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  • Open Access


    Shape Optimization in Time-Dependent Navier-Stokes Flows via Function Space Parametrization Technique1

    Zhiming Gao2, Yichen Ma3

    CMES-Computer Modeling in Engineering & Sciences, Vol.66, No.2, pp. 135-164, 2010, DOI:10.3970/cmes.2010.066.135

    Abstract Shape optimization technique has an increasing role in fluid dynamics problems governed by distributed parameter systems. In this paper, we present the problem of shape optimization of two dimensional viscous flow governed by the time dependent Navier-Stokes equations. The minimization problem of the viscous dissipated energy was established in the fluid domain. We derive the structure of continuous shape gradient of the cost functional by using the differentiability of a saddle point formulation with a function space parametrization technique. Finally a gradient type algorithm with mesh adaptation and mesh movement strategies is successfully and efficiently applied. More >

  • Open Access


    An Improved Unsplit and Convolutional Perfectly Matched Layer Absorbing Technique for the Navier-Stokes Equations Using Cut-Off Frequency Shift

    Roland Martin1, Carlos Couder-Castaneda1

    CMES-Computer Modeling in Engineering & Sciences, Vol.63, No.1, pp. 47-78, 2010, DOI:10.3970/cmes.2010.063.047

    Abstract We develop an unsplit convolutional perfectly matched layer (CPML) technique to absorb efficiently compressible viscous flows and their related supersonic or subsonic regimes at the outer boundary of a distorted computational domain. More particularly subsonic outgoing flows or subsonic wall-boundary layers close to the PML are well absorbed, which is difficult to obtain without creating numerical instabilities over long time periods. This new PML (CPML) introduces the calculation of auxiliary memory variables at each time step and allows an unsplit formulation of the PML. Damping functions involving a high shift in the frequency domain allow a much better absorption of… More >

  • Open Access


    Meshfree Point Collocation Schemes for 2D Steady State Incompressible Navier-Stokes Equations in Velocity-Vorticity Formulation for High Values of Reynolds Number

    G.C. Bourantas1, E.D. Skouras2,3, V.C. Loukopoulos4, G.C. Nikiforidis1

    CMES-Computer Modeling in Engineering & Sciences, Vol.59, No.1, pp. 31-64, 2010, DOI:10.3970/cmes.2010.059.031

    Abstract A meshfree point collocation method has been developed for the velocity-vorticity formulation of two-dimensional, steady state incompressible Navier-Stokes equations. Particular emphasis was placed on the application of the velocity-correc -tion method, ensuring the continuity equation. The Moving Least Squares (MLS) approximation is employed for the construction of the shape functions, in conjunction with the general framework of the point collocation method. Computations are obtained for regular and irregular nodal distributions, stressing the positivity conditions that make the matrix of the system stable and convergent. The accuracy and the stability of the proposed scheme are demonstrated through two representative, well-known, and… More >

  • Open Access


    Numerical Results for a Colocated Finite-Volume Scheme on Voronoi Meshes for Navier-Stokes Equations

    V.C. Mariani1, E.E.M. Alonso2, S. Peters3

    CMES-Computer Modeling in Engineering & Sciences, Vol.29, No.1, pp. 15-28, 2008, DOI:10.3970/cmes.2008.029.015

    Abstract An application of Newton's method for linearization of advective terms given by the discretization on unstructured Voronoi meshes for the incompressible Navier-Stokes equations is proposed and evaluated in this article. One of the major advantages of the unstructured approach is its application to very complex geometrical domains and the mesh is adaptable to features of the flow. Moreover, in this work comparisons with the literature results in bi-dimensional lid-driven cavities for different Reynolds numbers allow us to assess the numerical properties of the new proposed finite-volume scheme. Results for the components of the velocity, and the pressure collocated at the… More >

  • Open Access


    A Hybrid Multi-Region BEM / LBIE-RBF Velocity-Vorticity Scheme for the Two-Dimensional Navier-Stokes Equations

    E.J. Sellountos1, A. Sequeira1

    CMES-Computer Modeling in Engineering & Sciences, Vol.23, No.2, pp. 127-148, 2008, DOI:10.3970/cmes.2008.023.127

    Abstract In this work a hybrid velocity-vorticity scheme for the solution of the 2D Navier-Stokes equations is presented. The multi-region Local Boundary Integral Equation (LBIE) combined with Radial Basis Functions (RBF) interpolation is used for the solution of the kinematics and the multi-region BEM for the solution of the transport kinetics. The final system of equations is in band form for both methods. The issue of RBF discontinuities is resolved by constructing the RBF matrix locally in every region. The kinematics integral equation is used in three different forms, for coupling the velocity field on the boundary, on interior points and… More >

  • Open Access


    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


    On the Efficiency of the Parallel-in-Time Finite Volume Calculation of the Unsteady Navier-Stokes Equations

    J. M. F. Trindade1, J. C. F. Pereira2

    CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.1, pp. 1-10, 2007, DOI:10.3970/cmes.2007.020.001

    Abstract In this paper, we discuss the efficiency and speed-up of parallel-in-time calculations of the unsteady incompressible Navier-Stokes equations in a PC-cluster. The parallel-in-time method is based on the alternate use of coarse global sequential solvers with fine local parallel ones in an iterative predictor-corrector fashion. Therefore, the efficiency of parallel calculations is strongly dependent on the number of iterations required for convergence. The one-dimensional scalar transport equation and the two-dimensional incompressible unsteady form of the Navier-Stokes equations were used to conduct numerical experiments to derive some conclusions concerning the accuracy and convergence of the iterative method. A simple performance model… More >

  • Open Access


    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


    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 >

  • Open Access


    Non-Graded Adaptive Grid Approaches to the Incompressible Navier-Stokes Equations

    Frédéric Gibou1, Chohong Min2, Hector D. Ceniceros3

    FDMP-Fluid Dynamics & Materials Processing, Vol.3, No.1, pp. 37-48, 2007, DOI:10.3970/fdmp.2007.003.037

    Abstract We describe two finite difference schemes for simulating incompressible flows on nonuniform meshes using quadtree/octree data structures. The first one uses a cell-centered Poisson solver that yields first-order accurate solutions, while producing symmetric linear systems. The second uses a node-based Poisson solver that produces second-order accurate solutions and second-order accurate gradients, while producing nonsymmetric linear systems as the basis for a second-order accurate Navier-Stokes solver. The grids considered can be non-graded, i.e. the difference of level between two adjacent cells can be arbitrary. In both cases semi-Lagrangian methods are used to update the intermediate fluid velocity in a standard projection… More >

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