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  • Open Access


    Fractional Optimal Control of Navier-Stokes Equations

    Abd-Allah Hyder1, 2, *, M. El-Badawy3

    CMC-Computers, Materials & Continua, Vol.64, No.2, pp. 859-870, 2020, DOI:10.32604/cmc.2020.09897

    Abstract In this paper, the non-stationary incompressible fluid flows governed by the Navier-Stokes equations are studied in a bounded domain. This study focuses on the timefractional Navier-Stokes equations in the optimal control subject, where the control is distributed within the domain and the time-fractional derivative is proposed as RiemannLiouville sort. In addition, the control object is to minimize the quadratic cost functional. By using the Lax-Milgram lemma with the assistance of the fixed-point theorem, we demonstrate the existence and uniqueness of the weak solution to this system. Moreover, for a quadratic cost functional subject to the time-fractional Navier-Stokes equations, we prove… More >

  • Open Access


    Control of Karman Vortex Street By Using Plasma Actuators

    D. O. Redchyts1, E. A. Shkvar2,*, S. V. Moiseienko3

    FDMP-Fluid Dynamics & Materials Processing, Vol.15, No.5, pp. 509-525, 2019, DOI:10.32604/fdmp.2019.08266

    Abstract A mathematical model for unsteady electro- and aerodynamic processes in the presence of a plasma actuator has been elaborated through physical modeling of the dielectric barrier discharge. A specialized computational fluid dynamics package has been developed accordingly in order to calculate steady and unsteady laminar and turbulent flows. For the numerical simulation of the dielectric barrier discharge, in particular, two equations have been added to the Navier-Stokes equations and solved. They describe the distribution of the applied voltage and the charged particles density. The impact of the plasma actuator on air has been accounted for through the Lorentz force, included… More >

  • Open Access


    Numerical Solution of Non-Isothermal Fluid Flows Using Local Radial Basis Functions (LRBF) Interpolation and a Velocity-Correction Method

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

    CMES-Computer Modeling in Engineering & Sciences, Vol.64, No.2, pp. 187-212, 2010, DOI:10.3970/cmes.2010.064.187

    Abstract Meshfree point collocation method (MPCM) is developed, solving the velocity-vorticity formulation of Navier-Stokes equations, for two-dimensional, steady state incompressible viscous flow problems in the presence of heat transfer. Particular emphasis is placed on the application of the velocity-correction method, ensuring the continuity equation. The Gaussian Radial Basis Functions (GRBF) interpolation is employed to construct the shape functions in conjunction with the framework of the point collocation method. The cases of forced, natural and mixed convection in a 2D rectangular enclosure are examined. The accuracy and the stability of the proposed scheme are demonstrated through three representative, well known and established… More >

  • Open Access


    Enhanced transport phenomena in the Navier-Stokes shell-like slip layer

    Janusz Badur, MichaA, Karcz, Marcin LemaA"ski, Lucjan NastaA,ek

    The International Conference on Computational & Experimental Engineering and Sciences, Vol.19, No.3, pp. 91-92, 2011, DOI:10.3970/icces.2011.019.091

    Abstract Due to last mass flow rate measurements in gas micro and nano-channels several discrepancies in the mathematical modeling have been arise. The most important one, is the "flow enhancement" related with the wall slip phenomena. Thus, in the literature, there is opinion that the Navier-Stokes slip condition is correct only in certain restricted circumstances, particularly those restricted to the first order boundary conditions. A one possible way for solving of the above discrepancies, used recently in the literature, is developing a variety of so-called ßecond order boundary conditions". This way is incorrect since it always leads to an inconsistency between… More >

  • Open Access


    Using radial basis functions in a ''finite difference mode''

    A.I.Tolstykh, D.A. Shirobokov1

    CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 207-222, 2005, DOI:10.3970/cmes.2005.007.207

    Abstract A way of using RBF as the basis for PDE's solvers is presented, its essence being constructing approximate formulas for derivatives discretizations based on RBF interpolants with local supports similar to stencils in finite difference methods. Numerical results for different types of elasticity equations showing reasonable accuracy and good$h$-convergence properties of the technique are presented. Applications of the technique to problems with non-self-adjoint operators (like those for the Navier-Stokes equations) are also considered. More >

  • Open Access


    Computation of Incompressible Navier-Stokes Equations by Local RBF-based Differential Quadrature Method

    C. Shu1,2, H. Ding2, K.S. Yeo2

    CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 195-206, 2005, DOI:10.3970/cmes.2005.007.195

    Abstract Local radial basis function-based differential quadrature (RBF-DQ) method was recently proposed by us. The method is a natural mesh-free approach. It can be regarded as a combination of the conventional differential quadrature (DQ) method with the radial basis functions (RBFs) by means of taking the RBFs as the trial functions in the DQ scheme. With the computed weighting coefficients, the method works in a very similar fashion as conventional finite difference schemes. In this paper, we mainly concentrate on the applications of the method to incompressible flows in the steady and unsteady regions. The multiquadric (MQ) radial basis functions are… More >

  • Open Access


    A CFD/CSD Model for Transonic Flutter

    Tong-qing Guo, Zhi-liang Lu1

    CMC-Computers, Materials & Continua, Vol.2, No.2, pp. 105-112, 2005, DOI:10.3970/cmc.2005.002.105

    Abstract In this paper, a rapid deforming technique is developed to generate dynamic, three-dimensional, multi-block, mesh. The second-order Runge-Kutta time-marching method is used to solve the structural equations of motion. A dual-time method and finite volume discretization are applied for the unsteady Euler/Navier-Stokes equations to calculate the aerodynamic forces, in which the physical time step is synchronous with the structural equations of motion. The Spalart-Allmaras turbulence model is adopted for a turbulent flow. Due to mass dissimilarity, exiting in flutter calculations for a compressible flow, methods of variable mass and variable stiffness are developed to calculate the dynamic pressure of flutter… More >

  • Open Access


    On the Numerical Study of Capillary-driven Flow in a 3-D Microchannel Model

    C.T. Lee1, C.C. Lee2

    CMES-Computer Modeling in Engineering & Sciences, Vol.104, No.5, pp. 375-403, 2015, DOI:10.3970/cmes.2015.104.375

    Abstract In this article, we demonstrate a numerical 3-D chip, and studied the capillary dynamics inside the microchannel. We applied the level set method on the Navier-Stokes equation which incorporates the surface tension and two-phase flow characteristics. We analyzed the capillary dynamics near the junction of two microchannels. Such a highlighting point is important that it not only can provide the information of interface behavior when fluids are made into a head-on collision, but also emphasize the idea for the design of the chip. In addition, we study the pressure distribution of the fluids at the junction. It is shown that… More >

  • Open Access


    Pore-Scale Modeling of Navier-Stokes Flow in Distensible Networks and Porous Media

    Taha Sochi1

    CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.2, pp. 151-168, 2014, DOI:10.3970/cmes.2014.099.151

    Abstract In this paper, a pore-scale network modeling method, based on the flow continuity residual in conjunction with a Newton-Raphson non-linear iterative solving technique, is proposed and used to obtain the pressure and flow fields in a network of interconnected distensible ducts representing, for instance, blood vasculature or deformable porous media. A previously derived analytical expression correlating boundary pressures to volumetric flow rate in compliant tubes for a pressure-area constitutive elastic relation has been used to represent the underlying flow model. Comparison to a preceding equivalent method, the one-dimensional Navier-Stokes finite element, was made and the results were analyzed. The advantages… More >

  • Open Access


    Variable Viscosity and Density Biofilm Simulations using an Immersed Boundary Method, Part I: Numerical Scheme and Convergence Results

    Jason F. Hammond1, Elizabeth J. Stewart2, John G. Younger3, Michael J.Solomon2, David M. Bortz4,5

    CMES-Computer Modeling in Engineering & Sciences, Vol.98, No.3, pp. 295-340, 2014, DOI:10.32604/cmes.2014.098.295

    Abstract The overall goal of this work is to develop a numerical simulation which correctly describes a bacterial biofilm fluid-structure interaction and separation process. In this, the first of a two-part effort, we fully develop a convergent scheme and provide numerical evidence for the method order as well as a full 3D separation simulation. We use an immersed boundary-based method (IBM) to model and simulate a biofilm with density and viscosity values different from than that of the surrounding fluid. The simulation also includes breakable springs connecting the bacteria in the biofilm which allows the inclusion of erosion and detachment into… More >

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