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  • Open Access

    ARTICLE

    A Mesh Free Method for Simulations of Incompressible Fluid Flow

    M. Chatterjee, A.K. Mahendra, A.Sanyal, G. Gouthaman

    CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.4, pp. 385-402, 2012, DOI:10.3970/cmes.2012.083.385

    Abstract In this paper, we describe an Incompressible Navier-Stokes (INS) sol -ver using mesh less least square based discretisation on arbitrary distribution of points. The method uses modified Artificial Compressibility Method (ACM) with least square based discretisation. The Solver operates on an arbitrary distribution of points and uses a novel least squares based method that replaces the normal equations approach. This method generates the non-symmetric cross-product matrix by suitable selection of sub stencils such that the matrix is diagonally dominant and well conditioned. The INS solver has been validated with results available in literature for standard test cases. More >

  • Open Access

    ARTICLE

    2D Mixed Convection Viscous Incompressible Flows with Velocity-Vorticity Variables

    Alfredo Nicolás1, Blanca Bermúdez2

    CMES-Computer Modeling in Engineering & Sciences, Vol.82, No.3&4, pp. 163-178, 2011, DOI:10.32604/cmes.2011.082.163

    Abstract Mixed convection viscous incompressible fluid flows, under a gravitational system, in rectangular cavities are reported using the unsteady Boussinessq approximation in velocity-vorticity variables. The results are obtained using a numerical method based on a fixed point iterative process to solve the nonlinear elliptic system that results after time discretization; the iterative process leads to the solution of uncoupled, well-conditioned, symmetric linear elliptic problems for which efficient solvers exist regardless of the space discretization. Results with different aspect ratios A up to Grashof numbers Gr = 100000 and Reynolds numbers Re = 1000 for the lid driven cavity problem are reported.… More >

  • Open Access

    ARTICLE

    Adaptively Refined Hybrid FDM-RBF Meshless Scheme with Applications to Laminar and Turbulent Viscous Fluid Flows

    S. Gerace1, K. Erhart1, E. Divo1,2, A. Kassab1

    CMES-Computer Modeling in Engineering & Sciences, Vol.81, No.1, pp. 35-68, 2011, DOI:10.3970/cmes.2011.081.035

    Abstract The focus of this work is to demonstrate a novel approach to true CFD automation based on an adaptive Cartesian point distribution process coupled with a Meshless flow solution algorithm. As Meshless method solutions require only an underlying nodal distribution, this approach works well even for complex flow geometries with non-aligned domain boundaries. Through the addition of a so-called shadow layer of body-fitted nodes, application of boundary conditions is simplified considerably, eliminating the stair-casing issues of typical Cartesian-based techniques. This paper describes the approach taken to automatically generate the Meshless nodal distribution, along with the details of an automatic local… More >

  • Open Access

    ARTICLE

    A Preconditioned JFNK Algorithm Applied to Unsteady Incompressible Flow and Fluid Structure Interaction Problems

    Peter Lucas1, Alexander H. van Zuijlen1, Hester Bijl1

    CMES-Computer Modeling in Engineering & Sciences, Vol.59, No.1, pp. 79-106, 2010, DOI:10.3970/cmes.2010.059.079

    Abstract Despite the advances in computer power and numerical algorithms over the last decades, solutions to unsteady flow problems remain computing time intensive.
    In previous work [Lucas, P.,Bijl, H., and Zuijlen, A.H. van(2010)], we have shown that a Jacobian-free Newton-Krylov (JFNK) algorithm, preconditioned with an approximate factorization of the Jacobian which approximately matches the target residual operator, enables a speed up of a factor of 10 compared to nonlinear multigrid (NMG) for two-dimensional, large Reynolds number, unsteady flow computations. Furthermore, in [Lucas, P., Zuijlen, A.H. van, and Bijl, H. (2010)] we show that this algorithm also greatly outperforms NMG for parameter… More >

  • Open Access

    ARTICLE

    Solution of Incompressible Turbulent Flow by a Mesh-Free Method

    R. Vertnik1, B. Šarler2

    CMES-Computer Modeling in Engineering & Sciences, Vol.44, No.1, pp. 65-96, 2009, DOI:10.3970/cmes.2009.044.065

    Abstract The application of the mesh-free Local Radial Basis Function Collocation Method (LRBFCM) in solution of incompressible turbulent flow is explored in this paper. The turbulent flow equations are described by the low - Re number k-emodel with Jones and Launder [Jones and Launder (1971)] closure coefficients. The involved velocity, pressure, turbulent kinetic energy and dissipation fields are represented on overlapping 5-noded sub-domains through collocation by using multiquadrics Radial Basis Functions (RBF). The involved first and second derivatives of the fields are calculated from the respective derivatives of the RBF's. The velocity, turbulent kinetic energy and dissipation equations are solved through… More >

  • Open Access

    ARTICLE

    Recirculation of Viscous Incompressible Flows in Enclosures

    Elsa Báez, Alfredo Nicolás1

    CMES-Computer Modeling in Engineering & Sciences, Vol.41, No.2, pp. 107-130, 2009, DOI:10.3970/cmes.2009.041.107

    Abstract The unsteady Navier-Stokes equations in primitive variables that govern viscous incompressible fluid flow are numerically solved by a simple projection method which involves an operator splitting technique of three steps in the time discretization process. The numerical scheme does not involve any iteration, is independent of the spatial dimension, and its costly part relies on the solution of elliptic problems for which very efficient solvers exist regardless of the spatial discretization. The scheme is tested with the well known two-dimensional lid-driven cavity problem at moderate and high Reynolds numbers Re in the range 400 ≤ Re ≤ 15000. For moderate… More >

  • Open Access

    ARTICLE

    Viscous Incompressible Flows by the Velocity-Vorticity Navier-Stokes Equations

    Alfredo Nicolás1, Blanca Bermúdez2

    CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.2, pp. 73-84, 2007, DOI:10.3970/cmes.2007.020.073

    Abstract 2D viscous incompressible flows are presented from the unsteady Navier-Stokes equations in its velocity-vorticity formulation. The results are obtained using a simple numerical procedure based on a fixed point iterative process to solve the nonlinear elliptic system that results once a second order time discretization is performed. Flows on the un-regularized unit driven cavity problem are reported up to Reynolds numbers Re=4000 to compare them with those reported by other authors, mainly solving the steady problem, and supposed to be correct. Moreover, results are reported for Re = 1000, 4000, 5000, and 10000 to see how their flows look like… More >

  • Open Access

    ARTICLE

    A Solenoidal Initial Condition for the Numerical Solution of the Navier-Stokes Equations for Two-Phase Incompressible Flow

    F. Bierbrauer, S.-P. Zhu1

    CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.1, pp. 1-22, 2007, DOI:10.3970/cmes.2007.019.001

    Abstract Recently the use of the one-field formulation in the numerical solution of the Navier-Stokes equations for two-phase incompressible flow has become a very attractive approach in CFD (computational fluid dynamics). While the presence of material discontinuities across fluid interfaces presents some difficulty, it is their combination with a non-solenoidal discontinuous initial velocity field, commonly occurring in the mathematical formulation, that has provided the greatest hindrance in the numerical solution. This paper presents three analytical solutions, the Bounded Creeping Flow, Solenoidal and Conserved Solenoidal Solutions, which are both continuous, incompressible, retain as much of the original mathematical formulation as possible and… More >

  • Open Access

    ARTICLE

    The Meshless Local Petrov-Galerkin (MLPG) Method for Solving Incompressible Navier-Stokes Equations

    H. Lin, S.N. Atluri1

    CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 117-142, 2001, DOI:10.3970/cmes.2001.002.117

    Abstract The truly Meshless Local Petrov-Galerkin (MLPG) method is extended to solve the incompressible Navier-Stokes equations. The local weak form is modified in a very careful way so as to ovecome the so-called Babus~ka-Brezzi conditions. In addition, The upwinding scheme as developed in Lin and Atluri (2000a) and Lin and Atluri (2000b) is used to stabilize the convection operator in the streamline direction. Numerical results for benchmark problems show that the MLPG method is very promising to solve the convection dominated fluid mechanics problems. More >

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