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Incompressible Fluid Flow (incompressible + fluid_flow)
Selected AbstractsFast single domain,subdomain BEM algorithm for 3D incompressible fluid flow and heat transferINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2009Jure Ravnik Abstract 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 Hermite finite element method for incompressible fluid flowINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2010J. T. Holdeman Abstract We describe some Hermite stream function and velocity finite elements and a divergence-free finite element method for the computation of incompressible flow. Divergence-free velocity bases defined on (but not limited to) rectangles are presented, which produce pointwise divergence-free flow fields (,·uh,0). The discrete velocity satisfies a flow equation that does not involve pressure. The pressure can be recovered as a function of the velocity if needed. The method is formulated in primitive variables and applied to the stationary lid-driven cavity and backward-facing step test problems. Copyright © 2009 John Wiley & Sons, Ltd. [source] Performance analysis of IDEAL algorithm for three-dimensional incompressible fluid flow and heat transfer problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2009Dong-Liang Sun Abstract Recently, an efficient segregated algorithm for incompressible fluid flow and heat transfer problems, called inner doubly iterative efficient algorithm for linked equations (IDEAL), has been proposed by the present authors. In the algorithm there exist inner doubly iterative processes for pressure equation at each iteration level, which almost completely overcome two approximations in SIMPLE algorithm. Thus, the coupling between velocity and pressure is fully guaranteed, greatly enhancing the convergence rate and stability of solution process. However, validations have only been conducted for two-dimensional cases. In the present paper the performance of the IDEAL algorithm for three-dimensional incompressible fluid flow and heat transfer problems is analyzed and a systemic comparison is made between the algorithm and three other most widely used algorithms (SIMPLER, SIMPLEC and PISO). By the comparison of five application examples, it is found that the IDEAL algorithm is the most robust and the most efficient one among the four algorithms compared. For the five three-dimensional cases studied, when each algorithm works at its own optimal under-relaxation factor, the IDEAL algorithm can reduce the computation time by 12.9,52.7% over SIMPLER algorithm, by 45.3,73.4% over SIMPLEC algorithm and by 10.7,53.1% over PISO algorithm. Copyright © 2009 John Wiley & Sons, Ltd. [source] Finite-element simulation of incompressible fluid flow in an elastic vesselINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2003Harry Y. H. Chen Abstract Finite-element simulation was performed to predict the incompressible Navier,Stokes flow in a domain, partly bounded by an elastic vessel, which is allowed to vary with time. Besides satisfying the physical conservation laws, both surface and the volume conservation laws are satisfied at the discrete level for ensuring the balance between physical and geometrical variables. Several problems which are amenable to analytical solutions were tested for validating the method. The simulated results are observed to agree favourably with analytical solutions. Having verified the applicability of the finite-element code to problems involving moving grids, we consider an incompressible fluid flow bounded by rigid and elastic vessel walls. Our emphasis was placed on the validation of the formulation developed within the moving-grid framework. Copyright © 2003 John Wiley & Sons, Ltd. [source] Towards entropy detection of anomalous mass and momentum exchange in incompressible fluid flowINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2002G. F. Naterer An entropy-based approach is presented for assessment of computational accuracy in incompressible flow problems. It is shown that computational entropy can serve as an effective parameter in detecting erroneous or anomalous predictions of mass and momentum transport in the flow field. In the present paper, the fluid flow equations and second law of thermodynamics are discretized by a Galerkin finite-element method with linear, isoparametric triangular elements. It is shown that a weighted entropy residual is closely related to truncation error; this relationship is examined in an application problem involving incompressible flow through a converging channel. In particular, regions exhibiting anomalous flow behaviour, such as under-predicted velocities, appear together with analogous trends in the weighted entropy residual. It is anticipated that entropy-based error detection can provide important steps towards improved accuracy in computational fluid flow. Copyright © 2002 John Wiley & Sons, Ltd. [source] Practical techniques for a three-dimensional FEM analysis of incompressible fluid flow contained with slip walls and a downstream tube bundleINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2001Yuzuru Eguchi Abstract Two practical techniques are proposed in this paper to simulate a flow contained in a plenum with a downstream tube bundle under a PC environment. First, a technique to impose slip wall conditions on smooth-faced planes and sharp edges is proposed to compensate for the mesh coarseness relative to boundary layer thickness. In particular, a new type of Poisson equation is formulated to simultaneously satisfy both such velocity boundary conditions on walls and the incompressibility constraint. Second, a numerical model for a downstream tube bundle is proposed, where hydraulic resistance in a tube is imposed as a traction boundary condition on a fluid surface contacting the tube bundle end. The effectiveness of the techniques is numerically demonstrated in the application to a flow in a condenser water box. Copyright © 2001 John Wiley & Sons, Ltd. [source] Algebraic multigrid and 4th-order discrete-difference equations of incompressible fluid flowNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 4 2010R. Webster Abstract This paper investigates the effectiveness of two different Algebraic Multigrid (AMG) approaches to the solution of 4th-order discrete-difference equations for incompressible fluid flow (in this case for a discrete, scalar, stream-function field). One is based on a classical, algebraic multigrid, method (C-AMG) the other is based on a smoothed-aggregation method for 4th-order problems (SA-AMG). In the C-AMG case, the inter-grid transfer operators are enhanced using Jacobi relaxation. In the SA-AMG case, they are improved using a constrained energy optimization of the coarse-grid basis functions. Both approaches are shown to be effective for discretizations based on uniform, structured and unstructured, meshes. They both give good convergence factors that are largely independent of the mesh size/bandwidth. The SA-AMG approach, however, is more costly both in storage and operations. The Jacobi-relaxed C-AMG approach is faster, by a factor of between 2 and 4 for two-dimensional problems, even though its reduction factors are inferior to those of SA-AMG. For non-uniform meshes, the accuracy of this particular discretization degrades from 2nd to 1st order and the convergence factors for both methods then become mesh dependent. Copyright © 2009 John Wiley & Sons, Ltd. [source] Algebraic multigrid, mixed-order interpolation, and incompressible fluid flowNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 1 2010R. Webster Abstract This paper presents the results of numerical experiments on the use of equal-order and mixed-order interpolations in algebraic multigrid (AMG) solvers for the fully coupled equations of incompressible fluid flow. Several standard test problems are addressed for Reynolds numbers spanning the laminar range. The range of unstructured meshes spans over two orders of problem size (over one order of mesh bandwidth). Deficiencies in performance are identified for AMG based on equal-order interpolations (both zero-order and first-order). They take the form of poor, fragile, mesh-dependent convergence rates. The evidence suggests that a degraded representation of the inter-field coupling in the coarse-grid approximation is the cause. Mixed-order interpolation (first-order for the vectors, zero-order for the scalars) is shown to address these deficiencies. Convergence is then robust, independent of the number of coarse grids and (almost) of the mesh bandwidth. The AMG algorithms used are reviewed. Copyright © 2009 John Wiley & Sons, Ltd. [source] Fluid,structure interaction problems with strong added-mass effectINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2009S. R. Idelsohn Abstract In this paper, the so-called added-mass effect is investigated from a different point of view of previous publications. The monolithic fluid,structure problem is partitioned using a static condensation of the velocity terms. Following this procedure the classical stabilized projection method for incompressible fluid flows is introduced. The procedure allows obtaining a new pressure segregated scheme for fluid,structure interaction problems, which has good convergent characteristics even for biomechanical application, where the added-mass effect is strong. The procedure reveals its power when it is shown that the same projection technique must be implemented in staggered FSI methods. Copyright © 2009 John Wiley & Sons, Ltd. [source] Numerical implementation of Aristov,Pukhnachev's formulation for axisymmetric viscous incompressible flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2010N. P. Moshkin Abstract In the present work a finite-difference technique is developed for the implementation of a new method proposed by Aristov and Pukhnachev (Doklady Phys. 2004; 49(2):112,115) for modeling of the axisymmetric viscous incompressible fluid flows. A new function is introduced that is related to the pressure and a system similar to the vorticity/stream function formulation is derived for the cross-flow. This system is coupled to an equation for the azimuthal velocity component. The scheme and the algorithm treat the equations for the cross-flow as an inextricably coupled system, which allows one to satisfy two conditions for the stream function with no condition on the auxiliary function. The issue of singularity of the matrix is tackled by adding a small parameter in the boundary conditions. The scheme is thoroughly validated on grids with different resolutions. The new numerical tool is applied to the Taylor flow between concentric rotating cylinders when the upper and lower lids are allowed to rotate independently from the inner cylinder, while the outer cylinder is held at rest. The phenomenology of this flow is adequately represented by the numerical model, including the hysteresis that takes place near certain specific values of the Reynolds number. Thus, the present results can be construed to demonstrate the viability of the new model. The success can be attributed to the adequate physical nature of the auxiliary function. The proposed technique can be used in the future for in-depth investigations of the bifurcation phenomena in rotating flows. Copyright © 2009 John Wiley & Sons, Ltd. [source] A control volume finite-element method for numerical simulating incompressible fluid flows without pressure correctionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2007Ahmed Omri Abstract This paper presents a numerical model to study the laminar flows induced in confined spaces by natural convection. A control volume finite-element method (CVFEM) with equal-order meshing is employed to discretize the governing equations in the pressure,velocity formulation. In the proposed model, unknown variables are calculated in the same grid system using different specific interpolation functions without pressure correction. To manage memory storage requirements, a data storage format is developed for generated sparse banded matrices. The performance of various Krylov techniques, including Bi-CGSTAB (Bi-Conjugate Gradient STABilized) with an incomplete LU (ILU) factorization preconditioner is verified by applying it to three well-known test problems. The results are compared to those of independent numerical or theoretical solutions in literature. The iterative computer procedure is improved by using a coupled strategy, which consists of solving simultaneously the momentum and the continuity equation transformed in a pressure equation. Results show that the strategy provides useful benefits with respect to both reduction of storage requirements and central processing unit runtime. Copyright © 2006 John Wiley & Sons, Ltd. [source] Performance of algebraic multigrid methods for non-symmetric matrices arising in particle methodsNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 2-3 2010B. Seibold Abstract Large linear systems with sparse, non-symmetric matrices are known to arise in the modeling of Markov chains or in the discretization of convection,diffusion problems. Due to their potential of solving sparse linear systems with an effort that is linear in the number of unknowns, algebraic multigrid (AMG) methods are of fundamental interest for such systems. For symmetric positive definite matrices, fundamental theoretical convergence results are established, and efficient AMG solvers have been developed. In contrast, for non-symmetric matrices, theoretical convergence results have been provided only recently. A property that is sufficient for convergence is that the matrix be an M-matrix. In this paper, we present how the simulation of incompressible fluid flows with particle methods leads to large linear systems with sparse, non-symmetric matrices. In each time step, the Poisson equation is approximated by meshfree finite differences. While traditional least squares approaches do not guarantee an M-matrix structure, an approach based on linear optimization yields optimally sparse M-matrices. For both types of discretization approaches, we investigate the performance of a classical AMG method, as well as an algebraic multilevel iteration (AMLI) type method. While in the considered test problems, the M-matrix structure turns out not to be necessary for the convergence of AMG, problems can occur when it is violated. In addition, the matrices obtained by the linear optimization approach result in fast solution times due to their optimal sparsity. Copyright © 2010 John Wiley & Sons, Ltd. [source] | ||||||||||