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## Incompressible Navier (incompressible + navier)
Kinds of Incompressible Navier
## Selected Abstracts## Parallelization and scalability of a spectral element channel flow solver for incompressible Navier,Stokes equations CONCURRENCY AND COMPUTATION: PRACTICE & EXPERIENCE, Issue 10 2007C. W. HammanAbstract Direct numerical simulation (DNS) of turbulent flows is widely recognized to demand fine spatial meshes, small timesteps, and very long runtimes to properly resolve the flow field. To overcome these limitations, most DNS is performed on supercomputing machines. With the rapid development of terascale (and, eventually, petascale) computing on thousands of processors, it has become imperative to consider the development of DNS algorithms and parallelization methods that are capable of fully exploiting these massively parallel machines. A highly parallelizable algorithm for the simulation of turbulent channel flow that allows for efficient scaling on several thousand processors is presented. A model that accurately predicts the performance of the algorithm is developed and compared with experimental data. The results demonstrate that the proposed numerical algorithm is capable of scaling well on petascale computing machines and thus will allow for the development and analysis of high Reynolds number channel flows. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## The moment-of-fluid method in action INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2009Hyung Taek AhnAbstract The moment-of-fluid (MOF) method is a new volume-tracking method that accurately treats evolving material interfaces. The MOF method uses moment data, namely the material volume fraction, as well as the centroid, for a more accurate representation of the material configuration, interfaces and concomitant volume advection. In contrast, the volume-of-fluid method uses only volume fraction data for interface reconstruction and advection. Based on the moment data for each material, the material interfaces are reconstructed with second-order spatial accuracy in a strictly conservative manner. The MOF method is coupled with a stabilized finite element incompressible Navier,Stokes solver for two materials. The effectiveness of the MOF method is demonstrated with a free-surface dam-break and a two-material Rayleigh,Taylor problem. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## Numerical stability and error analysis for the incompressible Navier,Stokes equations INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2002S. PrudhommeAbstract This paper describes a strategy to control errors in finite element approximations of the time-dependent incompressible Navier,Stokes equations. The approach involves estimating the errors due to the discretization in space, using information from the residuals in the momentum and continuity equations. Following a numerical stability analysis of channel flows past a cylinder, it is concluded that the errors due to the residual in the continuity equation should be carefully controlled since it appears to be the source of unphysical perturbations artificially created by the spatial discretization. The performance of the adaptive strategy is then tested for lid-driven oblique cavity flows. Copyright © 2002 John Wiley & Sons, Ltd. [source] ## A priori pivoting in solving the Navier,Stokes equations INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2002S. Ř. WilleAbstract Mixed finite element formulations of incompressible Navier,Stokes Equations leads to non-positive definite algebraic systems inappropriate for iterative solution techniques. However, introducing a suitable preconditioner, the mixed finite element equation system becomes positive definite and solvable by iterative techniques. The present work suggests a priori pivoting sequences for parallel and serial implementations of incomplete Gaussian factorization. Tests are performed for the driven cavity problem in two and three dimensions. Copyright © 2002 John Wiley & Sons, Ltd. [source] ## CBS versus GLS stabilization of the incompressible Navier,Stokes equations and the role of the time step as stabilization parameter INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 2 2002R. CodinaAbstract In this work we compare two apparently different stabilization procedures for the finite element approximation of the incompressible Navier,Stokes equations. The first is the characteristic-based split (CBS). It combines the characteristic Galerkin method to deal with convection dominated flows with a classical splitting technique, which in some cases allows us to use equal velocity,pressure interpolations. The second approach is the Galerkin-least-squares (GLS) method, in which a least-squares form of the element residual is added to the basic Galerkin equations. It is shown that both formulations display similar stabilization mechanisms, provided the stabilization parameter of the GLS method is identified with the time step of the CBS approach. This identification can be understood from a formal Fourier analysis of the linearized problem. Copyright © 2001 John Wiley & Sons, Ltd. [source] ## A control analysis of interaction problem by fluid force INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2001Shoichiro KatoAbstract This paper presents a control analysis of displacement for a building. To control the vertical displacement of the building, control device of multi-balloons with water inside is introduced on the friction piles. Coupling through the water, soil, balloon and pile, the interaction problem is numerically solved. The soil is assumed to be a linear elastic body. The balloon and pile are also modelled as linear elastic truss and rigid-frame components. The water is assumed to be the two-dimensional incompressible Navier,Stokes flow. All components are discretized by the finite element method in space. The control analysis of vertical displacement by fluid force is performed for the purpose of keeping the building horizontal. One of the optimal control theory, the so-called Sakawa,Shindo method, is applied for the control analysis. Using this method, control flux of the water is determined so that position at the top of the balloon comes to be close to the objective position. Copyright © 2001 John Wiley & Sons, Ltd. [source] ## An embedded Dirichlet formulation for 3D continua INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2010A. GerstenbergerAbstract This paper presents a new approach for imposing Dirichlet conditions weakly on non-fitting finite element meshes. Such conditions, also called embedded Dirichlet conditions, are typically, but not exclusively, encountered when prescribing Dirichlet conditions in the context of the eXtended finite element method (XFEM). The method's key idea is the use of an additional stress field as the constraining Lagrange multiplier function. The resulting mixed/hybrid formulation is applicable to 1D, 2D and 3D problems. The method does not require stabilization for the Lagrange multiplier unknowns and allows the complete condensation of these unknowns on the element level. Furthermore, only non-zero diagonal-terms are present in the tangent stiffness, which allows the straightforward application of state-of-the-art iterative solvers, like algebraic multigrid (AMG) techniques. Within this paper, the method is applied to the linear momentum equation of an elastic continuum and to the transient, incompressible Navier,Stokes equations. Steady and unsteady benchmark computations show excellent agreement with reference values. The general formulation presented in this paper can also be applied to other continuous field problems. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## Fast single domain,subdomain BEM algorithm for 3D incompressible fluid flow and heat transfer INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2009Jure RavnikAbstract In this paper acceleration and computer memory reduction of an algorithm for the simulation of laminar viscous flows and heat transfer is presented. The algorithm solves the velocity,vorticity formulation of the incompressible Navier,Stokes equations in 3D. It is based on a combination of a subdomain boundary element method (BEM) and single domain BEM. The CPU time and storage requirements of the single domain BEM are reduced by implementing a fast multipole expansion method. The Laplace fundamental solution, which is used as a special weighting function in BEM, is expanded in terms of spherical harmonics. The computational domain and its boundary are recursively cut up forming a tree of clusters of boundary elements and domain cells. Data sparse representation is used in parts of the matrix, which correspond to boundary-domain clusters pairs that are admissible for expansion. Significant reduction of the complexity is achieved. The paper presents results of testing of the multipole expansion algorithm by exploring its effect on the accuracy of the solution and its influence on the non-linear convergence properties of the solver. Two 3D benchmark numerical examples are used: the lid-driven cavity and the onset of natural convection in a differentially heated enclosure. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## A discrete splitting finite element method for numerical simulations of incompressible Navier,Stokes flows INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2005Kenn K. Q. ZhangAbstract The presence of the pressure and the convection terms in incompressible Navier,Stokes equations makes their numerical simulation a challenging task. The indefinite system as a consequence of the absence of the pressure in continuity equation is ill-conditioned. This difficulty has been overcome by various splitting techniques, but these techniques incur the ambiguity of numerical boundary conditions for the pressure as well as for the intermediate velocity (whenever introduced). We present a new and straightforward discrete splitting technique which never resorts to numerical boundary conditions. The non-linear convection term can be treated by four different approaches, and here we present a new linear implicit time scheme. These two new techniques are implemented with a finite element method and numerical verifications are made. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## Efficient preconditioning techniques for finite-element quadratic discretization arising from linearized incompressible Navier,Stokes equations INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2010A. El MalikiAbstract We develop an efficient preconditioning techniques for the solution of large linearized stationary and non-stationary incompressible Navier,Stokes equations. These equations are linearized by the Picard and Newton methods, and linear extrapolation schemes in the non-stationary case. The time discretization procedure uses the Gear scheme and the second-order Taylor,Hood element P2,P1 is used for the approximation of the velocity and the pressure. Our purpose is to develop an efficient preconditioner for saddle point systems. Our tools are the addition of stabilization (penalization) term r,(div(·)), and the use of triangular block matrix as global preconditioner. This preconditioner involves the solution of two subsystems associated, respectively, with the velocity and the pressure and have to be solved efficiently. Furthermore, we use the P1,P2 hierarchical preconditioner recently proposed by the authors, for the block matrix associated with the velocity and an additive approach for the Schur complement approximation. Finally, several numerical examples illustrating the good performance of the preconditioning techniques are presented. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## Numerical simulation of free-surface flow using the level-set method with global mass correction INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2010Yali ZhangAbstract A new numerical method that couples the incompressible Navier,Stokes equations with the global mass correction level-set method for simulating fluid problems with free surfaces and interfaces is presented in this paper. The finite volume method is used to discretize Navier,Stokes equations with the two-step projection method on a staggered Cartesian grid. The free-surface flow problem is solved on a fixed grid in which the free surface is captured by the zero level set. Mass conservation is improved significantly by applying a global mass correction scheme, in a novel combination with third-order essentially non-oscillatory schemes and a five stage Runge,Kutta method, to accomplish advection and re-distancing of the level-set function. The coupled solver is applied to simulate interface change and flow field in four benchmark test cases: (1) shear flow; (2) dam break; (3) travelling and reflection of solitary wave and (4) solitary wave over a submerged object. The computational results are in excellent agreement with theoretical predictions, experimental data and previous numerical simulations using a RANS-VOF method. The simulations reveal some interesting free-surface phenomena such as the free-surface vortices, air entrapment and wave deformation over a submerged object. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## A level set-based immersed interface method for solving incompressible viscous flows with the prescribed velocity at the boundary INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2010Zhijun TanAbstract A second-order accurate immersed interface method (IIM) is presented for solving the incompressible Navier,Stokes equations with the prescribed velocity at the boundary, which is an extension of the IIM of Le et al. (J. Comput. Phys. 2006; 220:109,138) to a level set representation of the boundary in place of the Lagrangian representation of the boundary using control points on a uniform Cartesian grid. In order to enforce the prescribed velocity boundary condition, the singular forces at the immersed boundary are applied on the fluid. These forces are related to the jump in pressure and the jumps in the derivatives of both the pressure and velocity, and are approximated via using the local Hermite cubic spline interpolation. The strength of singular forces is determined by solving a small system of equations at each time step. The Navier,Stokes equations are discretized via using finite difference method with the incorporation of jump conditions on a staggered Cartesian grid and solved by a second-order accurate projection method. Numerical results demonstrate the accuracy and ability of the proposed method to simulate the viscous flows in irregular domains. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## A variational multiscale Newton,Schur approach for the incompressible Navier,Stokes equations INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2010D. Z. TurnerAbstract In the following paper, we present a consistent Newton,Schur (NS) solution approach for variational multiscale formulations of the time-dependent Navier,Stokes equations in three dimensions. The main contributions of this work are a systematic study of the variational multiscale method for three-dimensional problems and an implementation of a consistent formulation suitable for large problems with high nonlinearity, unstructured meshes, and non-symmetric matrices. In addition to the quadratic convergence characteristics of a Newton,Raphson-based scheme, the NS approach increases computational efficiency and parallel scalability by implementing the tangent stiffness matrix in Schur complement form. As a result, more computations are performed at the element level. Using a variational multiscale framework, we construct a two-level approach to stabilizing the incompressible Navier,Stokes equations based on a coarse and fine-scale subproblem. We then derive the Schur complement form of the consistent tangent matrix. We demonstrate the performance of the method for a number of three-dimensional problems for Reynolds number up to 1000 including steady and time-dependent flows. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## A collocated, iterative fractional-step method for incompressible large eddy simulation INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2008Giridhar JothiprasadAbstract Fractional-step methods are commonly used for the time-accurate solution of incompressible Navier,Stokes (NS) equations. In this paper, a popular fractional-step method that uses pressure corrections in the projection step and its iterative variants are investigated using block-matrix analysis and an improved algorithm with reduced computational cost is developed. Since the governing equations for large eddy simulation (LES) using linear eddy-viscosity-based sub-grid models are similar in form to the incompressible NS equations, the improved algorithm is implemented in a parallel LES solver. A collocated grid layout is preferred for ease of extension to curvilinear grids. The analyzed fractional-step methods are viewed as an iterative approximation to a temporally second-order discretization. At each iteration, a linear system that has an easier block-LU decomposition compared with the original system is inverted. In order to improve the numerical efficiency and parallel performance, modified ADI sub-iterations are used in the velocity step of each iteration. Block-matrix analysis is first used to determine the number of iterations required to reduce the iterative error to the discretization error of. Next, the computational cost is reduced through the use of a reduced stencil for the pressure Poisson equation (PPE). Energy-conserving, spatially fourth-order discretizations result in a 7-point stencil in each direction for the PPE. A smaller 5-point stencil is achieved by using a second-order spatial discretization for the pressure gradient operator correcting the volume fluxes. This is shown not to reduce the spatial accuracy of the scheme, and a fourth-order continuity equation is still satisfied to machine precision. The above results are verified in three flow problems including LES of a temporal mixing layer. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## A comparison of preconditioners for incompressible Navier,Stokes solvers INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2008M. ur RehmanAbstract We consider solution methods for large systems of linear equations that arise from the finite element discretization of the incompressible Navier,Stokes equations. These systems are of the so-called saddle point type, which means that there is a large block of zeros on the main diagonal. To solve these types of systems efficiently, several block preconditioners have been published. These types of preconditioners require adaptation of standard finite element packages. The alternative is to apply a standard ILU preconditioner in combination with a suitable renumbering of unknowns. We introduce a reordering technique for the degrees of freedom that makes the application of ILU relatively fast. We compare the performance of this technique with some block preconditioners. The performance appears to depend on grid size, Reynolds number and quality of the mesh. For medium-sized problems, which are of practical interest, we show that the reordering technique is competitive with the block preconditioners. Its simple implementation makes it worthwhile to implement it in the standard finite element method software. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## A hybrid immersed boundary and material point method for simulating 3D fluid,structure interaction problems INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2008Anvar GilmanovAbstract A numerical method is developed for solving the 3D, unsteady, incompressible Navier,Stokes equations in curvilinear coordinates containing immersed boundaries (IBs) of arbitrary geometrical complexity moving and deforming under forces acting on the body. Since simulations of flow in complex geometries with deformable surfaces require special treatment, the present approach combines a hybrid immersed boundary method (HIBM) for handling complex moving boundaries and a material point method (MPM) for resolving structural stresses and movement. This combined HIBM & MPM approach is presented as an effective approach for solving fluid,structure interaction (FSI) problems. In the HIBM, a curvilinear grid is defined and the variable values at grid points adjacent to a boundary are forced or interpolated to satisfy the boundary conditions. The MPM is used for solving the equations of solid structure and communicates with the fluid through appropriate interface-boundary conditions. The governing flow equations are discretized on a non-staggered grid layout using second-order accurate finite-difference formulas. The discrete equations are integrated in time via a second-order accurate dual time stepping, artificial compressibility scheme. Unstructured, triangular meshes are employed to discretize the complex surface of the IBs. The nodes of the surface mesh constitute a set of Lagrangian control points used for tracking the motion of the flexible body. The equations of the solid body are integrated in time via the MPM. At every instant in time, the influence of the body on the flow is accounted for by applying boundary conditions at stationary curvilinear grid nodes located in the exterior but in the immediate vicinity of the body by reconstructing the solution along the local normal to the body surface. The influence of the fluid on the body is defined through pressure and shear stresses acting on the surface of the body. The HIBM & MPM approach is validated for FSI problems by solving for a falling rigid and flexible sphere in a fluid-filled channel. The behavior of a capsule in a shear flow was also examined. Agreement with the published results is excellent. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## Optimal flow control for Navier,Stokes equations: drag minimization INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2007L. DedčAbstract Optimal control and shape optimization techniques have an increasing role in Fluid Dynamics problems governed by partial differential equations (PDEs). In this paper, we consider the problem of drag minimization for a body in relative motion in a fluid by controlling the velocity through the body boundary. With this aim, we handle with an optimal control approach applied to the steady incompressible Navier,Stokes equations. We use the Lagrangian functional approach and we consider the Lagrangian multiplier method for the treatment of the Dirichlet boundary conditions, which include the control function itself. Moreover, we express the drag coefficient, which is the functional to be minimized, through the variational form of the Navier,Stokes equations. In this way, we can derive, in a straightforward manner, the adjoint and sensitivity equations associated with the optimal control problem, even in the presence of Dirichlet control functions. The problem is solved numerically by an iterative optimization procedure applied to state and adjoint PDEs which we approximate by the finite element method. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## On the geometric conservation law in transient flow calculations on deforming domains INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2006Ch. FörsterAbstract This note revisits the derivation of the ALE form of the incompressible Navier,Stokes equations in order to retain insight into the nature of geometric conservation. It is shown that the flow equations can be written such that time derivatives of integrals over moving domains are avoided prior to discretization. The geometric conservation law is introduced into the equations and the resulting formulation is discretized in time and space without loss of stability and accuracy compared to the fixed grid version. There is no need for temporal averaging remaining. The formulation applies equally to different time integration schemes within a finite element context. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## Pressure boundary condition for the time-dependent incompressible Navier,Stokes equations INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2006R. L. SaniAbstract In Gresho and Sani (Int. J. Numer. Methods Fluids 1987; 7:1111,1145; Incompressible Flow and the Finite Element Method, vol. 2. Wiley: New York, 2000) was proposed an important hypothesis regarding the pressure Poisson equation (PPE) for incompressible flow: Stated there but not proven was a so-called equivalence theorem (assertion) that stated/asserted that if the Navier,Stokes momentum equation is solved simultaneously with the PPE whose boundary condition (BC) is the Neumann condition obtained by applying the normal component of the momentum equation on the boundary on which the normal component of velocity is specified as a Dirichlet BC, the solution (u, p) would be exactly the same as if the ,primitive' equations, in which the PPE plus Neumann BC is replaced by the usual divergence-free constraint (, · u = 0), were solved instead. This issue is explored in sufficient detail in this paper so as to actually prove the theorem for at least some situations. Additionally, like the original/primitive equations that require no BC for the pressure, the new results establish the same thing when the PPE approach is employed. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## Multiple semi-coarsened multigrid method with application to large eddy simulation INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2006F. E. HamAbstract The Multiple Semi-coarsened Grid (MSG) multigrid method of Mulder (J. Comput. Phys. 1989; 83:303,323) is developed as a solver for fully implicit discretizations of the time-dependent incompressible Navier,Stokes equations. The method is combined with the Symmetric Coupled Gauss,Seidel (SCGS) smoother of Vanka (Comput. Methods Appl. Mech. Eng. 1986; 55:321,338) and its robustness demonstrated by performing a number of large-eddy simulations, including bypass transition on a flat plate and the turbulent thermally-driven cavity flow. The method is consistently able to reduce the non-linear residual by 5 orders of magnitude in 40,80 work units for problems with significant and varying coefficient anisotropy. Some discussion of the parallel implementation of the method is also included. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## Fourth-order compact formulation of Navier,Stokes equations and driven cavity flow at high Reynolds numbers INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2006E. ErturkAbstract A new fourth-order compact formulation for the steady 2-D incompressible Navier,Stokes equations is presented. The formulation is in the same form of the Navier,Stokes equations such that any numerical method that solve the Navier,Stokes equations can easily be applied to this fourth-order compact formulation. In particular, in this work the formulation is solved with an efficient numerical method that requires the solution of tridiagonal systems using a fine grid mesh of 601 × 601. Using this formulation, the steady 2-D incompressible flow in a driven cavity is solved up to Reynolds number with Re = 20 000 fourth-order spatial accuracy. Detailed solutions are presented. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## Flow simulation on moving boundary-fitted grids and application to fluid,structure interaction problems INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2006Martin EngelAbstract We present a method for the parallel numerical simulation of transient three-dimensional fluid,structure interaction problems. Here, we consider the interaction of incompressible flow in the fluid domain and linear elastic deformation in the solid domain. The coupled problem is tackled by an approach based on the classical alternating Schwarz method with non-overlapping subdomains, the subproblems are solved alternatingly and the coupling conditions are realized via the exchange of boundary conditions. The elasticity problem is solved by a standard linear finite element method. A main issue is that the flow solver has to be able to handle time-dependent domains. To this end, we present a technique to solve the incompressible Navier,Stokes equation in three-dimensional domains with moving boundaries. This numerical method is a generalization of a finite volume discretization using curvilinear coordinates to time-dependent coordinate transformations. It corresponds to a discretization of the arbitrary Lagrangian,Eulerian formulation of the Navier,Stokes equations. Here the grid velocity is treated in such a way that the so-called Geometric Conservation Law is implicitly satisfied. Altogether, our approach results in a scheme which is an extension of the well-known MAC-method to a staggered mesh in moving boundary-fitted coordinates which uses grid-dependent velocity components as the primary variables. To validate our method, we present some numerical results which show that second-order convergence in space is obtained on moving grids. Finally, we give the results of a fully coupled fluid,structure interaction problem. It turns out that already a simple explicit coupling with one iteration of the Schwarz method, i.e. one solution of the fluid problem and one solution of the elasticity problem per time step, yields a convergent, simple, yet efficient overall method for fluid,structure interaction problems. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## A combined vortex and panel method for numerical simulations of viscous flows: a comparative study of a vortex particle method and a finite volume method INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2005Kwang-Soo KimAbstract This paper describes and compares two vorticity-based integral approaches for the solution of the incompressible Navier,Stokes equations. Either a Lagrangian vortex particle method or an Eulerian finite volume scheme is implemented to solve the vorticity transport equation with a vorticity boundary condition. The Biot,Savart integral is used to compute the velocity field from a vorticity distribution over a fluid domain. The vorticity boundary condition is improved by the use of an iteration scheme connected with the well-established panel method. In the early stages of development of flows around an impulsively started circular cylinder, and past an impulsively started foil with varying angles of attack, the computational results obtained by the Lagrangian vortex method are compared with those obtained by the Eulerian finite volume method. The comparison is performed separately for the pressure fields as well. The results obtained by the two methods are in good agreement, and give a better understanding of the vorticity-based methods. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## A semi-Lagrangian level set method for incompressible Navier,Stokes equations with free surface INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2005Leo Miguel González GutiérrezAbstract In this paper, we formulate a level set method in the framework of finite elements-semi-Lagrangian methods to compute the solution of the incompressible Navier,Stokes equations with free surface. In our formulation, we use a quasi-monotone semi-Lagrangian scheme, which is both unconditionally stable and essentially non oscillatory, to compute the advective terms in the Navier,Stokes equations, the transport equation and the equation of the reinitialization stage for the level set function. The method we propose is quite robust and flexible with regard to the mesh and the geometry of the domain, as well as the magnitude of the Reynolds number. We illustrate the performance of the method in several examples, which range from a benchmark problem to test the volume conservation property of the method to the flow past a NACA0012 foil at high Reynolds number. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## A preconditioned semi-staggered dilation-free finite volume method for the incompressible Navier,Stokes equations on all-hexahedral elements INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2005Mehmet SahinAbstract A new semi-staggered finite volume method is presented for the solution of the incompressible Navier,Stokes equations on all-quadrilateral (2D)/hexahedral (3D) meshes. The velocity components are defined at element node points while the pressure term is defined at element centroids. The continuity equation is satisfied exactly within each elements. The checkerboard pressure oscillations are prevented using a special filtering matrix as a preconditioner for the saddle-point problem resulting from second-order discretization of the incompressible Navier,Stokes equations. The preconditioned saddle-point problem is solved using block preconditioners with GMRES solver. In order to achieve higher performance FORTRAN source code is based on highly efficient PETSc and HYPRE libraries. As test cases the 2D/3D lid-driven cavity flow problem and the 3D flow past array of circular cylinders are solved in order to verify the accuracy of the proposed method. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## Retracted and replaced: A flow-condition-based interpolation finite element procedure for triangular grids INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2005Haruhiko KohnoAbstract A flow-condition-based interpolation finite element scheme is presented for use of triangular grids in the solution of the incompressible Navier,Stokes equations. The method provides spatially isotropic discretizations for low and high Reynolds number flows. Various example solutions are given to illustrate the capabilities of the procedure. This article and been retracted and replaced. See retraction and replacement notice DOI: 10.1002/fld.1247.abs. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## A level set characteristic Galerkin finite element method for free surface flows INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2005Ching-Long LinAbstract This paper presents a numerical method for free surface flows that couples the incompressible Navier,Stokes equations with the level set method in the finite element framework. The implicit characteristic-Galerkin approximation together with the fractional four-step algorithm is employed to discretize the governing equations. The schemes for solving the level set evolution and reinitialization equations are verified with several benchmark cases, including stationary circle, rotation of a slotted disk and stretching of a circular fluid element. The results are compared with those calculated from the level set finite volume method of Yue et al. (Int. J. Numer. Methods Fluids 2003; 42:853,884), which employed the third-order essentially non-oscillatory (ENO) schemes for advection of the level set function in a generalized curvilinear coordinate system. The comparison indicates that the characteristic Galerkin approximation of the level set equations yields more accurate solutions. The second-order accuracy of the Navier,Stokes solver is confirmed by simulation of decay vortex. The coupled system of the Navier,Stokes and level set equations then is validated by solitary wave and broken dam problems. The simulation results are in excellent agreement with experimental data. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## Finite volume solution of the Navier,Stokes equations in velocity,vorticity formulation INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2005Baoshan ZhuAbstract For the incompressible Navier,Stokes equations, vorticity-based formulations have many attractive features over primitive-variable velocity,pressure formulations. However, some features interfere with the use of the numerical methods based on the vorticity formulations, one of them being the lack of a boundary conditions on vorticity. In this paper, a novel approach is presented to solve the velocity,vorticity integro-differential formulations. The general numerical method is based on standard finite volume scheme. The velocities needed at the vertexes of each control volume are calculated by a so-called generalized Biot,Savart formula combined with a fast summation algorithm, which makes the velocity boundary conditions implicitly satisfied by maintaining the kinematic compatibility of the velocity and vorticity fields. The well-known fractional step approaches are used to solve the vorticity transport equation. The paper describes in detail how we accurately impose no normal-flow and no tangential-flow boundary conditions. We impose a no-flux boundary condition on solid objects by the introduction of a proper amount of vorticity at wall. The diffusion term in the transport equation is treated implicitly using a conservative finite update. The diffusive fluxes of vorticity into flow domain from solid boundaries are determined by an iterative process in order to satisfy the no tangential-flow boundary condition. As application examples, the impulsively started flows through a flat plate and a circular cylinder are computed using the method. The present results are compared with the analytical solution and other numerical results and show good agreement. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## Large eddy simulation of turbulent flows via domain decomposition techniques. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2005Part 2: applicationsAbstract The present paper discusses the application of large eddy simulation to incompressible turbulent flows in complex geometries. Algorithmic developments concerning the flow solver were provided in the companion paper (Int. J. Numer. Meth. Fluids, 2003; submitted), which addressed the development and validation of a multi-domain kernel suitable for the integration of the elliptic partial differential equations arising from the fractional step procedure applied to the incompressible Navier,Stokes equations. Numerical results for several test problems are compared to reference experimental and numerical data to demonstrate the potential of the method. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## Splitting methods for high order solution of the incompressible Navier,Stokes equations in 3D INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10-11 2005Arnim BrügerAbstract The incompressible Navier,Stokes equations are discretized in space by a hybrid method and integrated in time by the method of lines. The solution is determined on a staggered curvilinear grid in two space dimensions and by a Fourier expansion in the third dimension. The space derivatives are approximated by a compact finite difference scheme of fourth-order on the grid. The solution is advanced in time by a semi-implicit method. In each time step, systems of linear equations have to be solved for the velocity and the pressure. The iterations are split into one outer iteration and three inner iterations. The accuracy and efficiency of the method are demonstrated in a numerical experiment with rotated Poiseuille flow perturbed by Orr,Sommerfeld modes in a channel. Copyright © 2005 John Wiley & Sons, Ltd. [source] |