-01-01
Roč. 437, č. 1 (2016), s. 474-484 ISSN 0022-247X R&D Projects: GA ČR GA14-02067S Institutional support: RVO:67985874 Keywords : Navier - Stokes equations * regularity of solutions * regularity criteria Subject RIV: BK - Fluid Dynamics Impact factor: 1.064, year: 2016
Akintunde, Akinjide; Petculescu, Andi
2014-10-01
This paper presents the results of a pilot study comparing the use of continuum and non-continuum fluid dynamics to predict infrasound attenuation in the rarefied lower thermosphere. The continuum approach is embodied by the Navier-Stokes equations, while the non-continuum method is implemented via the Burnett equations [Proc. London Math. Soc. 39, 385-430 (1935); 40, 382-435 (1936)]. In the Burnett framework, the coupling between stress tensor and heat flux affects the dispersion equation, leading to an attenuation coefficient smaller than its Navier-Stokes counterpart by amounts of order 0.1 dB/km at 0.1 Hz, 10 dB/km at 1 Hz, and 100 dB/km at 10 Hz. It has been observed that many measured thermospheric arrivals are stronger than current predictions based on continuum mechanics. In this context, the consistently smaller Burnett-based absorption is cautiously encouraging.
Energy Technology Data Exchange (ETDEWEB)
Gastaldo, L
2007-11-15
We develop in this PhD thesis a simulation tool for bubbly flows encountered in some late phases of a core-melt accident in pressurized water reactors, when the flow of molten core and vessel structures comes to chemically interact with the concrete of the containment floor. The physical modelling is based on the so-called drift-flux model, consisting of mass balance and momentum balance equations for the mixture (Navier-Stokes equations) and a mass balance equation for the gaseous phase. First, we propose a pressure correction scheme for the compressible Navier-Stokes equations based on mixed non-conforming finite elements. An ad hoc discretization of the advection operator, by a finite volume technique based on a dual mesh, ensures the stability of the velocity prediction step. A priori estimates for the velocity and the pressure yields the existence of the solution. We prove that this scheme is stable, in the sense that the discrete entropy is decreasing. For the conservation equation of the gaseous phase, we build a finite volume discretization which satisfies a discrete maximum principle. From this last property, we deduce the existence and the uniqueness of the discrete solution. Finally, on the basis of these works, a conservative and monotone scheme which is stable in the low Mach number limit, is build for the drift-flux model. This scheme enjoys, moreover, the following property: the algorithm preserves a constant pressure and velocity through moving interfaces between phases (i.e. contact discontinuities of the underlying hyperbolic system). In order to satisfy this property at the discrete level, we build an original pressure correction step which couples the mass balance equation with the transport terms of the gas mass balance equation, the remaining terms of the gas mass balance being taken into account with a splitting method. We prove the existence of a discrete solution for the pressure correction step. Numerical results are presented; they
Espejo, Elio; Winkler, Michael
2018-04-01
The interplay of chemotaxis, convection and reaction terms is studied in the particular framework of a refined model for coral broadcast spawning, consisting of three equations describing the population densities of unfertilized sperms and eggs and the concentration of a chemical released by the latter, coupled to the incompressible Navier-Stokes equations. Under mild assumptions on the initial data, global existence of classical solutions to an associated initial-boundary value problem in bounded planar domains is established. Moreover, all these solutions are shown to approach a spatially homogeneous equilibrium in the large time limit.
A note on local interior regularity of a suitable weak solution to the Navier--Stokes problem
Czech Academy of Sciences Publication Activity Database
Neustupa, Jiří
2013-01-01
Roč. 6, č. 5 (2013), s. 1391-1400 ISSN 1937-1632 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier-Stokes equations * suitable weak solution * regularity Subject RIV: BA - General Mathematics http://aimsciences.org/journals/displayArticlesnew.jsp?paperID=8344
Jacobs, C. T.; Collins, G. S.; Piggott, M. D.; Kramer, S. C.; Wilson, C. R. G.
2013-02-01
Small-scale experiments of volcanic ash particle settling in water have demonstrated that ash particles can either settle slowly and individually, or rapidly and collectively as a gravitationally unstable ash-laden plume. This has important implications for the emplacement of tephra deposits on the seabed. Numerical modelling has the potential to extend the results of laboratory experiments to larger scales and explore the conditions under which plumes may form and persist, but many existing models are computationally restricted by the fixed mesh approaches that they employ. In contrast, this paper presents a new multiphase flow model that uses an adaptive unstructured mesh approach. As a simulation progresses, the mesh is optimized to focus numerical resolution in areas important to the dynamics and decrease it where it is not needed, thereby potentially reducing computational requirements. Model verification is performed using the method of manufactured solutions, which shows the correct solution convergence rates. Model validation and application considers 2-D simulations of plume formation in a water tank which replicate published laboratory experiments. The numerically predicted settling velocities for both individual particles and plumes, as well as instability behaviour, agree well with experimental data and observations. Plume settling is clearly hindered by the presence of a salinity gradient, and its influence must therefore be taken into account when considering particles in bodies of saline water. Furthermore, individual particles settle in the laminar flow regime while plume settling is shown (by plume Reynolds numbers greater than unity) to be in the turbulent flow regime, which has a significant impact on entrainment and settling rates. Mesh adaptivity maintains solution accuracy while providing a substantial reduction in computational requirements when compared to the same simulation performed using a fixed mesh, highlighting the benefits of an
HypGrid2D. A 2-d mesh generator
Energy Technology Data Exchange (ETDEWEB)
Soerensen, N N
1998-03-01
The implementation of a hyperbolic mesh generation procedure, based on an equation for orthogonality and an equation for the cell face area is described. The method is fast, robust and gives meshes with good smoothness and orthogonality. The procedure is implemented in a program called HypGrid2D. The HypGrid2D program is capable of generating C-, O- and `H`-meshes for use in connection with the EllipSys2D Navier-Stokes solver. To illustrate the capabilities of the program, some test examples are shown. First a series of C-meshes are generated around a NACA-0012 airfoil. Secondly a series of O-meshes are generated around a NACA-65-418 airfoil. Finally `H`-meshes are generated over a Gaussian hill and a linear escarpment. (au)
A convergent numerical method for the full Navier-Stokes-Fourier system in smooth physical domains
Czech Academy of Sciences Publication Activity Database
Feireisl, Eduard; Hošek, Radim; Michálek, Martin
2016-01-01
Roč. 54, č. 5 (2016), s. 3062-3082 ISSN 0036-1429 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : Navier-Stokes-Fourier system * finite element method * finite volume method Subject RIV: BA - General Mathematics Impact factor: 1.978, year: 2016 http://epubs.siam.org/doi/abs/10.1137/15M1011809
The incompressible limit of the full Navier-Stokes-Fourier system on domains with rough boundaries
Czech Academy of Sciences Publication Activity Database
Bucur, D.; Feireisl, Eduard
2009-01-01
Roč. 10, č. 5 (2009), s. 3203-3229 ISSN 1468-1218 R&D Projects: GA AV ČR(CZ) IAA100190606; GA MŠk LC06052 Institutional research plan: CEZ:AV0Z10190503 Keywords : low Mach number * Navier-Stokes-Fourier system * rough boundary Subject RIV: BA - General Mathematics Impact factor: 2.381, year: 2009
A convergent numerical method for the full Navier-Stokes-Fourier system in smooth physical domains
Czech Academy of Sciences Publication Activity Database
Feireisl, Eduard; Hošek, Radim; Michálek, Martin
2016-01-01
Roč. 54, č. 5 (2016), s. 3062-3082 ISSN 0036-1429 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : Navier-Stokes- Fourier system * finite element method * finite volume method Subject RIV: BA - General Mathematics Impact factor: 1.978, year: 2016 http://epubs.siam.org/doi/abs/10.1137/15M1011809
DEFF Research Database (Denmark)
Yang, Yang; Kær, Søren Knudsen
2012-01-01
The flow structure of one isothermal swirling case in the Sydney swirl flame database was studied using two numerical methods. Results from the Reynolds-averaged Navier-Stokes (RANS) approach and large eddy simulation (LES) were compared with experimental measurements. The simulations were applied...
Local lubrication model for spherical particles within incompressible Navier-Stokes flows
Lambert, B.; Weynans, L.; Bergmann, M.
2018-03-01
The lubrication forces are short-range hydrodynamic interactions essential to describe suspension of the particles. Usually, they are underestimated in direct numerical simulations of particle-laden flows. In this paper, we propose a lubrication model for a coupled volume penalization method and discrete element method solver that estimates the unresolved hydrodynamic forces and torques in an incompressible Navier-Stokes flow. Corrections are made locally on the surface of the interacting particles without any assumption on the global particle shape. The numerical model has been validated against experimental data and performs as well as existing numerical models that are limited to spherical particles.
Local lubrication model for spherical particles within incompressible Navier-Stokes flows.
Lambert, B; Weynans, L; Bergmann, M
2018-03-01
The lubrication forces are short-range hydrodynamic interactions essential to describe suspension of the particles. Usually, they are underestimated in direct numerical simulations of particle-laden flows. In this paper, we propose a lubrication model for a coupled volume penalization method and discrete element method solver that estimates the unresolved hydrodynamic forces and torques in an incompressible Navier-Stokes flow. Corrections are made locally on the surface of the interacting particles without any assumption on the global particle shape. The numerical model has been validated against experimental data and performs as well as existing numerical models that are limited to spherical particles.
Lagrange–Galerkin methods for the incompressible Navier-Stokes equations: a review
Directory of Open Access Journals (Sweden)
Bermejo Rodolfo
2016-09-01
Full Text Available We review in this paper the development of Lagrange-Galerkin (LG methods to integrate the incompressible Navier-Stokes equations (NSEs for engineering applications. These methods were introduced in the computational fluid dynamics community in the early eighties of the past century, and at that time they were considered good methods for both their theoretical stability properties and the way of dealing with the nonlinear terms of the equations; however, the numerical experience gained with the application of LG methods to different problems has identified drawbacks of them, such as the calculation of specific integrals that arise in their formulation and the calculation of the ow trajectories, which somehow have hampered the applicability of LG methods. In this paper, we focus on these issues and summarize the convergence results of LG methods; furthermore, we shall briefly introduce a new stabilized LG method suitable for high Reynolds numbers.
Czech Academy of Sciences Publication Activity Database
Feireisl, Eduard; Laurençot, P.
2007-01-01
Roč. 88, - (2007), s. 325-349 ISSN 0021-7824 R&D Projects: GA ČR GA201/05/0164 Institutional research plan: CEZ:AV0Z10190503 Keywords : Navier-Stokes-Fourier- Poisson system * Smoluchowski- Poisson system * singular limit Subject RIV: BA - General Mathematics Impact factor: 1.118, year: 2007
Simulation of Rotary-Wing Near-Wake Vortex Structures Using Navier-Stokes CFD Methods
Kenwright, David; Strawn, Roger; Ahmad, Jasim; Duque, Earl; Warmbrodt, William (Technical Monitor)
1997-01-01
This paper will use high-resolution Navier-Stokes computational fluid dynamics (CFD) simulations to model the near-wake vortex roll-up behind rotor blades. The locations and strengths of the trailing vortices will be determined from newly-developed visualization and analysis software tools applied to the CFD solutions. Computational results for rotor nearwake vortices will be used to study the near-wake vortex roll up for highly-twisted tiltrotor blades. These rotor blades typically have combinations of positive and negative spanwise loading and complex vortex wake interactions. Results of the computational studies will be compared to vortex-lattice wake models that are frequently used in rotorcraft comprehensive codes. Information from these comparisons will be used to improve the rotor wake models in the Tilt-Rotor Acoustic Code (TRAC) portion of NASA's Short Haul Civil Transport program (SHCT). Accurate modeling of the rotor wake is an important part of this program and crucial to the successful design of future civil tiltrotor aircraft. The rotor wake system plays an important role in blade-vortex interaction noise, a major problem for all rotorcraft including tiltrotors.
Iterative methods for compressible Navier-Stokes and Euler equations
Energy Technology Data Exchange (ETDEWEB)
Tang, W.P.; Forsyth, P.A.
1996-12-31
This workshop will focus on methods for solution of compressible Navier-Stokes and Euler equations. In particular, attention will be focused on the interaction between the methods used to solve the non-linear algebraic equations (e.g. full Newton or first order Jacobian) and the resulting large sparse systems. Various types of block and incomplete LU factorization will be discussed, as well as stability issues, and the use of Newton-Krylov methods. These techniques will be demonstrated on a variety of model transonic and supersonic airfoil problems. Applications to industrial CFD problems will also be presented. Experience with the use of C++ for solution of large scale problems will also be discussed. The format for this workshop will be four fifteen minute talks, followed by a roundtable discussion.
Schroeder, Craig
2012-02-01
We present a method for applying semi-implicit forces on a Lagrangian mesh to an Eulerian discretization of the Navier Stokes equations in a way that produces a sparse symmetric positive definite system. The resulting method has semi-implicit and fully-coupled viscosity, pressure, and Lagrangian forces. We apply our new framework for forces on a Lagrangian mesh to the case of a surface tension force, which when treated explicitly leads to a tight time step restriction. By applying surface tension as a semi-implicit Lagrangian force, the resulting method benefits from improved stability and the ability to take larger time steps. The resulting discretization is also able to maintain parasitic currents at low levels. © 2011.
Multigrid solution of the Navier-Stokes equations at low speeds with large temperature variations
International Nuclear Information System (INIS)
Sockol, Peter M.
2003-01-01
Multigrid methods for the Navier-Stokes equations at low speeds and large temperature variations are investigated. The compressible equations with time-derivative preconditioning and preconditioned flux-difference splitting of the inviscid terms are used. Three implicit smoothers have been incorporated into a common multigrid procedure. Both full coarsening and semi-coarsening with directional fine-grid defect correction have been studied. The resulting methods have been tested on four 2D laminar problems over a range of Reynolds numbers on both uniform and highly stretched grids. Two of the three methods show efficient and robust performance over the entire range of conditions. In addition, none of the methods has any difficulty with the large temperature variations
International Nuclear Information System (INIS)
Sani, R.L.; Gresho, P.M.; Lee, R.L.
1979-01-01
The spurious pressures and acceptable velocities generated when using certain combinations of velocity and pressure approximations in a Galerkin finite element discretization of the primitive variable form of the incompressible Navier-Stokes equations are analyzed both theoretically and numerically for grids composed of quadrilateral finite elements. Schemes for obtaining usable pressure fields from the spurious numerical results are presented for certain cases
Directory of Open Access Journals (Sweden)
Jian Liu
2013-09-01
Full Text Available In this article, we consider the free boundary value problem for one-dimensional compressible bipolar Navier-Stokes-Possion (BNSP equations with density-dependent viscosities. For general initial data with finite energy and the density connecting with vacuum continuously, we prove the global existence of the weak solution. This extends the previous results for compressible NS [27] to NSP.
International Nuclear Information System (INIS)
Gastaldo, L.
2007-11-01
We develop in this PhD thesis a simulation tool for bubbly flows encountered in some late phases of a core-melt accident in pressurized water reactors, when the flow of molten core and vessel structures comes to chemically interact with the concrete of the containment floor. The physical modelling is based on the so-called drift-flux model, consisting of mass balance and momentum balance equations for the mixture (Navier-Stokes equations) and a mass balance equation for the gaseous phase. First, we propose a pressure correction scheme for the compressible Navier-Stokes equations based on mixed non-conforming finite elements. An ad hoc discretization of the advection operator, by a finite volume technique based on a dual mesh, ensures the stability of the velocity prediction step. A priori estimates for the velocity and the pressure yields the existence of the solution. We prove that this scheme is stable, in the sense that the discrete entropy is decreasing. For the conservation equation of the gaseous phase, we build a finite volume discretization which satisfies a discrete maximum principle. From this last property, we deduce the existence and the uniqueness of the discrete solution. Finally, on the basis of these works, a conservative and monotone scheme which is stable in the low Mach number limit, is build for the drift-flux model. This scheme enjoys, moreover, the following property: the algorithm preserves a constant pressure and velocity through moving interfaces between phases (i.e. contact discontinuities of the underlying hyperbolic system). In order to satisfy this property at the discrete level, we build an original pressure correction step which couples the mass balance equation with the transport terms of the gas mass balance equation, the remaining terms of the gas mass balance being taken into account with a splitting method. We prove the existence of a discrete solution for the pressure correction step. Numerical results are presented; they
Veldman, A.E.P.
1973-01-01
A numerical method is presented for the solution of the Navier-Stokes equations for flow past a paraboloid of revolution. The flow field has been computed for a large range of Reynolds numbers. Results are presented for the skinfriction and the pressure together with their respective drag
Paardekooper, S.-J.
2017-08-01
We present a new method for numerical hydrodynamics which uses a multidimensional generalization of the Roe solver and operates on an unstructured triangular mesh. The main advantage over traditional methods based on Riemann solvers, which commonly use one-dimensional flux estimates as building blocks for a multidimensional integration, is its inherently multidimensional nature, and as a consequence its ability to recognize multidimensional stationary states that are not hydrostatic. A second novelty is the focus on graphics processing units (GPUs). By tailoring the algorithms specifically to GPUs, we are able to get speedups of 100-250 compared to a desktop machine. We compare the multidimensional upwind scheme to a traditional, dimensionally split implementation of the Roe solver on several test problems, and we find that the new method significantly outperforms the Roe solver in almost all cases. This comes with increased computational costs per time-step, which makes the new method approximately a factor of 2 slower than a dimensionally split scheme acting on a structured grid.
Conformal Field Theory as Microscopic Dynamics of Incompressible Euler and Navier-Stokes Equations
International Nuclear Information System (INIS)
Fouxon, Itzhak; Oz, Yaron
2008-01-01
We consider the hydrodynamics of relativistic conformal field theories at finite temperature. We show that the limit of slow motions of the ideal hydrodynamics leads to the nonrelativistic incompressible Euler equation. For viscous hydrodynamics we show that the limit of slow motions leads to the nonrelativistic incompressible Navier-Stokes equation. We explain the physical reasons for the reduction and discuss the implications. We propose that conformal field theories provide a fundamental microscopic viewpoint of the equations and the dynamics governed by them
Conformal field theory as microscopic dynamics of incompressible Euler and Navier-Stokes equations.
Fouxon, Itzhak; Oz, Yaron
2008-12-31
We consider the hydrodynamics of relativistic conformal field theories at finite temperature. We show that the limit of slow motions of the ideal hydrodynamics leads to the nonrelativistic incompressible Euler equation. For viscous hydrodynamics we show that the limit of slow motions leads to the nonrelativistic incompressible Navier-Stokes equation. We explain the physical reasons for the reduction and discuss the implications. We propose that conformal field theories provide a fundamental microscopic viewpoint of the equations and the dynamics governed by them.
Level Set Projection Method for Incompressible Navier-Stokes on Arbitrary Boundaries
Williams-Rioux, Bertrand
2012-01-12
Second order level set projection method for incompressible Navier-Stokes equations is proposed to solve flow around arbitrary geometries. We used rectilinear grid with collocated cell centered velocity and pressure. An explicit Godunov procedure is used to address the nonlinear advection terms, and an implicit Crank-Nicholson method to update viscous effects. An approximate pressure projection is implemented at the end of the time stepping using multigrid as a conventional fast iterative method. The level set method developed by Osher and Sethian [17] is implemented to address real momentum and pressure boundary conditions by the advection of a distance function, as proposed by Aslam [3]. Numerical results for the Strouhal number and drag coefficients validated the model with good accuracy for flow over a cylinder in the parallel shedding regime (47 < Re < 180). Simulations for an array of cylinders and an oscillating cylinder were performed, with the latter demonstrating our methods ability to handle dynamic boundary conditions.
A Finite Element Method for Simulation of Compressible Cavitating Flows
Shams, Ehsan; Yang, Fan; Zhang, Yu; Sahni, Onkar; Shephard, Mark; Oberai, Assad
2016-11-01
This work focuses on a novel approach for finite element simulations of multi-phase flows which involve evolving interface with phase change. Modeling problems, such as cavitation, requires addressing multiple challenges, including compressibility of the vapor phase, interface physics caused by mass, momentum and energy fluxes. We have developed a mathematically consistent and robust computational approach to address these problems. We use stabilized finite element methods on unstructured meshes to solve for the compressible Navier-Stokes equations. Arbitrary Lagrangian-Eulerian formulation is used to handle the interface motions. Our method uses a mesh adaptation strategy to preserve the quality of the volumetric mesh, while the interface mesh moves along with the interface. The interface jump conditions are accurately represented using a discontinuous Galerkin method on the conservation laws. Condensation and evaporation rates at the interface are thermodynamically modeled to determine the interface velocity. We will present initial results on bubble cavitation the behavior of an attached cavitation zone in a separated boundary layer. We acknowledge the support from Army Research Office (ARO) under ARO Grant W911NF-14-1-0301.
Solving the incompressible surface Navier-Stokes equation by surface finite elements
Reuther, Sebastian; Voigt, Axel
2018-01-01
We consider a numerical approach for the incompressible surface Navier-Stokes equation on surfaces with arbitrary genus g (S ) . The approach is based on a reformulation of the equation in Cartesian coordinates of the embedding R3, penalization of the normal component, a Chorin projection method, and discretization in space by surface finite elements for each component. The approach thus requires only standard ingredients which most finite element implementations can offer. We compare computational results with discrete exterior calculus simulations on a torus and demonstrate the interplay of the flow field with the topology by showing realizations of the Poincaré-Hopf theorem on n-tori.
An Equal-Order DG Method for the Incompressible Navier-Stokes Equations
Cockburn, Bernardo
2008-12-20
We introduce and analyze a discontinuous Galerkin method for the incompressible Navier-Stokes equations that is based on finite element spaces of the same polynomial order for the approximation of the velocity and the pressure. Stability of this equal-order approach is ensured by a pressure stabilization term. A simple element-by-element post-processing procedure is used to provide globally divergence-free velocity approximations. For small data, we prove the existence and uniqueness of discrete solutions and carry out an error analysis of the method. A series of numerical results are presented that validate our theoretical findings. © 2008 Springer Science+Business Media, LLC.
Towards a Navier Stokes-Darcy Upscaling Based on Permeability Tensor Computation
Lieb, M.
2012-06-02
The micro scale simulation of CO2 sequestration involves complex, porous-like geometries. For the generation of such geometries, we present two approaches: In 2D, we construct a fractured domain by channel networks. In 3D, we approximate sand grain-like scenarios by dense sphere packings. The flow through these structures is simulated with the incompressible Navier-Stokes solver of the PDE framework Peano. Using an upscaling scheme, the results of the micro scale are used as input data for a Darcy solver on the coarse scales. The coupling concept and the scenario generators are presented together with first simulation results showing the validity of the approach.
Towards a Navier Stokes-Darcy Upscaling Based on Permeability Tensor Computation
Lieb, M.; Neckel, T.; Bungartz, H.-J.; Sun, Shuyu
2012-01-01
The micro scale simulation of CO2 sequestration involves complex, porous-like geometries. For the generation of such geometries, we present two approaches: In 2D, we construct a fractured domain by channel networks. In 3D, we approximate sand grain-like scenarios by dense sphere packings. The flow through these structures is simulated with the incompressible Navier-Stokes solver of the PDE framework Peano. Using an upscaling scheme, the results of the micro scale are used as input data for a Darcy solver on the coarse scales. The coupling concept and the scenario generators are presented together with first simulation results showing the validity of the approach.
Fehn, Niklas; Wall, Wolfgang A.; Kronbichler, Martin
2017-12-01
The present paper deals with the numerical solution of the incompressible Navier-Stokes equations using high-order discontinuous Galerkin (DG) methods for discretization in space. For DG methods applied to the dual splitting projection method, instabilities have recently been reported that occur for small time step sizes. Since the critical time step size depends on the viscosity and the spatial resolution, these instabilities limit the robustness of the Navier-Stokes solver in case of complex engineering applications characterized by coarse spatial resolutions and small viscosities. By means of numerical investigation we give evidence that these instabilities are related to the discontinuous Galerkin formulation of the velocity divergence term and the pressure gradient term that couple velocity and pressure. Integration by parts of these terms with a suitable definition of boundary conditions is required in order to obtain a stable and robust method. Since the intermediate velocity field does not fulfill the boundary conditions prescribed for the velocity, a consistent boundary condition is derived from the convective step of the dual splitting scheme to ensure high-order accuracy with respect to the temporal discretization. This new formulation is stable in the limit of small time steps for both equal-order and mixed-order polynomial approximations. Although the dual splitting scheme itself includes inf-sup stabilizing contributions, we demonstrate that spurious pressure oscillations appear for equal-order polynomials and small time steps highlighting the necessity to consider inf-sup stability explicitly.
On lower bounds for possible blow-up solutions to the periodic Navier-Stokes equation
International Nuclear Information System (INIS)
Cortissoz, Jean C.; Montero, Julio A.; Pinilla, Carlos E.
2014-01-01
We show a new lower bound on the H .3/2 (T 3 ) norm of a possible blow-up solution to the Navier-Stokes equation, and also comment on the extension of this result to the whole space. This estimate can be seen as a natural limiting result for Leray's blow-up estimates in L p (R 3 ), 3 .5/2 (T 3 ), and give the corresponding extension to the case of the whole space
Euler and Navier endash Stokes limits of the Uehling endash Uhlenbeck quantum kinetic equations
International Nuclear Information System (INIS)
Arlotti, L.; Lachowicz, M.
1997-01-01
The Uehling endash Uhlenbeck evolution equations for gases of identical quantum particles either fermions or bosons, in the case in which the collision kernel does not depend on the distribution function, are considered. The existence of solutions and their asymptotic relations with solutions of the hydrodynamic equations both at the level of the Euler system and at the level of the Navier endash Stokes system are proved. copyright 1997 American Institute of Physics
Implementation of an Euler/Navier-Stokes finite element algorithm on the Connection Machine
International Nuclear Information System (INIS)
Shapiro, R.A.
1991-01-01
Massively parallel computers such as the Connection Machine (CM-2) have the potential to reduce significantly the computational cost for large problems of interest to the aerospace community. This paper examines the applicability of the CM-2 to an explicit, time-marching finite element solution method for the Euler and Navier-Stokes equations. The CM-2 architecture and the CM FORTRAN language are introduced. The paper points out some of the pitfalls involved in putting this code on the CM-2, with emphasis on interprocessor communications issues. The use of the FastGraph communication compiler and grid renumbering to reduce communication costs is discussed. Performance comparisons which indicate the approximate equivalence of a uniprocessor Cray and 1/8 of a CM-2 (8192 processors) for some typical problems are presented. 8 refs
Stream function-vorticity finite elements and the resolution of the Navier-Stokes equations
International Nuclear Information System (INIS)
Almeida, R.C.C. de.
1987-07-01
A stream function-vorticity finite element formulation for the solution of the Navier-Stokes equations is proposed. The present work shows a procedure to solve the problem posed by the no-slip conditions on solid frontiers which can also be applied to flow problems in a multi-connected domain. Moreover, a methodology to solve the pressure is developed using the stream function-vorticity approximate solution. Numerical experiments were conducted for some steady and unsteady problems and the performance of the proposed methods is discussed. (author) [pt
Study of blade-tower interaction using a 2D Navier-Stokes solver
Energy Technology Data Exchange (ETDEWEB)
Bertagnolio, F [Risoe National Lab., Wind Energy and Atmospheric Physics Dept., Roskilde (Denmark)
1999-03-01
The aim of this work is to model and study the dynamic interaction of the fluid flow with the structure which occurs when the blades of a wind turbine are passing in front of (or possibly behind) the tower. In order to capture the whole complexity of this phenomenon, the full unsteady Navier-Stokes equations for an incompressible fluid are used as a model. A new computational technique is described. For the sake of simplicity, we restrict ourselves to two-dimensional cases. The present methodology is illustrated by the computation of a wind turbine-like configuration in a periodic domain. (au)
On a modified form of navier-stokes equations for three-dimensional flows.
Venetis, J
2015-01-01
A rephrased form of Navier-Stokes equations is performed for incompressible, three-dimensional, unsteady flows according to Eulerian formalism for the fluid motion. In particular, we propose a geometrical method for the elimination of the nonlinear terms of these fundamental equations, which are expressed in true vector form, and finally arrive at an equivalent system of three semilinear first order PDEs, which hold for a three-dimensional rectangular Cartesian coordinate system. Next, we present the related variational formulation of these modified equations as well as a general type of weak solutions which mainly concern Sobolev spaces.
Navier-Stokes hydrodynamics of thermal collapse in a freely cooling granular gas.
Kolvin, Itamar; Livne, Eli; Meerson, Baruch
2010-08-01
We show that, in dimension higher than one, heat diffusion and viscosity cannot arrest thermal collapse in a freely evolving dilute granular gas, even in the absence of gravity. Thermal collapse involves a finite-time blowup of the gas density. It was predicted earlier in ideal, Euler hydrodynamics of dilute granular gases in the absence of gravity, and in nonideal, Navier-Stokes granular hydrodynamics in the presence of gravity. We determine, analytically and numerically, the dynamic scaling laws that characterize the gas flow close to collapse. We also investigate bifurcations of a freely evolving dilute granular gas in circular and wedge-shaped containers. Our results imply that, in general, thermal collapse can only be arrested when the gas density becomes comparable with the close-packing density of grains. This provides a natural explanation to the formation of densely packed clusters of particles in a variety of initially dilute granular flows.
Boscheri, Walter; Dumbser, Michael
2014-10-01
In this paper we present a new family of high order accurate Arbitrary-Lagrangian-Eulerian (ALE) one-step ADER-WENO finite volume schemes for the solution of nonlinear systems of conservative and non-conservative hyperbolic partial differential equations with stiff source terms on moving tetrahedral meshes in three space dimensions. A WENO reconstruction technique is used to achieve high order of accuracy in space, while an element-local space-time Discontinuous Galerkin finite element predictor on moving curved meshes is used to obtain a high order accurate one-step time discretization. Within the space-time predictor the physical element is mapped onto a reference element using a high order isoparametric approach, where the space-time basis and test functions are given by the Lagrange interpolation polynomials passing through a predefined set of space-time nodes. Since our algorithm is cell-centered, the final mesh motion is computed by using a suitable node solver algorithm. A rezoning step as well as a flattener strategy are used in some of the test problems to avoid mesh tangling or excessive element deformations that may occur when the computation involves strong shocks or shear waves. The ALE algorithm presented in this article belongs to the so-called direct ALE methods because the final Lagrangian finite volume scheme is based directly on a space-time conservation formulation of the governing PDE system, with the rezoned geometry taken already into account during the computation of the fluxes. We apply our new high order unstructured ALE schemes to the 3D Euler equations of compressible gas dynamics, for which a set of classical numerical test problems has been solved and for which convergence rates up to sixth order of accuracy in space and time have been obtained. We furthermore consider the equations of classical ideal magnetohydrodynamics (MHD) as well as the non-conservative seven-equation Baer-Nunziato model of compressible multi-phase flows with
Coupling Navier-stokes and Cahn-hilliard Equations in a Two-dimensional Annular flow Configuration
Vignal, Philippe
2015-06-01
In this work, we present a novel isogeometric analysis discretization for the Navier-Stokes- Cahn-Hilliard equation, which uses divergence-conforming spaces. Basis functions generated with this method can have higher-order continuity, and allow to directly discretize the higher- order operators present in the equation. The discretization is implemented in PetIGA-MF, a high-performance framework for discrete differential forms. We present solutions in a two- dimensional annulus, and model spinodal decomposition under shear flow.
Navier-Stokes equations an introduction with applications
Łukaszewicz, Grzegorz
2016-01-01
This volume is devoted to the study of the Navier–Stokes equations, providing a comprehensive reference for a range of applications: from students to engineers and mathematicians involved in research on fluid mechanics, dynamical systems, and mathematical modeling. Equipped with only a basic knowledge of calculus, functional analysis, and partial differential equations, the reader is introduced to the concept and applications of the Navier–Stokes equations through a series of fully self-contained chapters. Including lively illustrations that complement and elucidate the text, and a collection of exercises at the end of each chapter, this book is an indispensable, accessible, classroom-tested tool for teaching and understanding the Navier–Stokes equations. Incompressible Navier–Stokes equations describe the dynamic motion (flow) of incompressible fluid, the unknowns being the velocity and pressure as functions of location (space) and time variables. A solution to these equations predicts the behavior o...
Czech Academy of Sciences Publication Activity Database
Donatelli, D.; Feireisl, Eduard; Novotný, A.
2010-01-01
Roč. 13, č. 4 (2010), s. 783-798 ISSN 1531-3492 R&D Projects: GA MŠk LC06052; GA ČR GA201/08/0315 Institutional research plan: CEZ:AV0Z10190503 Keywords : Navier-Stokes equations * singular limits * low Mach number * compressible fluids * unbounded domains Subject RIV: BA - General Mathematics Impact factor: 0.874, year: 2010 http://www.aimsciences.org/journals/displayArticles.jsp?paperID=4976
National Research Council Canada - National Science Library
Edge, Harris
1999-01-01
...), computational fluid dynamics (CFD) 6 project. Under the project, a proven zonal Navier-Stokes solver was rewritten for scalable parallel performance on both shared memory and distributed memory high performance computers...
A GPU-based incompressible Navier-Stokes solver on moving overset grids
Chandar, Dominic D. J.; Sitaraman, Jayanarayanan; Mavriplis, Dimitri J.
2013-07-01
In pursuit of obtaining high fidelity solutions to the fluid flow equations in a short span of time, graphics processing units (GPUs) which were originally intended for gaming applications are currently being used to accelerate computational fluid dynamics (CFD) codes. With a high peak throughput of about 1 TFLOPS on a PC, GPUs seem to be favourable for many high-resolution computations. One such computation that involves a lot of number crunching is computing time accurate flow solutions past moving bodies. The aim of the present paper is thus to discuss the development of a flow solver on unstructured and overset grids and its implementation on GPUs. In its present form, the flow solver solves the incompressible fluid flow equations on unstructured/hybrid/overset grids using a fully implicit projection method. The resulting discretised equations are solved using a matrix-free Krylov solver using several GPU kernels such as gradient, Laplacian and reduction. Some of the simple arithmetic vector calculations are implemented using the CU++: An Object Oriented Framework for Computational Fluid Dynamics Applications using Graphics Processing Units, Journal of Supercomputing, 2013, doi:10.1007/s11227-013-0985-9 approach where GPU kernels are automatically generated at compile time. Results are presented for two- and three-dimensional computations on static and moving grids.
A composite velocity procedure for the compressible Navier-Stokes equations
Khosla, P. K.; Rubin, S. G.
1982-01-01
A new boundary-layer relaxation procedure is presented. In the spirit of the theory of matched asymptotic expansions, a multiplicative composite of the appropriate velocity representations for the inviscid and viscous regions is prescribed. The resulting equations are structured so that far from the surface of the body the momentum equations lead to the Bernoulli relation for the pressure, while the continuity equation reduces to the familiar compressible potential equation. Close to the body surface, the governing equations and solution techniques are characteristic of those describing interacting boundary-layers; although, the full Navier-Stokes equations are considered here. Laminar flow calculations for the subsonic flow over an axisymmetric boattail simulator geometry are presented for a variety of Reynolds and Mach numbers. A strongly implicit solution method is applied for the coupled velocity components.
Quantification of topological changes of vorticity contours in two-dimensional Navier-Stokes flow.
Ohkitani, Koji; Al Sulti, Fayeza
2010-06-01
A characterization of reconnection of vorticity contours is made by direct numerical simulations of the two-dimensional Navier-Stokes flow at a relatively low Reynolds number. We identify all the critical points of the vorticity field and classify them by solving an eigenvalue problem of its Hessian matrix on the basis of critical-point theory. The numbers of hyperbolic (saddles) and elliptic (minima and maxima) points are confirmed to satisfy Euler's index theorem numerically. Time evolution of these indices is studied for a simple initial condition. Generally speaking, we have found that the indices are found to decrease in number with time. This result is discussed in connection with related works on streamline topology, in particular, the relationship between stagnation points and the dissipation. Associated elementary procedures in physical space, the merging of vortices, are studied in detail for a number of snapshots. A similar analysis is also done using the stream function.
Guermond, Jean-Luc; Minev, Peter D.; Salgado, Abner J.
2012-01-01
We provide a convergence analysis for a new fractional timestepping technique for the incompressible Navier-Stokes equations based on direction splitting. This new technique is of linear complexity, unconditionally stable and convergent, and suitable for massive parallelization. © 2012 American Mathematical Society.
Hydrodynamics beyond Navier-Stokes: the slip flow model.
Yudistiawan, Wahyu P; Ansumali, Santosh; Karlin, Iliya V
2008-07-01
Recently, analytical solutions for the nonlinear Couette flow demonstrated the relevance of the lattice Boltzmann (LB) models to hydrodynamics beyond the continuum limit [S. Ansumali, Phys. Rev. Lett. 98, 124502 (2007)]. In this paper, we present a systematic study of the simplest LB kinetic equation-the nine-bit model in two dimensions--in order to quantify it as a slip flow approximation. Details of the aforementioned analytical solution are presented, and results are extended to include a general shear- and force-driven unidirectional flow in confined geometry. Exact solutions for the velocity, as well as for pertinent higher-order moments of the distribution functions, are obtained in both Couette and Poiseuille steady-state flows for all values of rarefaction parameter (Knudsen number). Results are compared with the slip flow solution by Cercignani, and a good quantitative agreement is found for both flow situations. Thus, the standard nine-bit LB model is characterized as a valid and self-consistent slip flow model for simulations beyond the Navier-Stokes approximation.
Disentangling the triadic interactions in Navier-Stokes equations.
Sahoo, Ganapati; Biferale, Luca
2015-10-01
We study the role of helicity in the dynamics of energy transfer in a modified version of the Navier-Stokes equations with explicit breaking of the mirror symmetry. We select different set of triads participating in the dynamics on the basis of their helicity content. In particular, we remove the negative helically polarized Fourier modes at all wave numbers except for those falling on a localized shell of wave number, |k| ~ k(m). Changing k(m) to be above or below the forcing scale, k(f), we are able to assess the energy transfer of triads belonging to different interaction classes. We observe that when the negative helical modes are present only at a wave number smaller than the forced wave numbers, an inverse energy cascade develops with an accumulation of energy on a stationary helical condensate. Vice versa, when negative helical modes are present only at a wave number larger than the forced wave numbers, a transition from backward to forward energy transfer is observed in the regime when the minority modes become energetic enough.
Existence and Stability of Spatial Plane Waves for the Incompressible Navier-Stokes in R^3
Correia, Simão; Figueira, Mário
2018-03-01
We consider the three-dimensional incompressible Navier-Stokes equation on the whole space. We observe that this system admits a L^∞ family of global spatial plane wave solutions, which are connected with the two-dimensional equation. We then proceed to prove local well-posedness over a space which includes L^3(R^3) and these solutions. Finally, we prove L^3-stability of spatial plane waves, with no condition on their size.
Angelidis, Dionysios; Chawdhary, Saurabh; Sotiropoulos, Fotis
2016-11-01
A novel numerical method is developed for solving the 3D, unsteady, incompressible Navier-Stokes equations on locally refined fully unstructured Cartesian grids in domains with arbitrarily complex immersed boundaries. Owing to the utilization of the fractional step method on an unstructured Cartesian hybrid staggered/non-staggered grid layout, flux mismatch and pressure discontinuity issues are avoided and the divergence free constraint is inherently satisfied to machine zero. Auxiliary/hanging nodes are used to facilitate the discretization of the governing equations. The second-order accuracy of the solver is ensured by using multi-dimension Lagrange interpolation operators and appropriate differencing schemes at the interface of regions with different levels of refinement. The sharp interface immersed boundary method is augmented with local near-boundary refinement to handle arbitrarily complex boundaries. The discrete momentum equation is solved with the matrix free Newton-Krylov method and the Krylov-subspace method is employed to solve the Poisson equation. The second-order accuracy of the proposed method on unstructured Cartesian grids is demonstrated by solving the Poisson equation with a known analytical solution. A number of three-dimensional laminar flow simulations of increasing complexity illustrate the ability of the method to handle flows across a range of Reynolds numbers and flow regimes. Laminar steady and unsteady flows past a sphere and the oblique vortex shedding from a circular cylinder mounted between two end walls demonstrate the accuracy, the efficiency and the smooth transition of scales and coherent structures across refinement levels. Large-eddy simulation (LES) past a miniature wind turbine rotor, parameterized using the actuator line approach, indicates the ability of the fully unstructured solver to simulate complex turbulent flows. Finally, a geometry resolving LES of turbulent flow past a complete hydrokinetic turbine illustrates
Bhalla, Amneet Pal Singh; Johansen, Hans; Graves, Dan; Martin, Dan; Colella, Phillip; Applied Numerical Algorithms Group Team
2017-11-01
We present a consistent cell-averaged discretization for incompressible Navier-Stokes equations on complex domains using embedded boundaries. The embedded boundary is allowed to freely cut the locally-refined background Cartesian grid. Implicit-function representation is used for the embedded boundary, which allows us to convert the required geometric moments in the Taylor series expansion (upto arbitrary order) of polynomials into an algebraic problem in lower dimensions. The computed geometric moments are then used to construct stencils for various operators like the Laplacian, divergence, gradient, etc., by solving a least-squares system locally. We also construct the inter-level data-transfer operators like prolongation and restriction for multi grid solvers using the same least-squares system approach. This allows us to retain high-order of accuracy near coarse-fine interface and near embedded boundaries. Canonical problems like Taylor-Green vortex flow and flow past bluff bodies will be presented to demonstrate the proposed method. U.S. Department of Energy, Office of Science, ASCR (Award Number DE-AC02-05CH11231).
Arteaga, Santiago Egido
1998-12-01
The steady-state Navier-Stokes equations are of considerable interest because they are used to model numerous common physical phenomena. The applications encountered in practice often involve small viscosities and complicated domain geometries, and they result in challenging problems in spite of the vast attention that has been dedicated to them. In this thesis we examine methods for computing the numerical solution of the primitive variable formulation of the incompressible equations on distributed memory parallel computers. We use the Galerkin method to discretize the differential equations, although most results are stated so that they apply also to stabilized methods. We also reformulate some classical results in a single framework and discuss some issues frequently dismissed in the literature, such as the implementation of pressure space basis and non- homogeneous boundary values. We consider three nonlinear methods: Newton's method, Oseen's (or Picard) iteration, and sequences of Stokes problems. All these iterative nonlinear methods require solving a linear system at every step. Newton's method has quadratic convergence while that of the others is only linear; however, we obtain theoretical bounds showing that Oseen's iteration is more robust, and we confirm it experimentally. In addition, although Oseen's iteration usually requires more iterations than Newton's method, the linear systems it generates tend to be simpler and its overall costs (in CPU time) are lower. The Stokes problems result in linear systems which are easier to solve, but its convergence is much slower, so that it is competitive only for large viscosities. Inexact versions of these methods are studied, and we explain why the best timings are obtained using relatively modest error tolerances in solving the corresponding linear systems. We also present a new damping optimization strategy based on the quadratic nature of the Navier-Stokes equations, which improves the robustness of all the
Cappelli, Daniele; Mansour, Nagi N.
2012-01-01
Separation can be seen in most aerodynamic flows, but accurate prediction of separated flows is still a challenging problem for computational fluid dynamics (CFD) tools. The behavior of several Reynolds Averaged Navier-Stokes (RANS) models in predicting the separated ow over a wall-mounted hump is studied. The strengths and weaknesses of the most popular RANS models (Spalart-Allmaras, k-epsilon, k-omega, k-omega-SST) are evaluated using the open source software OpenFOAM. The hump ow modeled in this work has been documented in the 2004 CFD Validation Workshop on Synthetic Jets and Turbulent Separation Control. Only the baseline case is treated; the slot flow control cases are not considered in this paper. Particular attention is given to predicting the size of the recirculation bubble, the position of the reattachment point, and the velocity profiles downstream of the hump.
International Nuclear Information System (INIS)
Boergers, C.; Peskin, C.S.
1987-01-01
In the Lagrangian fractional step method introduced in this paper, the fluid velocity and pressure are defined on a collection of N fluid markers. At each time step, these markers are used to generate a Voronoi diagram, and this diagram is used to construct finite-difference operators corresponding to the divergence, gradient, and Laplacian. The splitting of the Navier--Stokes equations leads to discrete Helmholtz and Poisson problems, which we solve using a two-grid method. The nonlinear convection terms are modeled simply by the displacement of the fluid markers. We have implemented this method on a periodic domain in the plane. We describe an efficient algorithm for the numerical construction of periodic Voronoi diagrams, and we report on numerical results which indicate the the fractional step method is convergent of first order. The overall work per time step is proportional to N log N. copyright 1987 Academic Press, Inc
The Navier-Stokes equations an elementary functional analytic approach
Sohr, Hermann
2001-01-01
The primary objective of this monograph is to develop an elementary and self contained approach to the mathematical theory of a viscous incompressible fluid in a domain 0 of the Euclidean space ]Rn, described by the equations of Navier Stokes. The book is mainly directed to students familiar with basic functional analytic tools in Hilbert and Banach spaces. However, for readers' convenience, in the first two chapters we collect without proof some fundamental properties of Sobolev spaces, distributions, operators, etc. Another important objective is to formulate the theory for a completely general domain O. In particular, the theory applies to arbitrary unbounded, non-smooth domains. For this reason, in the nonlinear case, we have to restrict ourselves to space dimensions n = 2,3 that are also most significant from the physical point of view. For mathematical generality, we will develop the lin earized theory for all n 2 2. Although the functional-analytic approach developed here is, in principle, known ...
The Navier-Stokes equations an elementary functional analytic approach
Sohr, Hermann
2001-01-01
The primary objective of this monograph is to develop an elementary and self-contained approach to the mathematical theory of a viscous, incompressible fluid in a domain of the Euclidean space, described by the equations of Navier-Stokes. Moreover, the theory is presented for completely general domains, in particular, for arbitrary unbounded, nonsmooth domains. Therefore, restriction was necessary to space dimensions two and three, which are also the most significant from a physical point of view. For mathematical generality, however, the linearized theory is expounded for general dimensions higher than one. Although the functional analytic approach developed here is, in principle, known to specialists, the present book fills a gap in the literature providing a systematic treatment of a subject that has been documented until now only in fragments. The book is mainly directed to students familiar with basic tools in Hilbert and Banach spaces. However, for the readers’ convenience, some fundamental properties...
An Arbitrary Lagrangian-Eulerian Discretization of MHD on 3D Unstructured Grids
Energy Technology Data Exchange (ETDEWEB)
Rieben, R N; White, D A; Wallin, B K; Solberg, J M
2006-06-12
We present an arbitrary Lagrangian-Eulerian (ALE) discretization of the equations of resistive magnetohydrodynamics (MHD) on unstructured hexahedral grids. The method is formulated using an operator-split approach with three distinct phases: electromagnetic diffusion, Lagrangian motion, and Eulerian advection. The resistive magnetic dynamo equation is discretized using a compatible mixed finite element method with a 2nd order accurate implicit time differencing scheme which preserves the divergence-free nature of the magnetic field. At each discrete time step, electromagnetic force and heat terms are calculated and coupled to the hydrodynamic equations to compute the Lagrangian motion of the conducting materials. By virtue of the compatible discretization method used, the invariants of Lagrangian MHD motion are preserved in a discrete sense. When the Lagrangian motion of the mesh causes significant distortion, that distortion is corrected with a relaxation of the mesh, followed by a 2nd order monotonic remap of the electromagnetic state variables. The remap is equivalent to Eulerian advection of the magnetic flux density with a fictitious mesh relaxation velocity. The magnetic advection is performed using a novel variant of constrained transport (CT) that is valid for unstructured hexahedral grids with arbitrary mesh velocities. The advection method maintains the divergence free nature of the magnetic field and is second order accurate in regions where the solution is sufficiently smooth. For regions in which the magnetic field is discontinuous (e.g. MHD shocks) the method is limited using a novel variant of algebraic flux correction (AFC) which is local extremum diminishing (LED) and divergence preserving. Finally, we verify each stage of the discretization via a set of numerical experiments.
Yang, Qixiang; Yang, Haibo
2018-04-01
For fractional Navier-Stokes equations and critical initial spaces X, one used to establish the well-posedness in the solution space which is contained in C (R+ , X). In this paper, for heat flow, we apply parameter Meyer wavelets to introduce Y spaces Y m , β where Y m , β is not contained in C (R+, B˙∞ 1 - 2 β , ∞). Consequently, for 1/2 global well-posedness of fractional Navier-Stokes equations with small initial data in all the critical oscillation spaces. The critical oscillation spaces may be any Besov-Morrey spaces (B˙p,q γ1 ,γ2 (Rn)) n or any Triebel-Lizorkin-Morrey spaces (F˙p,q γ1 ,γ2 (Rn)) n where 1 ≤ p , q ≤ ∞ , 0 ≤γ2 ≤ n/p, γ1 -γ2 = 1 - 2 β. These critical spaces include many known spaces. For example, Besov spaces, Sobolev spaces, Bloch spaces, Q-spaces, Morrey spaces and Triebel-Lizorkin spaces etc.
Entropic lattice Boltzmann representations required to recover Navier-Stokes flows.
Keating, Brian; Vahala, George; Yepez, Jeffrey; Soe, Min; Vahala, Linda
2007-03-01
There are two disparate formulations of the entropic lattice Boltzmann scheme: one of these theories revolves around the analog of the discrete Boltzmann H function of standard extensive statistical mechanics, while the other revolves around the nonextensive Tsallis entropy. It is shown here that it is the nonenforcement of the pressure tensor moment constraints that lead to extremizations of entropy resulting in Tsallis-like forms. However, with the imposition of the pressure tensor moment constraint, as is fundamentally necessary for the recovery of the Navier-Stokes equations, it is proved that the entropy function must be of the discrete Boltzmann form. Three-dimensional simulations are performed which illustrate some of the differences between standard lattice Boltzmann and entropic lattice Boltzmann schemes, as well as the role played by the number of phase-space velocities used in the discretization.
Jurcisinová, E; Jurcisin, M; Remecký, R
2009-10-01
The influence of weak uniaxial small-scale anisotropy on the stability of the scaling regime and on the anomalous scaling of the single-time structure functions of a passive scalar advected by the velocity field governed by the stochastic Navier-Stokes equation is investigated by the field theoretic renormalization group and operator-product expansion within one-loop approximation of a perturbation theory. The explicit analytical expressions for coordinates of the corresponding fixed point of the renormalization-group equations as functions of anisotropy parameters are found, the stability of the three-dimensional Kolmogorov-like scaling regime is demonstrated, and the dependence of the borderline dimension d(c) is an element of (2,3] between stable and unstable scaling regimes is found as a function of the anisotropy parameters. The dependence of the turbulent Prandtl number on the anisotropy parameters is also briefly discussed. The influence of weak small-scale anisotropy on the anomalous scaling of the structure functions of a passive scalar field is studied by the operator-product expansion and their explicit dependence on the anisotropy parameters is present. It is shown that the anomalous dimensions of the structure functions, which are the same (universal) for the Kraichnan model, for the model with finite time correlations of the velocity field, and for the model with the advection by the velocity field driven by the stochastic Navier-Stokes equation in the isotropic case, can be distinguished by the assumption of the presence of the small-scale anisotropy in the systems even within one-loop approximation. The corresponding comparison of the anisotropic anomalous dimensions for the present model with that obtained within the Kraichnan rapid-change model is done.
Czech Academy of Sciences Publication Activity Database
Farwig, R.; Guenther, R.; Thomann, E.; Nečasová, Šárka
2014-01-01
Roč. 34, č. 2 (2014), s. 511-529 ISSN 1078-0947 R&D Projects: GA ČR(CZ) GAP201/11/1304; GA MŠk LC06052 Institutional support: RVO:67985840 Keywords : fundamental solution * linearized problem * Navier-Stokes problem Subject RIV: BA - General Mathematics Impact factor: 0.826, year: 2014 http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=8831
A fast Poisson solver for unsteady incompressible Navier-Stokes equations on the half-staggered grid
Golub, G. H.; Huang, L. C.; Simon, H.; Tang, W. -P.
1995-01-01
In this paper, a fast Poisson solver for unsteady, incompressible Navier-Stokes equations with finite difference methods on the non-uniform, half-staggered grid is presented. To achieve this, new algorithms for diagonalizing a semi-definite pair are developed. Our fast solver can also be extended to the three dimensional case. The motivation and related issues in using this second kind of staggered grid are also discussed. Numerical testing has indicated the effectiveness of this algorithm.
Discretely Self-Similar Solutions to the Navier-Stokes Equations with Besov Space Data
Bradshaw, Zachary; Tsai, Tai-Peng
2017-12-01
We construct self-similar solutions to the three dimensional Navier-Stokes equations for divergence free, self-similar initial data that can be large in the critical Besov space {\\dot{B}_{p,∞}^{3/p-1}} where 3 1. These results extend those of uc(Bradshaw) and uc(Tsai) (Ann Henri Poincaré 2016. https://doi.org/10.1007/s00023-016-0519-0) which dealt with initial data in L 3 w since {L^3_w\\subsetneq \\dot{B}_{p,∞}^{3/p-1}} for p > 3. We also provide several concrete examples of vector fields in the relevant function spaces.
Ida, Masato; Taniguchi, Nobuyuki
2003-09-01
This paper introduces a candidate for the origin of the numerical instabilities in large eddy simulation repeatedly observed in academic and practical industrial flow computations. Without resorting to any subgrid-scale modeling, but based on a simple assumption regarding the streamwise component of flow velocity, it is shown theoretically that in a channel-flow computation, the application of the Gaussian filtering to the incompressible Navier-Stokes equations yields a numerically unstable term, a cross-derivative term, which is similar to one appearing in the Gaussian filtered Vlasov equation derived by Klimas [J. Comput. Phys. 68, 202 (1987)] and also to one derived recently by Kobayashi and Shimomura [Phys. Fluids 15, L29 (2003)] from the tensor-diffusivity subgrid-scale term in a dynamic mixed model. The present result predicts that not only the numerical methods and the subgrid-scale models employed but also only the applied filtering process can be a seed of this numerical instability. An investigation concerning the relationship between the turbulent energy scattering and the unstable term shows that the instability of the term does not necessarily represent the backscatter of kinetic energy which has been considered a possible origin of numerical instabilities in large eddy simulation. The present findings raise the question whether a numerically stable subgrid-scale model can be ideally accurate.
Examination of wall functions for a Parabolized Navier-Stokes code for supersonic flow
Energy Technology Data Exchange (ETDEWEB)
Alsbrooks, T.H. [New Mexico Univ., Albuquerque, NM (United States). Dept. of Mechanical Engineering
1993-04-01
Solutions from a Parabolized Navier-Stokes (PNS) code with an algebraic turbulence model are compared with wall functions. The wall functions represent the turbulent flow profiles in the viscous sublayer, thus removing many grid points from the solution procedure. The wall functions are intended to replace the computed profiles between the body surface and a match point in the logarithmic region. A supersonic adiabatic flow case was examined first. This adiabatic case indicates close agreement between computed velocity profiles near the wall and the wall function for a limited range of suitable match points in the logarithmic region. In an attempt to improve marching stability, a laminar to turbulent transition routine was implemented at the start of the PNS code. Implementing the wall function with the transitional routine in the PNS code is expected to reduce computational time while maintaining good accuracy in computed skin friction.
Examination of wall functions for a Parabolized Navier-Stokes code for supersonic flow
Energy Technology Data Exchange (ETDEWEB)
Alsbrooks, T.H. (New Mexico Univ., Albuquerque, NM (United States). Dept. of Mechanical Engineering)
1993-01-01
Solutions from a Parabolized Navier-Stokes (PNS) code with an algebraic turbulence model are compared with wall functions. The wall functions represent the turbulent flow profiles in the viscous sublayer, thus removing many grid points from the solution procedure. The wall functions are intended to replace the computed profiles between the body surface and a match point in the logarithmic region. A supersonic adiabatic flow case was examined first. This adiabatic case indicates close agreement between computed velocity profiles near the wall and the wall function for a limited range of suitable match points in the logarithmic region. In an attempt to improve marching stability, a laminar to turbulent transition routine was implemented at the start of the PNS code. Implementing the wall function with the transitional routine in the PNS code is expected to reduce computational time while maintaining good accuracy in computed skin friction.
Sanderse, B.; Verstappen, R.W.C.P.; Koren, B.
2014-01-01
A discretization method for the incompressible Navier–Stokes equations conserving the secondary quantities kinetic energy and vorticity was introduced, besides the primary quantities mass and momentum. This method was extended to fourth order accuracy. In this paper we propose a new consistent
Gibbon, John D; Pal, Nairita; Gupta, Anupam; Pandit, Rahul
2016-12-01
We consider the three-dimensional (3D) Cahn-Hilliard equations coupled to, and driven by, the forced, incompressible 3D Navier-Stokes equations. The combination, known as the Cahn-Hilliard-Navier-Stokes (CHNS) equations, is used in statistical mechanics to model the motion of a binary fluid. The potential development of singularities (blow-up) in the contours of the order parameter ϕ is an open problem. To address this we have proved a theorem that closely mimics the Beale-Kato-Majda theorem for the 3D incompressible Euler equations [J. T. Beale, T. Kato, and A. J. Majda, Commun. Math. Phys. 94, 61 (1984)CMPHAY0010-361610.1007/BF01212349]. By taking an L^{∞} norm of the energy of the full binary system, designated as E_{∞}, we have shown that ∫_{0}^{t}E_{∞}(τ)dτ governs the regularity of solutions of the full 3D system. Our direct numerical simulations (DNSs) of the 3D CHNS equations for (a) a gravity-driven Rayleigh Taylor instability and (b) a constant-energy-injection forcing, with 128^{3} to 512^{3} collocation points and over the duration of our DNSs confirm that E_{∞} remains bounded as far as our computations allow.
Czech Academy of Sciences Publication Activity Database
Neustupa, Jiří; Penel, P.
2018-01-01
Roč. 2018, March (2018), č. článku 4617020. ISSN 1687-9120 R&D Projects: GA ČR(CZ) GA17-01747S Institutional support: RVO:67985840 Keywords : Navier-Stokes equations Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.643, year: 2016 https://www.hindawi.com/journals/amp/2018/4617020/
Czech Academy of Sciences Publication Activity Database
Dell'Oro, Filippo; Feireisl, Eduard
2015-01-01
Roč. 128, November (2015), s. 136-148 ISSN 0362-546X R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : compressible Navier-Stokes equations * unbounded domain * weak solutions * energy inequality Subject RIV: BA - General Mathematics Impact factor: 1.125, year: 2015 http://www.sciencedirect.com/science/article/pii/S0362546X15002692
Identification of severe wind conditions using a Reynolds Averaged Navier-Stokes solver
International Nuclear Information System (INIS)
Soerensen, N N; Bechmann, A; Johansen, J; Myllerup, L; Botha, P; Vinther, S; Nielsen, B S
2007-01-01
The present paper describes the application of a Navier-Stokes solver to predict the presence of severe flow conditions in complex terrain, capturing conditions that may be critical to the siting of wind turbines in the terrain. First it is documented that the flow solver is capable of predicting the flow in the complex terrain by comparing with measurements from two meteorology masts. Next, it is illustrated how levels of turbulent kinetic energy can be used to easily identify areas with severe flow conditions, relying on a high correlation between high turbulence intensity and severe flow conditions, in the form of high wind shear and directional shear which may seriously lower the lifetime of a wind turbine
Detailed Aerodynamic Analysis of a Shrouded Tail Rotor Using an Unstructured Mesh Flow Solver
Lee, Hee Dong; Kwon, Oh Joon
The detailed aerodynamics of a shrouded tail rotor in hover has been numerically studied using a parallel inviscid flow solver on unstructured meshes. The numerical method is based on a cell-centered finite-volume discretization and an implicit Gauss-Seidel time integration. The calculation was made for a single blade by imposing a periodic boundary condition between adjacent rotor blades. The grid periodicity was also imposed at the periodic boundary planes to avoid numerical inaccuracy resulting from solution interpolation. The results were compared with available experimental data and those from a disk vortex theory for validation. It was found that realistic three-dimensional modeling is important for the prediction of detailed aerodynamics of shrouded rotors including the tip clearance gap flow.
Sengupta, Tapan K.; Sharma, Nidhi; Sengupta, Aditi
2018-05-01
An enstrophy-based non-linear instability analysis of the Navier-Stokes equation for two-dimensional (2D) flows is presented here, using the Taylor-Green vortex (TGV) problem as an example. This problem admits a time-dependent analytical solution as the base flow, whose instability is traced here. The numerical study of the evolution of the Taylor-Green vortices shows that the flow becomes turbulent, but an explanation for this transition has not been advanced so far. The deviation of the numerical solution from the analytical solution is studied here using a high accuracy compact scheme on a non-uniform grid (NUC6), with the fourth-order Runge-Kutta method. The stream function-vorticity (ψ, ω) formulation of the governing equations is solved here in a periodic square domain with four vortices at t = 0. Simulations performed at different Reynolds numbers reveal that numerical errors in computations induce a breakdown of symmetry and simultaneous fragmentation of vortices. It is shown that the actual physical instability is triggered by the growth of disturbances and is explained by the evolution of disturbance mechanical energy and enstrophy. The disturbance evolution equations have been traced by looking at (a) disturbance mechanical energy of the Navier-Stokes equation, as described in the work of Sengupta et al., "Vortex-induced instability of an incompressible wall-bounded shear layer," J. Fluid Mech. 493, 277-286 (2003), and (b) the creation of rotationality via the enstrophy transport equation in the work of Sengupta et al., "Diffusion in inhomogeneous flows: Unique equilibrium state in an internal flow," Comput. Fluids 88, 440-451 (2013).
Czech Academy of Sciences Publication Activity Database
Feireisl, Eduard; Hošek, Radim; Maltese, D.; Novotný, A.
2017-01-01
Roč. 51, č. 1 (2017), s. 279-319 ISSN 0764-583X EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : Navier-Stokes system * finite element numerical method * finite volume numerical method Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.727, year: 2016 http://www.esaim-m2an.org/ articles /m2an/abs/2017/01/m2an150157/m2an150157.html
International Nuclear Information System (INIS)
Capdevila, R.; Perez-Segarra, C.D.; Oliva, A.
2010-01-01
In the present work four different spatial numerical schemes have been developed with the aim of reducing the false-scattering of the numerical solutions obtained with the discrete ordinates (DOM) and the finite volume (FVM) methods. These schemes have been designed specifically for unstructured meshes by means of the extrapolation of nodal values of intensity on the studied radiative direction. The schemes have been tested and compared in several 3D benchmark test cases using both structured orthogonal and unstructured grids.
Finite Volume Method for Unstructured Grid
International Nuclear Information System (INIS)
Casmara; Kardana, N.D.
1997-01-01
The success of a computational method depends on the solution algorithm and mesh generation techniques. cell distributions are needed, which allow the solution to be calculated over the entire body surface with sufficient accuracy. to handle the mesh generation for multi-connected region such as multi-element bodies, the unstructured finite volume method will be applied. the advantages of the unstructured meshes are it provides a great deal more flexibility for generating meshes about complex geometries and provides a natural setting for the use of adaptive meshing. the governing equations to be discretized are inviscid and rotational euler equations. Applications of the method will be evaluated on flow around single and multi-component bodies
Navier--Stokes relaxation to sinh--Poisson states at finite Reynolds numbers
International Nuclear Information System (INIS)
Montgomery, D.; Shan, X.; Matthaeus, W.H.
1993-01-01
A mathematical framework is proposed in which it seems possible to justify the computationally-observed relaxation of a two-dimensional Navier--Stokes fluid to a ''most probable,'' or maximum entropy, state. The relaxation occurs at large but finite Reynolds numbers, and involves substantial decay of higher-order ideal invariants such as enstrophy. A two-fluid formulation, involving interpenetrating positive and negative vorticity fluxes (continuous and square integrable) is developed, and is shown to be intimately related to the passive scalar decay problem. Increasing interpenetration of the two fluids corresponds to the decay of vorticity flux due to viscosity. It is demonstrated numerically that, in two dimensions, passive scalars decay rapidly, relative to mean-square vorticity (enstrophy). This observation provides a basis for assigning initial data to the two-fluid field variables
Sozer, Emre; Brehm, Christoph; Kiris, Cetin C.
2014-01-01
A survey of gradient reconstruction methods for cell-centered data on unstructured meshes is conducted within the scope of accuracy assessment. Formal order of accuracy, as well as error magnitudes for each of the studied methods, are evaluated on a complex mesh of various cell types through consecutive local scaling of an analytical test function. The tests highlighted several gradient operator choices that can consistently achieve 1st order accuracy regardless of cell type and shape. The tests further offered error comparisons for given cell types, leading to the observation that the "ideal" gradient operator choice is not universal. Practical implications of the results are explored via CFD solutions of a 2D inviscid standing vortex, portraying the discretization error properties. A relatively naive, yet largely unexplored, approach of local curvilinear stencil transformation exhibited surprisingly favorable properties
Abdol-Hamid, Khaled S.; Ghaffari, Farhad
2011-01-01
Numerical predictions of the longitudinal aerodynamic characteristics for the Ares I class of vehicles, along with the associated error estimate derived from an iterative convergence grid refinement, are presented. Computational results are based on the unstructured grid, Reynolds-averaged Navier-Stokes flow solver USM3D, with an assumption that the flow is fully turbulent over the entire vehicle. This effort was designed to complement the prior computational activities conducted over the past five years in support of the Ares I Project with the emphasis on the vehicle s last design cycle designated as the A106 configuration. Due to a lack of flight data for this particular design s outer mold line, the initial vehicle s aerodynamic predictions and the associated error estimates were first assessed and validated against the available experimental data at representative wind tunnel flow conditions pertinent to the ascent phase of the trajectory without including any propulsion effects. Subsequently, the established procedures were then applied to obtain the longitudinal aerodynamic predictions at the selected flight flow conditions. Sample computed results and the correlations with the experimental measurements are presented. In addition, the present analysis includes the relevant data to highlight the balance between the prediction accuracy against the grid size and, thus, the corresponding computer resource requirements for the computations at both wind tunnel and flight flow conditions. NOTE: Some details have been removed from selected plots and figures in compliance with the sensitive but unclassified (SBU) restrictions. However, the content still conveys the merits of the technical approach and the relevant results.
Czech Academy of Sciences Publication Activity Database
Neustupa, Jiří
2014-01-01
Roč. 139, č. 4 (2014), s. 685-698 ISSN 0862-7959 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier-Stokes equation * suitable weak solution * regularity Subject RIV: BA - General Mathematics http://hdl.handle.net/10338.dmlcz/144145
Parallel CFD Algorithms for Aerodynamical Flow Solvers on Unstructured Meshes. Parts 1 and 2
Barth, Timothy J.; Kwak, Dochan (Technical Monitor)
1995-01-01
The Advisory Group for Aerospace Research and Development (AGARD) has requested my participation in the lecture series entitled Parallel Computing in Computational Fluid Dynamics to be held at the von Karman Institute in Brussels, Belgium on May 15-19, 1995. In addition, a request has been made from the US Coordinator for AGARD at the Pentagon for NASA Ames to hold a repetition of the lecture series on October 16-20, 1995. I have been asked to be a local coordinator for the Ames event. All AGARD lecture series events have attendance limited to NATO allied countries. A brief of the lecture series is provided in the attached enclosure. Specifically, I have been asked to give two lectures of approximately 75 minutes each on the subject of parallel solution techniques for the fluid flow equations on unstructured meshes. The title of my lectures is "Parallel CFD Algorithms for Aerodynamical Flow Solvers on Unstructured Meshes" (Parts I-II). The contents of these lectures will be largely review in nature and will draw upon previously published work in this area. Topics of my lectures will include: (1) Mesh partitioning algorithms. Recursive techniques based on coordinate bisection, Cuthill-McKee level structures, and spectral bisection. (2) Newton's method for large scale CFD problems. Size and complexity estimates for Newton's method, modifications for insuring global convergence. (3) Techniques for constructing the Jacobian matrix. Analytic and numerical techniques for Jacobian matrix-vector products, constructing the transposed matrix, extensions to optimization and homotopy theories. (4) Iterative solution algorithms. Practical experience with GIVIRES and BICG-STAB matrix solvers. (5) Parallel matrix preconditioning. Incomplete Lower-Upper (ILU) factorization, domain-decomposed ILU, approximate Schur complement strategies.
A spectral/B-spline method for the Navier-Stokes equations in unbounded domains
Dufresne, L
2003-01-01
The numerical method presented in this paper aims at solving the incompressible Navier-Stokes equations in unbounded domains. The problem is formulated in cylindrical coordinates and the method is based on a Galerkin approximation scheme that makes use of vector expansions that exactly satisfy the continuity constraint. More specifically, the divergence-free basis vector functions are constructed with Fourier expansions in the theta and z directions while mapped B-splines are used in the semi-infinite radial direction. Special care has been taken to account for the particular analytical behaviors at both end points r=0 and r-> infinity. A modal reduction algorithm has also been implemented in the azimuthal direction, allowing for a relaxation of the CFL constraint on the timestep size and a possibly significant reduction of the number of DOF. The time marching is carried out using a mixed quasi-third order scheme. Besides the advantages of a divergence-free formulation and a quasi-spectral convergence, the lo...
3D Navier-Stokes simulations of a rotor designed for maximum aerodynamic efficiency
DEFF Research Database (Denmark)
Johansen, Jeppe; Madsen Aagaard, Helge; Gaunaa, Mac
2007-01-01
a constant load was assumed. The rotor design was obtained using an Actuator Disc model and was subsequently verified using both a free wake Lifting Line method and a full 3D Navier-Stokes solver. Excellent agreement was obtained using the three models. Global mechanical power coefficient, CP, reached...... a value of slightly above 0.51, while global thrust coefficient, CT, was 0.87. The local power coefficient, Cp, increased to slightly above the Betz limit on the inner part of the rotor as well as the local thrust coefficient, Ct, increased to a value above 1.1. This agrees well with the theory of de...
Parallel FE Electron-Photon Transport Analysis on 2-D Unstructured Mesh
International Nuclear Information System (INIS)
Drumm, C.R.; Lorenz, J.
1999-01-01
A novel solution method has been developed to solve the coupled electron-photon transport problem on an unstructured triangular mesh. Instead of tackling the first-order form of the linear Boltzmann equation, this approach is based on the second-order form in conjunction with the conventional multi-group discrete-ordinates approximation. The highly forward-peaked electron scattering is modeled with a multigroup Legendre expansion derived from the Goudsmit-Saunderson theory. The finite element method is used to treat the spatial dependence. The solution method is unique in that the space-direction dependence is solved simultaneously, eliminating the need for the conventional inner iterations, a method that is well suited for massively parallel computers
Generalized extended Navier-Stokes theory: multiscale spin relaxation in molecular fluids.
Hansen, J S
2013-09-01
This paper studies the relaxation of the molecular spin angular velocity in the framework of generalized extended Navier-Stokes theory. Using molecular dynamics simulations, it is shown that for uncharged diatomic molecules the relaxation time decreases with increasing molecular moment of inertia per unit mass. In the regime of large moment of inertia the fast relaxation is wave-vector independent and dominated by the coupling between spin and the fluid streaming velocity, whereas for small inertia the relaxation is slow and spin diffusion plays a significant role. The fast wave-vector-independent relaxation is also observed for highly packed systems. The transverse and longitudinal spin modes have, to a good approximation, identical relaxation, indicating that the longitudinal and transverse spin viscosities have same value. The relaxation is also shown to be isomorphic invariant. Finally, the effect of the coupling in the zero frequency and wave-vector limit is quantified by a characteristic length scale; if the system dimension is comparable to this length the coupling must be included into the fluid dynamical description. It is found that the length scale is independent of moment of inertia but dependent on the state point.
Czech Academy of Sciences Publication Activity Database
Neustupa, Jiří; Penel, P.
2014-01-01
Roč. 46, č. 2 (2014), s. 1681-1700 ISSN 0036-1410 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier-Stokes equations * weak solution * regularity criteria Subject RIV: BA - General Mathematics Impact factor: 1.265, year: 2014 http://epubs.siam.org/doi/abs/10.1137/120874874
Stochastic solutions of Navier-Stokes equations: an experimental evidence.
Djurek, Ivan; Djurek, Danijel; Petosić, Antonio
2010-12-01
An electrodynamic loudspeaker has been operated in anharmonic regime indicated by the nonlinear ordinary differential equation when spring constant γ in restoring term, as well as, viscoelasticity of the membrane material, increases with displacement. For driving currents in the range of 2.8-3.3 A, doubling of the vibration period appears, while for currents in the range of 3.3-3.6 A, multiple sequences of subharmonic vibrations begin with f/4 and 3f/4. An application of currents higher than 3.6 A results in a spectrum, characteristic for the chaotic state. The loudspeaker was then operated in a closed chamber, and subharmonic vibrations disappeared by an evacuation. Subsequent injection of air revoked them again at ∼ 120 mbar (Re(')=476) when air viscous forces dominate the Morse convection. At 430 mbar (Re=538) single vibration state was restored, and the phenomenon is in an agreement with prediction of the five mode truncation procedure applied to the Navier-Stokes equations describing a two-dimensional incompressible fluid. © 2010 American Institute of Physics.
The Vlasov-Navier-Stokes System in a 2D Pipe: Existence and Stability of Regular Equilibria
Glass, Olivier; Han-Kwan, Daniel; Moussa, Ayman
2018-05-01
In this paper, we study the Vlasov-Navier-Stokes system in a 2D pipe with partially absorbing boundary conditions. We show the existence of stationary states for this system near small Poiseuille flows for the fluid phase, for which the kinetic phase is not trivial. We prove the asymptotic stability of these states with respect to appropriately compactly supported perturbations. The analysis relies on geometric control conditions which help to avoid any concentration phenomenon for the kinetic phase.
Fast chemical reaction in two-dimensional Navier-Stokes flow: initial regime.
Ait-Chaalal, Farid; Bourqui, Michel S; Bartello, Peter
2012-04-01
This paper studies an infinitely fast bimolecular chemical reaction in a two-dimensional biperiodic Navier-Stokes flow. The reactants in stoichiometric quantities are initially segregated by infinite gradients. The focus is placed on the initial stage of the reaction characterized by a well-defined one-dimensional material contact line between the reactants. Particular attention is given to the effect of the diffusion κ of the reactants. This study is an idealized framework for isentropic mixing in the lower stratosphere and is motivated by the need to better understand the effect of resolution on stratospheric chemistry in climate-chemistry models. Adopting a Lagrangian straining theory approach, we relate theoretically the ensemble mean of the length of the contact line, of the gradients along it, and of the modulus of the time derivative of the space-average reactant concentrations (here called the chemical speed) to the joint probability density function of the finite-time Lyapunov exponent λ with two times τ and τ[over ̃]. The time 1/λ measures the stretching time scale of a Lagrangian parcel on a chaotic orbit up to a finite time t, while τ measures it in the recent past before t, and τ[over ̃] in the early part of the trajectory. We show that the chemical speed scales like κ(1/2) and that its time evolution is determined by rare large events in the finite-time Lyapunov exponent distribution. The case of smooth initial gradients is also discussed. The theoretical results are tested with an ensemble of direct numerical simulations (DNSs) using a pseudospectral model.
Nonperturbative renormalization group study of the stochastic Navier-Stokes equation.
Mejía-Monasterio, Carlos; Muratore-Ginanneschi, Paolo
2012-07-01
We study the renormalization group flow of the average action of the stochastic Navier-Stokes equation with power-law forcing. Using Galilean invariance, we introduce a nonperturbative approximation adapted to the zero-frequency sector of the theory in the parametric range of the Hölder exponent 4-2ε of the forcing where real-space local interactions are relevant. In any spatial dimension d, we observe the convergence of the resulting renormalization group flow to a unique fixed point which yields a kinetic energy spectrum scaling in agreement with canonical dimension analysis. Kolmogorov's -5/3 law is, thus, recovered for ε = 2 as also predicted by perturbative renormalization. At variance with the perturbative prediction, the -5/3 law emerges in the presence of a saturation in the ε dependence of the scaling dimension of the eddy diffusivity at ε = 3/2 when, according to perturbative renormalization, the velocity field becomes infrared relevant.
A narrow-band k-distribution model with single mixture gas assumption for radiative flows
Jo, Sung Min; Kim, Jae Won; Kwon, Oh Joon
2018-06-01
In the present study, the narrow-band k-distribution (NBK) model parameters for mixtures of H2O, CO2, and CO are proposed by utilizing the line-by-line (LBL) calculations with a single mixture gas assumption. For the application of the NBK model to radiative flows, a radiative transfer equation (RTE) solver based on a finite-volume method on unstructured meshes was developed. The NBK model and the RTE solver were verified by solving two benchmark problems including the spectral radiance distribution emitted from one-dimensional slabs and the radiative heat transfer in a truncated conical enclosure. It was shown that the results are accurate and physically reliable by comparing with available data. To examine the applicability of the methods to realistic multi-dimensional problems in non-isothermal and non-homogeneous conditions, radiation in an axisymmetric combustion chamber was analyzed, and then the infrared signature emitted from an aircraft exhaust plume was predicted. For modeling the plume flow involving radiative cooling, a flow-radiation coupled procedure was devised in a loosely coupled manner by adopting a Navier-Stokes flow solver based on unstructured meshes. It was shown that the predicted radiative cooling for the combustion chamber is physically more accurate than other predictions, and is as accurate as that by the LBL calculations. It was found that the infrared signature of aircraft exhaust plume can also be obtained accurately, equivalent to the LBL calculations, by using the present narrow-band approach with a much improved numerical efficiency.
Validation of the actuator line/Navier Stokes technique using mexico measurements
DEFF Research Database (Denmark)
Shen, Wen Zhong; Zhu, Wei Jun; Sørensen, Jens Nørkær
2010-01-01
This paper concerns the contribution of DTU MEK in the international research collaboration project (MexNext) within the framework of IEA Annex 29 to validate aerodynamic models or CFD codes using the existing measurements made in the previous EU funded projectMEXICO (Model Experiments in Control......This paper concerns the contribution of DTU MEK in the international research collaboration project (MexNext) within the framework of IEA Annex 29 to validate aerodynamic models or CFD codes using the existing measurements made in the previous EU funded projectMEXICO (Model Experiments...... in Controlled Conditions). The Actuator Line/Navier Stokes (AL/NS) technique developed at DTU is validated against the detailed MEXICO measurements. The AL/NS computations without the DNW wind tunnel with speeds of 10m/s, 15m/s and 24m/s. Comparisons of blade loading between computations and measurements show...
On full-tensor permeabilities of porous media from numerical solutions of the Navier-Stokes equation
Wang, Y.; Sun, S.; Yu, B.
2013-01-01
A numerical method is proposed to compute full-tensor permeability of porous media without artificial simplification. Navier-Stokes (N-S) equation and Darcy's law are combined to design these numerical experiments. This method can successfully detect the permeability values in principle directions of the porous media and the anisotropic degrees. It is found that the same configuration of porous media may possess isotropic features at lower Reynolds numbers while manifesting anisotropic features at higher Reynolds numbers due to the nonlinearity from convection. Anisotropy becomes pronounced especially when convection is dominant. 2013 Yi Wang et al.
A parallel adaptive mesh refinement algorithm for predicting turbulent non-premixed combusting flows
International Nuclear Information System (INIS)
Gao, X.; Groth, C.P.T.
2005-01-01
A parallel adaptive mesh refinement (AMR) algorithm is proposed for predicting turbulent non-premixed combusting flows characteristic of gas turbine engine combustors. The Favre-averaged Navier-Stokes equations governing mixture and species transport for a reactive mixture of thermally perfect gases in two dimensions, the two transport equations of the κ-ψ turbulence model, and the time-averaged species transport equations, are all solved using a fully coupled finite-volume formulation. A flexible block-based hierarchical data structure is used to maintain the connectivity of the solution blocks in the multi-block mesh and facilitate automatic solution-directed mesh adaptation according to physics-based refinement criteria. This AMR approach allows for anisotropic mesh refinement and the block-based data structure readily permits efficient and scalable implementations of the algorithm on multi-processor architectures. Numerical results for turbulent non-premixed diffusion flames, including cold- and hot-flow predictions for a bluff body burner, are described and compared to available experimental data. The numerical results demonstrate the validity and potential of the parallel AMR approach for predicting complex non-premixed turbulent combusting flows. (author)
International Nuclear Information System (INIS)
Knoll, D.A.; McHugh, P.R.; Krasheninnikov, S.I.; Sigmar, D.J.
1996-01-01
A combined edge plasma/Navier-Stokes neutral transport model is used to simulate dissipative divertor plasmas in the collisional limit for neutrals on a simplified two-dimensional slab geometry with ITER-like plasma conditions and scale lengths. The neutral model contains three momentum equations which are coupled to the plasma through ionization, recombination, and ion-neutral elastic collisions. The neutral transport coefficients are evaluated including both ion-neutral and neutral-neutral collisions. (orig.)
Miranda, Rodrigo A; Rempel, Erico L; Chian, Abraham C-L; Seehafer, Norbert; Toledo, Benjamin A; Muñoz, Pablo R
2013-09-01
We study a transition to hyperchaos in the two-dimensional incompressible Navier-Stokes equations with periodic boundary conditions and an external forcing term. Bifurcation diagrams are constructed by varying the Reynolds number, and a transition to hyperchaos (HC) is identified. Before the onset of HC, there is coexistence of two chaotic attractors and a hyperchaotic saddle. After the transition to HC, the two chaotic attractors merge with the hyperchaotic saddle, generating random switching between chaos and hyperchaos, which is responsible for intermittent bursts in the time series of energy and enstrophy. The chaotic mixing properties of the flow are characterized by detecting Lagrangian coherent structures. After the transition to HC, the flow displays complex Lagrangian patterns and an increase in the level of Lagrangian chaoticity during the bursty periods that can be predicted statistically by the hyperchaotic saddle prior to HC transition.
Energy Technology Data Exchange (ETDEWEB)
Henandez Rosete, Alejandro; Mazur C, Zdzislaw [Instituto de Investigaciones Electricas, Cuernavaca, Morelos (Mexico)
2007-11-15
The results of the simulation by CFD (Computacional Fluid Dynamics) realized to the first stage of a gas turbine GE Frame 7 are presented. The analysis includes the 3D modeling of the flow channel in the nozzle and the movable blade to know the velocities distributions, temperatures and pressures of the main hot gas flow that are developed in the Inter stage. The results are influenced by the imposed border conditions in the properties of the main flow, the rotation of the movable blade, as well as the simulation of cooling air injection in the nozzle. The present study focuses in the validation of the model of the meshes of the ensemble nozzle-blade, for later realize an analysis of conjugated heat transfer in a model with ceramic lining type heat barrier (THB) in the movable blade. The analysis is realized in a CFD commercial code oriented to turbo-machinery using the equations of unstable flows 3D of Navier Stokes. [Spanish] Se presentan los resultados de la simulacion por CFD (Computacional Fluid Dynamics) realizada a la primera etapa de una turbina de gas GE Frame 7. El analisis incluye la modelacion tridimensional del canal de flujo en la tobera y el alabe movil para conocer las distribuciones de las velocidades, temperaturas y presiones del flujo principal de gases calientes que se desarrollan en la inter etapa. Los resultados son influenciados por las condiciones de frontera impuestos en las propiedades del flujo principal, la rotacion del alabe movil, asi como la simulacion de inyeccion de aire de enfriamiento en la tobera. El presente estudio se enfoca en la validacion del modelo de la malla del conjunto tobera-alabe, para posteriormente realizar un analisis de transferencia de calor conjugada en un modelo con recubrimiento ceramico tipo barrera termica (TBC) en el alabe movil. El analisis es realizado en un codigo de CFD comercial orientado a turbomaquinaria utilizando las ecuaciones de flujos inestables 3D de Navier Stokes.
Development of a Two-Phase Flow Analysis Code based on a Unstructured-Mesh SIMPLE Algorithm
Energy Technology Data Exchange (ETDEWEB)
Kim, Jong Tae; Park, Ik Kyu; Cho, Heong Kyu; Yoon, Han Young; Kim, Kyung Doo; Jeong, Jae Jun
2008-09-15
For analyses of multi-phase flows in a water-cooled nuclear power plant, a three-dimensional SIMPLE-algorithm based hydrodynamic solver CUPID-S has been developed. As governing equations, it adopts a two-fluid three-field model for the two-phase flows. The three fields represent a continuous liquid, a dispersed droplets, and a vapour field. The governing equations are discretized by a finite volume method on an unstructured grid to handle the geometrical complexity of the nuclear reactors. The phasic momentum equations are coupled and solved with a sparse block Gauss-Seidel matrix solver to increase a numerical stability. The pressure correction equation derived by summing the phasic volume fraction equations is applied on the unstructured mesh in the context of a cell-centered co-located scheme. This paper presents the numerical method and the preliminary results of the calculations.
Mimetic finite difference method for the stokes problem on polygonal meshes
Energy Technology Data Exchange (ETDEWEB)
Lipnikov, K [Los Alamos National Laboratory; Beirao Da Veiga, L [DIPARTIMENTO DI MATE; Gyrya, V [PENNSYLVANIA STATE UNIV; Manzini, G [ISTIUTO DI MATEMATICA
2009-01-01
Various approaches to extend the finite element methods to non-traditional elements (pyramids, polyhedra, etc.) have been developed over the last decade. Building of basis functions for such elements is a challenging task and may require extensive geometry analysis. The mimetic finite difference (MFD) method has many similarities with low-order finite element methods. Both methods try to preserve fundamental properties of physical and mathematical models. The essential difference is that the MFD method uses only the surface representation of discrete unknowns to build stiffness and mass matrices. Since no extension inside the mesh element is required, practical implementation of the MFD method is simple for polygonal meshes that may include degenerate and non-convex elements. In this article, we develop a MFD method for the Stokes problem on arbitrary polygonal meshes. The method is constructed for tensor coefficients, which will allow to apply it to the linear elasticity problem. The numerical experiments show the second-order convergence for the velocity variable and the first-order for the pressure.
Barker, T.
2018-03-01
The main subject of this paper concerns the establishment of certain classes of initial data, which grant short time uniqueness of the associated weak Leray-Hopf solutions of the three dimensional Navier-Stokes equations. In particular, our main theorem that this holds for any solenodial initial data, with finite L_2(R^3) norm, that also belongs to certain subsets of {it{VMO}}^{-1}(R^3). As a corollary of this, we obtain the same conclusion for any solenodial u0 belonging to L2(R^3)\\cap \\dot{B}^{-1+3/p}_{p,∞}(R^3), for any 3norm is sufficiently small, where 3
Entropy Stable Wall Boundary Conditions for the Compressible Navier-Stokes Equations
Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.
2014-01-01
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite volume, finite difference, discontinuous Galerkin, and flux reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.
Reynolds-Averaged Navier-Stokes Analysis of Zero Efflux Flow Control over a Hump Model
Rumsey, Christopher L.
2006-01-01
The unsteady flow over a hump model with zero efflux oscillatory flow control is modeled computationally using the unsteady Reynolds-averaged Navier-Stokes equations. Three different turbulence models produce similar results, and do a reasonably good job predicting the general character of the unsteady surface pressure coefficients during the forced cycle. However, the turbulent shear stresses are underpredicted in magnitude inside the separation bubble, and the computed results predict too large a (mean) separation bubble compared with experiment. These missed predictions are consistent with earlier steady-state results using no-flow-control and steady suction, from a 2004 CFD validation workshop for synthetic jets.
High order spectral volume and spectral difference methods on unstructured grids
Kannan, Ravishekar
The spectral volume (SV) and the spectral difference (SD) methods were developed by Wang and Liu and their collaborators for conservation laws on unstructured grids. They were introduced to achieve high-order accuracy in an efficient manner. Recently, these methods were extended to three-dimensional systems and to the Navier Stokes equations. The simplicity and robustness of these methods have made them competitive against other higher order methods such as the discontinuous Galerkin and residual distribution methods. Although explicit TVD Runge-Kutta schemes for the temporal advancement are easy to implement, they suffer from small time step limited by the Courant-Friedrichs-Lewy (CFL) condition. When the polynomial order is high or when the grid is stretched due to complex geometries or boundary layers, the convergence rate of explicit schemes slows down rapidly. Solution strategies to remedy this problem include implicit methods and multigrid methods. A novel implicit lower-upper symmetric Gauss-Seidel (LU-SGS) relaxation method is employed as an iterative smoother. It is compared to the explicit TVD Runge-Kutta smoothers. For some p-multigrid calculations, combining implicit and explicit smoothers for different p-levels is also studied. The multigrid method considered is nonlinear and uses Full Approximation Scheme (FAS). An overall speed-up factor of up to 150 is obtained using a three-level p-multigrid LU-SGS approach in comparison with the single level explicit method for the Euler equations for the 3rd order SD method. A study of viscous flux formulations was carried out for the SV method. Three formulations were used to discretize the viscous fluxes: local discontinuous Galerkin (LDG), a penalty method and the 2nd method of Bassi and Rebay. Fourier analysis revealed some interesting advantages for the penalty method. These were implemented in the Navier Stokes solver. An implicit and p-multigrid method was also implemented for the above. An overall speed
Czech Academy of Sciences Publication Activity Database
Neustupa, Jiří
2015-01-01
Roč. 35, č. 3 (2015), s. 201-212 ISSN 0174-4747 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : steady Navier-Stokes problem * slip boundary conditions Subject RIV: BA - General Mathematics http://www.degruyter.com/view/j/anly.2015.35.issue-3/anly-2014-1304/anly-2014-1304. xml
KIM, Jong Woon; LEE, Young-Ouk
2017-09-01
As computing power gets better and better, computer codes that use a deterministic method seem to be less useful than those using the Monte Carlo method. In addition, users do not like to think about space, angles, and energy discretization for deterministic codes. However, a deterministic method is still powerful in that we can obtain a solution of the flux throughout the problem, particularly as when particles can barely penetrate, such as in a deep penetration problem with small detection volumes. Recently, a new state-of-the-art discrete-ordinates code, ATTILA, was developed and has been widely used in several applications. ATTILA provides the capabilities to solve geometrically complex 3-D transport problems by using an unstructured tetrahedral mesh. Since 2009, we have been developing our own code by benchmarking ATTILA. AETIUS is a discrete ordinates code that uses an unstructured tetrahedral mesh such as ATTILA. For pre- and post- processing, Gmsh is used to generate an unstructured tetrahedral mesh by importing a CAD file (*.step) and visualizing the calculation results of AETIUS. Using a CAD tool, the geometry can be modeled very easily. In this paper, we describe a brief overview of AETIUS and provide numerical results from both AETIUS and a Monte Carlo code, MCNP5, in a deep penetration problem with small detection volumes. The results demonstrate the effectiveness and efficiency of AETIUS for such calculations.
Two-level method for unsteady Navier-Stokes equations based on a new projection
International Nuclear Information System (INIS)
Hou Yanren; Li Kaitai
2004-12-01
A two-level algorithm for the two dimensional unsteady Navier-Stokes equations based on a new projection is proposed and investigated. The approximate solution is solved as a sum of a large eddy component and a small eddy component, which are in the sense of the new projection, constructed in this paper. These two terms advance in time explicitly. Actually, the new algorithm proposed here can be regarded as a sort of postprocessing algorithm for the standard Galerkin method (SGM). The large eddy part is solved by SGM in the usual L 2 -based large eddy subspace while the small eddy part (the correction part) is obtained in its complement subspace in the sense of the new projection. The stability analysis indicates the improvement of the stability comparing with SGM of the same scale, and the L 2 -error estimate shows that the scheme can improve the accuracy of SGM approximation for half order. We also propose a numerical implementation based on Lagrange multiplier for this two-level algorithm. (author)
Notes on the Mesh Handler and Mesh Data Conversion
International Nuclear Information System (INIS)
Lee, Sang Yong; Park, Chan Eok
2009-01-01
At the outset of the development of the thermal-hydraulic code (THC), efforts have been made to utilize the recent technology of the computational fluid dynamics. Among many of them, the unstructured mesh approach was adopted to alleviate the restriction of the grid handling system. As a natural consequence, a mesh handler (MH) has been developed to manipulate the complex mesh data from the mesh generator. The mesh generator, Gambit, was chosen at the beginning of the development of the code. But a new mesh generator, Pointwise, was introduced to get more flexible mesh generation capability. An open source code, Paraview, was chosen as a post processor, which can handle unstructured as well as structured mesh data. Overall data processing system for THC is shown in Figure-1. There are various file formats to save the mesh data in the permanent storage media. A couple of dozen of file formats are found even in the above mentioned programs. A competent mesh handler should have the capability to import or export mesh data as many as possible formats. But, in reality, there are two aspects that make it difficult to achieve the competence. The first aspect to consider is the time and efforts to program the interface code. And the second aspect, which is even more difficult one, is the fact that many mesh data file formats are proprietary information. In this paper, some experience of the development of the format conversion programs will be presented. File formats involved are Gambit neutral format, Ansys-CFX grid file format, VTK legacy file format, Nastran format and CGNS
On full-tensor permeabilities of porous media from numerical solutions of the Navier-Stokes equation
Wang, Y.
2013-01-01
A numerical method is proposed to compute full-tensor permeability of porous media without artificial simplification. Navier-Stokes (N-S) equation and Darcy\\'s law are combined to design these numerical experiments. This method can successfully detect the permeability values in principle directions of the porous media and the anisotropic degrees. It is found that the same configuration of porous media may possess isotropic features at lower Reynolds numbers while manifesting anisotropic features at higher Reynolds numbers due to the nonlinearity from convection. Anisotropy becomes pronounced especially when convection is dominant. 2013 Yi Wang et al.
Energy Technology Data Exchange (ETDEWEB)
Fischer, P.F. [Brown Univ., Providence, RI (United States)
1996-12-31
Efficient solution of the Navier-Stokes equations in complex domains is dependent upon the availability of fast solvers for sparse linear systems. For unsteady incompressible flows, the pressure operator is the leading contributor to stiffness, as the characteristic propagation speed is infinite. In the context of operator splitting formulations, it is the pressure solve which is the most computationally challenging, despite its elliptic origins. We seek to improve existing spectral element iterative methods for the pressure solve in order to overcome the slow convergence frequently observed in the presence of highly refined grids or high-aspect ratio elements.
National Aeronautics and Space Administration — Unstructured HIRENASD mesh: - coarse size (5.7 million nodes, 14.4 million elements) - for node centered solvers - 01.06.2011 - caution: dimensions in mm
McDonough, J M
2009-06-01
Outline of the derivation and mathematical and physical interpretations are presented for a discrete dynamical system known as the "poor man's Navier-Stokes equation." Numerical studies demonstrate that velocity fields produced by this dynamical system are similar to those seen in laboratory experiments and in detailed simulations, and they lead to scaling for the turbulence kinetic energy spectrum in accord with Kolmogorov K41 theory.
Directory of Open Access Journals (Sweden)
JONG WOON KIM
2014-04-01
In this paper, we introduce a modified scattering kernel approach to avoid the unnecessarily repeated calculations involved with the scattering source calculation, and used it with parallel computing to effectively reduce the computation time. Its computational efficiency was tested for three-dimensional full-coupled photon-electron transport problems using our computer program which solves the multi-group discrete ordinates transport equation by using the discontinuous finite element method with unstructured tetrahedral meshes for complicated geometrical problems. The numerical tests show that we can improve speed up to 17∼42 times for the elapsed time per iteration using the modified scattering kernel, not only in the single CPU calculation but also in the parallel computing with several CPUs.
Energy exchange analysis in droplet dynamics via the Navier-Stokes-Cahn-Hilliard model
Espath, L. F. R.; Sarmiento, A. F.; Vignal, P.; Varga, B. O. N.; Cortes, A. M. A.; Dalcin, L.; Calo, V. M.
2016-06-01
We develop the energy budget equation of the coupled Navier-Stokes-Cahn-Hilliard (NSCH) system. We use the NSCH equations to model the dynamics of liquid droplets in a liquid continuum. Buoyancy effects are accounted for through the Boussinesq assumption. We physically interpret each quantity involved in the energy exchange to further insight into the model. Highly resolved simulations involving density-driven flows and merging of droplets allow us to analyze these energy budgets. In particular, we focus on the energy exchanges when droplets merge, and describe flow features relevant to this phenomenon. By comparing our numerical simulations to analytical predictions and experimental results available in the literature, we conclude that modeling droplet dynamics within the framework of NSCH equations is a sensible approach worth further research.
Projection of the rotation form Navier-Stokes equation onto the half-staggered grid
Energy Technology Data Exchange (ETDEWEB)
Cho, Ji Ryong [Inje University, Kimhae (Korea, Republic of)
2016-07-15
A projection method for computing incompressible fluid flow is proposed. For the method, the rotation form Navier-Stokes equation (NSE), for which the velocity and the total pressure are employed, is discretized on the half-staggered, finite difference spatial grid. The total pressure couples the static pressure gradient and the convection of momentum in the continuous NSE while the half-staggered grid provides weak pressure-velocity coupling in discrete space. These two features interact synergistically for the discretized NSE to produce smooth pressure fields without additional numerical artifacts such as the momentum interpolation. The method preserves the kinetic energy at the inviscid limit condition. Numerical solutions of the decaying Taylor vortex, the inviscid Taylor vortex, the sudden expansion channel and the square-prism wake are presented.
Energy Technology Data Exchange (ETDEWEB)
Wathen, A. [Oxford Univ. (United Kingdom); Golub, G. [Stanford Univ., CA (United States)
1996-12-31
A simple fixed point linearisation of the Navier-Stokes equations leads to the Oseen problem which after appropriate discretisation yields large sparse linear systems with coefficient matrices of the form (A B{sup T} B -C). Here A is non-symmetric but its symmetric part is positive definite, and C is symmetric and positive semi-definite. Such systems arise in other situations. In this talk we will describe and present some analysis for an iteration based on an indefinite and symmetric preconditioner of the form (D B{sup T} B -C).
Czech Academy of Sciences Publication Activity Database
Feireisl, Eduard; Medviďová-Lukáčová, M.; Nečasová, Šárka; Novotný, A.; She, Bangwei
2018-01-01
Roč. 16, č. 1 (2018), s. 150-183 ISSN 1540-3459 R&D Projects: GA ČR GA16-03230S EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : Navier-Stokes system * finite element numerical method * finite volume numerical method * asymptotic preserving schemes Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.865, year: 2016 http://epubs.siam.org/doi/10.1137/16M1094233
Chamorro, Diego; Lemarié-Rieusset, Pierre-Gilles; Mayoufi, Kawther
2018-04-01
We study the role of the pressure in the partial regularity theory for weak solutions of the Navier-Stokes equations. By introducing the notion of dissipative solutions, due to D uchon and R obert (Nonlinearity 13:249-255, 2000), we will provide a generalization of the Caffarelli, Kohn and Nirenberg theory. Our approach sheels new light on the role of the pressure in this theory in connection to Serrin's local regularity criterion.
Divergent expansion, Borel summability and three-dimensional Navier-Stokes equation.
Costin, Ovidiu; Luo, Guo; Tanveer, Saleh
2008-08-13
We describe how the Borel summability of a divergent asymptotic expansion can be expanded and applied to nonlinear partial differential equations (PDEs). While Borel summation does not apply for non-analytic initial data, the present approach generates an integral equation (IE) applicable to much more general data. We apply these concepts to the three-dimensional Navier-Stokes (NS) system and show how the IE approach can give rise to local existence proofs. In this approach, the global existence problem in three-dimensional NS systems, for specific initial condition and viscosity, becomes a problem of asymptotics in the variable p (dual to 1/t or some positive power of 1/t). Furthermore, the errors in numerical computations in the associated IE can be controlled rigorously, which is very important for nonlinear PDEs such as NS when solutions are not known to exist globally.Moreover, computation of the solution of the IE over an interval [0,p0] provides sharper control of its p-->infinity behaviour. Preliminary numerical computations give encouraging results.
A Krylov Subspace Method for Unstructured Mesh SN Transport Computation
International Nuclear Information System (INIS)
Yoo, Han Jong; Cho, Nam Zin; Kim, Jong Woon; Hong, Ser Gi; Lee, Young Ouk
2010-01-01
Hong, et al., have developed a computer code MUST (Multi-group Unstructured geometry S N Transport) for the neutral particle transport calculations in three-dimensional unstructured geometry. In this code, the discrete ordinates transport equation is solved by using the discontinuous finite element method (DFEM) or the subcell balance methods with linear discontinuous expansion. In this paper, the conventional source iteration in the MUST code is replaced by the Krylov subspace method to reduce computing time and the numerical test results are given