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  • Articles  (18)
  • Navier-Stokes  (18)
  • Wiley-Blackwell  (18)
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  • Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics  (18)
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  • Wiley-Blackwell  (18)
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  • Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics  (18)
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  • 1
    Electronic Resource
    Electronic Resource
    A composite multigrid method for calculating unsteady incompressible flows in geometrically complex domains (1995)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 20 (1995), S. 341-361 
    Details
    ISSN: 0271-2091
    Keywords: Navier-Stokes ; unsteady ; composite multigrid ; incompressible ; non-staggered grid ; semi-implicit ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A time-accurate, finite volume method for solving the three-dimensional, incompressible Navier-Stokes equations on a composite grid with arbitrary subgrid overlapping is presented. The governing equations are written in a non-orthogonal curvilinear co-ordinate system and are discretized on a non-staggered grid. A semi-implicit, fractional step method with approximate factorization is employed for time advancement. Multigrid combined with intergrid iteration is used to solve the pressure Poisson equation. Inter-grid communication is facilitated by an iterative boundary velocity scheme which ensures that the governing equations are well-posed on each subdomain. Mass conservation on each subdomain is preserved by using a mass imbalance correction scheme which is secondorder-accurate. Three test cases are used to demonstrate the method's consistency, accuracy and efficiency.
    Additional Material: 16 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650200502
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  • 2
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    A vector-parallel scheme for Navier-Stokes computations at multi-gigaflop performance rates (1995)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 21 (1995), S. 445-466 
    Details
    ISSN: 0271-2091
    Keywords: vector-parallel computing ; Navier-Stokes ; Runge-Kutta ; domain decompostion ; CFD ; gigaflop ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A class of vector-parallel schemes for solution of steady compressible or incompressible viscous flow is developed and performance studies carried out. The algorithms employ an artificial transient treatment that permits rapid integration to a steady state. In the present work a four-stage explicit Runge-Kutta scheme employing variable local step size is utilized for the ODE system integration. The RK-4 scheme is restructured to allow vectorization and enhance concurrency in the calculation for a streamfunction-vorticity formulation of the flow problem. The parameters of the resulting RK scheme can be selected to accelerate convergence of the RK recursion. Four main procedures are considered which permit vector-parallel solution: a Jacobi update, a hybrid of the Jacobi and Gauss-Seidel method, red-black ordering and domain decomposition. Numerical performance studies are conducted with a representative viscous incompressible flow calculation. Results indicate that a scheme involving domain decomposition with a Gauss-Seidel type of update for the RK four-stage scheme is most effective and provides performance in excess of 8 Gflops on the Cray C-90.
    Additional Material: 13 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650210602
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  • 3
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    SOLUTION ALGORITHM FOR LOW-PECLET-NUMBER REACTING FLOW (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 25 (1997), S. 225-243 
    Details
    ISSN: 0271-2091
    Keywords: Navier-Stokes ; low Peclet number ; chemical vapour deposition ; low Mach number ; finite volume ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An enhanced solution strategy based on the SIMPLER algorithm is presented for low-Peclet-number mass transport calculations with applications in low-pressure material processing. The accurate solution of highly diffusive flows requires boundary conditions that preserve specified chemical species mass fluxes. The implementation of such boundary conditions in the standard SIMPLER solution procedure leads to degraded convergence that scales with the Peclet number. Modifications to both the non-linear and linear parts of the solution algorithm remove the slow convergence problem. In particular, the linearized species transport equations must be implicitly coupled to the boundary condition equations and the combined system must be solved exactly at each non-linear iteration. The pressure correction boundary conditions are reformulated to ensure that continuity is preserved in each finite volume at each iteration. The boundary condition scaling problem is demonstrated with a simple linear model problem. The enhanced solution strategy is implemented in a baseline computer code that is used to solve the multicomponent Navier-Stokes equations on a generalized, multiple-block grid system. Accelerated convergence rates are demonstrated for several material-processing example problems. © 1997 John Wiley & Sons, Ltd.
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  • 4
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    SINGLE-LAYER FINITE ELEMENT APPROXIMATION OF 3D NAVIER-STOKES EQUATIONS WITH FREE BOUNDARIES FOR SHALLOW WATER FLOWS (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 23 (1996), S. 143-161 
    Details
    ISSN: 0271-2091
    Keywords: finite element ; incompressible ; Navier-Stokes ; free surface flows ; shallow water ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In order to simulate flows in the shallow water limit, the full incompressible Navier-Stokes equations with free boundaries are solved using a single layer of finite elements. This implies a polynomial approximation of the velocity profile in the vertical direction, which in turn distorts the wave speed. This fact is verified by numerical results: the wave speed depends on the vertical discretization. When at least two layers of finite elements are used, the boundary layer at the bottom can be simulated and the correct solution for the shallow water limit is recovered. Then this algorithm is applied to the prediction of Tsunami event.
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  • 5
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    PEGASE: A NAVIER-STOKES SOLVER FOR DIRECT NUMERICAL SIMULATION OF INCOMPRESSIBLE FLOWS (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 833-861 
    Details
    ISSN: 0271-2091
    Keywords: Navier-Stokes ; incompressible ; unsteady ; finite difference ; finite element ; non-staggered grid ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A hybrid conservative finite difference/finite element scheme is proposed for the solution of the unsteady incompressible Navier-Stokes equations. Using velocity-pressure variables on a non-staggeredgrid system, the solution is obtained with a projection method basedon the resolution of a pressure Poisson equation.The new proposed scheme is derived from the finite element spatial discretization using the Galerkin method with piecewise bilinear polynomial basis functions defined on quadrilateral elements. It is applied to the pressure gradient term and to the non-linear convection term as in the so-called group finite element method. It ensures strong coupling between spatial directions, inhibiting the development of oscillations during long-term computations, as demonstrated by the validation studies.Two- and three-dimensional unsteady separated flows with open boundaries have been simulated with the proposed method using Cartesian uniform mesh grids. Several examples of calculations on the backward-facing step configuration are reported and the results obtained are compared with those given by other methods. © 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids 24: 833-861, 1997.
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  • 6
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    Parallel overlapping scheme for viscous incompressible flows (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 1341-1352 
    Details
    ISSN: 0271-2091
    Keywords: parallel ; overlapping ; FEM/FDM ; Navier-Stokes ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A 3D parallel overlapping scheme for viscous incompressible flow problems is presented that combines the finite element method, which is best suited for analysing flow in any arbitrarily shaped flow geometry, with the finite difference method, which is advantageous in terms of both computing time and computer storage. A modified ABMAC method is used as the solution algorithm, to which a sophisticated time integration scheme proposed by the present authors has been applied. Parallelization is based on the domain decomposition method. The RGB (recursive graph bisection) algorithm is used for the decomposition of the FEM mesh and simple slice decomposition is used for the FDM mesh. Some estimates of the parallel performance of FEM, FDM and overlapping computations are presented. © 1997 John Wiley & Sons, Ltd.
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  • 7
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    Three-dimensional incompressible Navier-Stokes equations on non-orthogonal staggered grids using the velocity-vorticity formulation (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 917-943 
    Details
    ISSN: 0271-2091
    Keywords: Navier-Stokes ; incompressible flow ; velocity-vorticity formulation ; generalized curvilinear co-ordinates ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper is concerned with the numerical resolution of the incompressible Navier-Stokes equations in the velocity-vorticity form on non-orthogonal structured grids. The discretization is performed in such a way, that the discrete operators mimic the properties of the continuous ones. This allows the discrete equivalence between the primitive and velocity-vorticity formulations to be proved. This last formulation can thus be seen as a particular technique for solving the primitive equations. The difficulty associated with non-simply connected computational domains and with the implementation of the boundary conditions are discussed. One of the main drawback of the velocity-vorticity formulation, relative to the additional computational work required for solving the additional unknowns, is alleviated. Two- and three-dimensional numerical test cases validate the proposed method. © 1998 John Wiley & Sons, Ltd.
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  • 8
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    An hp adaptive strategy for finite element approximations of the Navier-Stokes equations (1995)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 20 (1995), S. 831-851 
    Details
    ISSN: 0271-2091
    Keywords: error estimation ; adaptivity ; hp-methods ; Navier-Stokes ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Recently, a rigorous a posteriori error estimate, based on the element residual method, for the steady-state Navier-Stokes equations has been derived. In this paper, by using this error estimate, we construct an hp adaptive strategy to minimize the total computation costs while achieving a targeted accuracy for steady incompressible viscous flow problems. The basic hp adaptive strategy is to solve the approximate problem in three consecutive stages corresponding to three different meshes, i.e. an initial mesh, an intermediate adaptive h-mesh, and a final adaptive hp mesh. Our numerical result shows that the three-step hp adaptive strategy for the incompressible flow problems indeed provides an accurate approximate solution while keeping the computational costs under control.
    Additional Material: 13 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650200810
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  • 9
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    On identification of flow separation and vortices in internal periodic flows (1995)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 21 (1995), S. 323-335 
    Details
    ISSN: 0271-2091
    Keywords: flow separation ; time-periodic, unsteady ; vortices ; incompressible ; Navier-Stokes ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: To permit simplified analysis of complex time-dependent flows, possible relationship between the near-wall flow, flow separation and vortices are studied numerically for a flow in a constricted two-dimensional channel. The pulsating incoming wave-form consists of a steady flow, followed by a half-sinus flow superimposed on the steady component. One pair of vortices is created in each cycle, one vortex near each wall. The vortices propagate downstream in the next cycles, promoting flow separation as they move. Existing flow separation criteria were not found to be uniformly valid. A relation between the near-wall flow and the vortical system exists only during the steady incoming flow phase of the cycle. It seems that local criteria of flow separation cannot be found for complex internal pulsating flow fields. However, the vorticity field can be utilized, even in complex time-periodic flows, for identifying vortices that have been formed by the roll-up of shear layers.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650210405
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  • 10
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    An adaptive finite element method for forced convection (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 25 (1997), S. 803-823 
    Details
    ISSN: 0271-2091
    Keywords: incompressible ; Navier-Stokes ; heat transfer ; adaptive FEM ; forced convection ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents an adaptive finite element method to solve forced convective heat transfer. Solutions are obtained in primitive variables using a high-order finite element approximation on unstructured grids. Two general-purpose error estimators are developed to analyse finite element solutions and to determine the characteristics of an improved mesh which is adaptively regenerated by the advancing front method. The adaptive methodology is validated on a problem with a known analytical solution. The methodology is then applied to heat transfer predictions for two cases of practical interest. Predictions of the Nusselt number compare well with measurements and constitute an improvement over previous results. © 1997 John Wiley & Sons, Ltd.
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  • 11
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    Numerical simulations of laminar flow over a 3D backward-facing step (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 1159-1183 
    Details
    ISSN: 0271-2091
    Keywords: backward-facing step ; laminar flow ; Navier-Stokes ; finite elements ; 3D ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical investigation of laminar flow over a three-dimensional backward-facing step is presented with comparisons with detailed experimental data, available in the literature, serving to validate the numerical results. The continuity constraint method, implemented via a finite element weak statement, was employed to solve the unsteady three-dimensional Navier-Stokes equations for incompressible laminar isothermal flow. Two-dimensional numerical simulations of this step geometry underestimate the experimentally determined extent of the primary separation region for Reynolds numbers Re greater than 400. It has been postulated that this disagreement between physical and computational experiments is due to the onset of three-dimensional flow near Re ≈ 400. This paper presents a full three-dimensional simulation of the step geometry for 100≤ Re≤ 800 and correctly predicts the primary reattachment lengths, thus confirming the influence of three-dimensionality. Previous numerical studies have discussed possible instability modes which could induce a sudden onset of three-dimensional flow at certain critical Reynolds numbers. The current study explores the influence of the sidewall on the development of three-dimensional flow for Re greater than 400. Of particular interest is the characterization of three-dimensional vortices in the primary separation region immediately downstream of the step. The complex interaction of a wall jet, located at the step plane near the sidewall, with the mainstream flow reveals a mechanism for the increasing penetration (with increasing Reynolds number) of three-dimensional flow structures into a region of essentially two-dimensional flow near the midplane of the channel. The character and extent of the sidewall-induced flow are investigated for 100≤Re≤ 800. © 1997 John Wiley & Sons, Ltd.
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  • 12
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    A SEGREGATED SOLUTION ALGORITHM FOR INCOMPRESSIBLE FLOWS IN GENERAL CO-ORDINATES (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 515-548 
    Details
    ISSN: 0271-2091
    Keywords: incompressible ; Navier-Stokes ; contravariant velocities ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: To analyse an incompressible Navier-Stokes flow problem in a boundary- fitted curvilinear co-ordinate system is definitely not a trivial task. In the primitive variable formulation, choices between working variables and their storage points have to be made judiciously. The present work engages contravariant velocity components and scalar pressure which stagger each other in the mesh to prevent even-odd pressure oscillations from emerging. Now that smoothness of the pressure field is attainable, the remaining task is to ensure a discrete divergence-free velocity field for an incompressible flow simulation. Aside from the flux discretizations, the indispensable metric tensors, Jacobian and Christoffel symbols in the transformed equations should be approximated with care. The guiding idea is to get the property of geometric identity pertaining to these grid-sensitive discretizations. In addition, how to maintain the revertible one-to-one equivalence at the discrete level between primitive and contravariant velocities is another theme in the present staggered formulation. A semi-implicit segregated solution algorithm felicitous for a large-scale flow simulation was utilized to solve the entire set of basic equations iteratively. Also of note is that the present segregated solution algorithm has the virtue of requiring no user-specified relaxation parameters for speeding up the satisfaction of incompressibility in an optimal sense. Three benchmark problems, including an analytic problem, were investigated to justify the capability of the present formulation in handling problems with complex geometry. The test cases considered and the results obtained herein make a useful contribution in solving problems subsuming cells with arbitrary shapes in a boundary-fitted grid system.
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  • 13
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    A 3D AGGLOMERATION MULTIGRID SOLVER FOR THE REYNOLDS-AVERAGED NAVIER-STOKES EQUATIONS ON UNSTRUCTURED MESHES (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 23 (1996), S. 527-544 
    Details
    ISSN: 0271-2091
    Keywords: multigrid ; unstructured ; Navier-Stokes ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An agglomeration multigrid strategy is developed and implemented for the solution of three-dimensional steady viscous flows. The method enables convergence acceleration with minimal additional memory overhead and is completely automated in that it can deal with grids of arbitrary construction. The multigrid technique is validated by comparing the delivered convergence rates with those obtained by a previously developed overset-mesh multigrid approach and by demonstrating grid-independent convergence rates for aerodynamic problems on very large grids. Prospects for further increases in multigrid efficiency for high-Reynolds-number viscous flows on highly stretched meshes are discussed.
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  • 14
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    Computing the flow around a moving profile by numerically integrating the Navier-Stokes equations (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 125-143 
    Details
    ISSN: 0271-2091
    Keywords: Navier-Stokes ; unsteady separated flow ; laminar flow ; vorticity ; non-inertial frame ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A vorticity velocity formulation is proposed for the solution of the equations for viscous flow around a moving profile. A non-inertial reference frame is used and the velocities are computed from a Poincaré integral formula. The studies are directed towards the need to understand helicopter blade aerodynamics. Worked examples are given which validate the method and programme for laminar flows, at least for low Reynolds numbers. © 1998 John Wiley & Sons, Ltd.
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  • 15
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    A projection method for shallow water equations (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 27 (1998), S. 81-95 
    Details
    ISSN: 0271-2091
    Keywords: shallow waters ; Navier-Stokes ; lagoons ; projections ; parallel computations ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The dynamics of shallow water has been studied and an algorithm for this dynamics has been developed. Results have been obtained with data of the Venice lagoon using a model made expressively by a semi-implicit method based on a finite element method in space. Comparison has been made between field data and the results of the simulation. Very good agreement is shown over a long period of simulation. © 1998 John Wiley & Sons, Ltd.
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  • 16
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    Asymptotic-Newton method for solving incompressible flows (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 25 (1997), S. 861-878 
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    ISSN: 0271-2091
    Keywords: Navier-Stokes ; non-linear methods ; asymptotic-Newton method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this paper we present a comparative study of three non-linear schemes for solving finite element systems of Navier-Stokes incompressible flows. The first scheme is the classical Newton-Raphson linearization, the second one is the modified Newton-Raphson linearization and the last one is a new scheme called the asymptotic-Newton method. The relative efficiency of these approaches is evaluated over a large number of examples. © 1997 John Wiley & Sons, Ltd.
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  • 17
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    Adaptive hybrid (prismatic-tetrahedral) grids for incompressible flows (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 1085-1105 
    Details
    ISSN: 0271-2091
    Keywords: adaptive ; hybrid grids ; incompressible ; Navier-Stokes ; finite volume ; pressure correction ; 3-D ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Hybrid grids consisting of prisms and tetrahedra are employed for the solution of the 3-D Navier-Stokes equations of incompressible flow. A pressure correction scheme is employed with a finite volume-finite element spatial discretization. The traditional staggered grid formulation has been substituted with a collocated mesh approach which uses fourth-order artificial dissipation. The hybrid grid is refined adaptively in local regions of appreciable flow variations. The scheme operations are performed on an edge-wise basis which unifies treatment of both types of grid elements. The adaptive method is employed for incompressible flows in both single and multiply-connected domains. © 1998 John Wiley & Sons, Ltd.
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  • 18
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    AN ADAPTIVE FINITE ELEMENT METHOD FOR A TWO-EQUATION TURBULENCE MODEL IN WALL-BOUNDED FLOWS (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 101-120 
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    ISSN: 0271-2091
    Keywords: incompressible ; Navier-Stokes ; adaptive FEM ; turbulencek-∊ model ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents an adaptive finite element method for solving incompressible turbulent flows using a k-∊ model of turbulence. Solutions are obtained in primitive variables using a highly accurate quadratic finite element on unstructured grids. A projection error estimator is presented that takes into account the relative importance of the errors in velocity, pressure and turbulence variables. The efficiency and convergence rate of the methodology are evaluated by solving problems with known analytical solutions. The method is then applied to turbulent flow over a backward-facing step and predictions are compared with experimental measurements. © 1997 John Wiley & Sons, Ltd.
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