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  • Open Access



    V. S. Sampath Kumara , N. P. Paia,† , B. Devakia

    Frontiers in Heat and Mass Transfer, Vol.16, No.1, pp. 1-7, 2021, DOI:10.5098/hmt.16.3

    Abstract A study is carried out for the two dimensional laminar flow of conducting fluid in presence of magnetic field. The governing non-linear equations of motion are transformed in to dimensionaless form. A solution is obtained by homotopy perturbation method and it is valid for moderately large Reynolds numbers for injection at the wall. Also an efficient algorithm based finite difference scheme is developed to solve the reduced coupled ordinary differential equations with necessary boundary conditions. The effects of Reynolds number, the magnetic parameter and the pradantle number on flow velocity and tempratare distribution is analysed by both the methods and… More >

  • Open Access


    Impact of Artificial Compressibility on the Numerical Solution of Incompressible Nanofluid Flow

    Tohid Adibi1, Shams Forruque Ahmed2,*, Seyed Esmail Razavi3, Omid Adibi4, Irfan Anjum Badruddin5, Syed Javed5

    CMC-Computers, Materials & Continua, Vol.74, No.3, pp. 5123-5139, 2023, DOI:10.32604/cmc.2023.034008

    Abstract The numerical solution of compressible flows has become more prevalent than that of incompressible flows. With the help of the artificial compressibility approach, incompressible flows can be solved numerically using the same methods as compressible ones. The artificial compressibility scheme is thus widely used to numerically solve incompressible Navier-Stokes equations. Any numerical method highly depends on its accuracy and speed of convergence. Although the artificial compressibility approach is utilized in several numerical simulations, the effect of the compressibility factor on the accuracy of results and convergence speed has not been investigated for nanofluid flows in previous studies. Therefore, this paper… More >

  • Open Access


    A Staggered Grid Method for Solving Incompressible Flow on Unstructured Meshes

    Huawen Shu, Minghai Xu, Xinyue Duan*, Yongtong Li, Yu Sun, Ruitian Li, Peng Ding

    CMES-Computer Modeling in Engineering & Sciences, Vol.123, No.2, pp. 509-523, 2020, DOI:10.32604/cmes.2020.08806

    Abstract A finite volume method based unstructured grid is presented to solve the two dimensional viscous and incompressible flow. The method is based on the pressure-correction concept and solved by using a semi-staggered grid technique. The computational procedure can handle cells of arbitrary shapes, although solutions presented in this paper were only involved with triangular and quadrilateral cells. The pressure or pressure-correction value was stored on the vertex of cells. The mass conservation equation was discretized on the dual cells surrounding the vertex of primary cells, while the velocity components and other scale variables were saved on the central of primary… More >

  • Open Access


    A Hybrid Atomistic–Continuum Formulation for Unsteady, Viscous, Incompressible Flows

    H.S. Wijesinghe1, N.G. Hadjiconstantinou2

    CMES-Computer Modeling in Engineering & Sciences, Vol.5, No.6, pp. 515-526, 2004, DOI:10.3970/cmes.2004.005.515

    Abstract We present an implicit hybrid atomisticcontinuum formulation for unsteady, viscous, incompressible flows. The coupling procedure is derived from a domain decomposition method known as the Schwarz alternating method. A dilute gas impulsive Couette flow test problem is used to verify the hybridscheme. Finally, a method to reduce computational costs through limited ensemble averaging is presented. The implicit formulation proposed here is expected to be significantly faster than a time explicit approach based on a compressible formulation for the simulation of low speed flows such as those found in micro- and nano–scale devices. More >

  • Open Access


    IRBFEs for the numerical solution of steady incompressible flows

    D.-A. An-Vo, N. Mai-Duy, T. Tran-Cong

    The International Conference on Computational & Experimental Engineering and Sciences, Vol.16, No.3, pp. 87-88, 2011, DOI:10.3970/icces.2011.016.087

    Abstract In this paper, we develop a control-volume technique based on 2-node integrated-radial-basis-function elements (IRBFEs) for the numerical solution of steady incompressible flows governed by the stream function-vorticity formulation. The fluid domain is discretised by a Cartesian grid from which non-overlapping rectangular control- volumes are formed. Line integrals arising from the integration of the diffusion and convection terms over control volumes are evaluated using the middle-point rule. The convection term is effectively treated by the upwind scheme with deferred correction strategy. Instead of using conventional low-order polynomials, all physical quantities at the interfaces are presently estimated by means of 2-node IRBFEs.… 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


    An Adaptive Discretization of Incompressible Flow using Node-Based Local Meshes

    Weiwei Zhang1, Yufeng Nie1, Li Cai1, Nan Qi2

    CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.1, pp. 55-82, 2014, DOI:10.3970/cmes.2014.102.055

    Abstract In this paper, we derive an adaptive mesh generation method for discretizing the incompressible flow using node-based local grids. The flow problem is described by the Stokes equations which are solved by a stabilized low-order P1-P1 (linear velocity, linear pressure) mixed finite element method. The proposed node-based adaptive mesh generation method consists of four components: mesh size modification, a node placement procedure, a node-based local mesh generation strategy and an error estimation technique, which are combined so as to guarantee obtaining a conforming refined/coarsened mesh. The nodes are considered as particles with interaction forces, which are generated by dynamic simulation… More >

  • Open Access


    MLPG6 for the Solution of Incompressible Flow Equations

    V. C. Loukopoulos1, G. C. Bourantas2

    CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.6, pp. 531-558, 2012, DOI:10.3970/cmes.2012.088.531

    Abstract Meshless Local Petrov-Galerkin (MLPG) approach is used for the solution of the Navier-Stokes and energy equations. More specific as a special case we apply the MLPG6 approach. In the MLPG6 method, the test function is chosen to be the same as the trial function (Galerkin method). The MLPG local weak form is written over a local sub-domain which is completely independent from the trial or test functions. The sizes of nodal trial and test function domains, as well as the size of the local sub-domain over which the local weak-form is considered, can be arbitrary. This may lead to either… More >

  • Open Access


    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


    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 >

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