An implicit potential method along with a meshless technique for incompressible fluid flows for regular and irregular geometries in 2D and 3D

G. C. Bourantas, V. C. Loukopoulos, H. A. Chowdhury, G. R. Joldes, K. Miller, S. P A Bordas

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    Abstract

    We present the Implicit Potential (IPOT) numerical scheme developed in the framework of meshless point collocation. The proposed scheme is used for the numerical solution of the steady state, incompressible Navier-Stokes (N-S) equations in their primitive variable (u-v-w-p) formulation. The governing equations are solved in their strong form using either a collocated or a semi-staggered type meshless nodal configuration. The unknown field functions and derivatives are calculated using the Modified Moving Least Squares (MMLS) interpolation method. Both velocity-correction and pressure-correction methods applied ensure the incompressibility constraint and mass conservation. The proposed meshless point collocation (MPC) scheme has the following characteristics: (i) it can be applied, in a straightforward manner to: steady, unsteady, internal and external fluid flows in 2D and 3D, (ii) it equally applies to regular an irregular geometries, (iii) a distribution of points is sufficient, no numerical integration in space nor any mesh structure are required, (iv) there is no need for pressure boundary conditions since no pressure constitutive equation is solved, (v) it is quite simple and accurate, (vi) results can be obtained using collocated or semi-staggered nodal distributions, (vii) there is no need to compute the velocity potential nor the unit normal vectors and (viii) there is no need for a curvilinear system of coordinates. Simulations of fluid flow in 2D and 3D for regular and irregular geometries indicate the validity of the proposed methodology.

    Original languageEnglish
    Pages (from-to)0
    Number of pages15
    JournalEngineering Analysis with Boundary Elements
    Volume77
    Early online date3 Feb 2017
    DOIs
    Publication statusPublished - 1 Apr 2017

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    Meshless
    Incompressible Flow
    Incompressible Fluid
    Fluid Flow
    Irregular
    Flow of fluids
    Collocation
    Geometry
    Pressure Correction
    Unit normal vector
    Moving Least Squares
    Incompressibility
    Mass Conservation
    Interpolation Method
    Incompressible Navier-Stokes Equations
    Function Fields
    Constitutive Equation
    Constitutive equations
    Least Square Method
    Numerical integration

    Cite this

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    title = "An implicit potential method along with a meshless technique for incompressible fluid flows for regular and irregular geometries in 2D and 3D",
    abstract = "We present the Implicit Potential (IPOT) numerical scheme developed in the framework of meshless point collocation. The proposed scheme is used for the numerical solution of the steady state, incompressible Navier-Stokes (N-S) equations in their primitive variable (u-v-w-p) formulation. The governing equations are solved in their strong form using either a collocated or a semi-staggered type meshless nodal configuration. The unknown field functions and derivatives are calculated using the Modified Moving Least Squares (MMLS) interpolation method. Both velocity-correction and pressure-correction methods applied ensure the incompressibility constraint and mass conservation. The proposed meshless point collocation (MPC) scheme has the following characteristics: (i) it can be applied, in a straightforward manner to: steady, unsteady, internal and external fluid flows in 2D and 3D, (ii) it equally applies to regular an irregular geometries, (iii) a distribution of points is sufficient, no numerical integration in space nor any mesh structure are required, (iv) there is no need for pressure boundary conditions since no pressure constitutive equation is solved, (v) it is quite simple and accurate, (vi) results can be obtained using collocated or semi-staggered nodal distributions, (vii) there is no need to compute the velocity potential nor the unit normal vectors and (viii) there is no need for a curvilinear system of coordinates. Simulations of fluid flow in 2D and 3D for regular and irregular geometries indicate the validity of the proposed methodology.",
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    An implicit potential method along with a meshless technique for incompressible fluid flows for regular and irregular geometries in 2D and 3D. / Bourantas, G. C.; Loukopoulos, V. C.; Chowdhury, H. A.; Joldes, G. R.; Miller, K.; Bordas, S. P A.

    In: Engineering Analysis with Boundary Elements, Vol. 77, 01.04.2017, p. 0.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - An implicit potential method along with a meshless technique for incompressible fluid flows for regular and irregular geometries in 2D and 3D

    AU - Bourantas, G. C.

    AU - Loukopoulos, V. C.

    AU - Chowdhury, H. A.

    AU - Joldes, G. R.

    AU - Miller, K.

    AU - Bordas, S. P A

    PY - 2017/4/1

    Y1 - 2017/4/1

    N2 - We present the Implicit Potential (IPOT) numerical scheme developed in the framework of meshless point collocation. The proposed scheme is used for the numerical solution of the steady state, incompressible Navier-Stokes (N-S) equations in their primitive variable (u-v-w-p) formulation. The governing equations are solved in their strong form using either a collocated or a semi-staggered type meshless nodal configuration. The unknown field functions and derivatives are calculated using the Modified Moving Least Squares (MMLS) interpolation method. Both velocity-correction and pressure-correction methods applied ensure the incompressibility constraint and mass conservation. The proposed meshless point collocation (MPC) scheme has the following characteristics: (i) it can be applied, in a straightforward manner to: steady, unsteady, internal and external fluid flows in 2D and 3D, (ii) it equally applies to regular an irregular geometries, (iii) a distribution of points is sufficient, no numerical integration in space nor any mesh structure are required, (iv) there is no need for pressure boundary conditions since no pressure constitutive equation is solved, (v) it is quite simple and accurate, (vi) results can be obtained using collocated or semi-staggered nodal distributions, (vii) there is no need to compute the velocity potential nor the unit normal vectors and (viii) there is no need for a curvilinear system of coordinates. Simulations of fluid flow in 2D and 3D for regular and irregular geometries indicate the validity of the proposed methodology.

    AB - We present the Implicit Potential (IPOT) numerical scheme developed in the framework of meshless point collocation. The proposed scheme is used for the numerical solution of the steady state, incompressible Navier-Stokes (N-S) equations in their primitive variable (u-v-w-p) formulation. The governing equations are solved in their strong form using either a collocated or a semi-staggered type meshless nodal configuration. The unknown field functions and derivatives are calculated using the Modified Moving Least Squares (MMLS) interpolation method. Both velocity-correction and pressure-correction methods applied ensure the incompressibility constraint and mass conservation. The proposed meshless point collocation (MPC) scheme has the following characteristics: (i) it can be applied, in a straightforward manner to: steady, unsteady, internal and external fluid flows in 2D and 3D, (ii) it equally applies to regular an irregular geometries, (iii) a distribution of points is sufficient, no numerical integration in space nor any mesh structure are required, (iv) there is no need for pressure boundary conditions since no pressure constitutive equation is solved, (v) it is quite simple and accurate, (vi) results can be obtained using collocated or semi-staggered nodal distributions, (vii) there is no need to compute the velocity potential nor the unit normal vectors and (viii) there is no need for a curvilinear system of coordinates. Simulations of fluid flow in 2D and 3D for regular and irregular geometries indicate the validity of the proposed methodology.

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    KW - Incompressible flow

    KW - Meshless method

    KW - MMLS

    KW - Strong form

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