References of "Loukopoulos, Vasilios"
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See detailMeshfree Point Collocation Schemes for 2D Steady State Incompressible Navier-Stokes Equations in Velocity-Vorticity Formulation for High Values of Reynolds Number
Bourantas, Georgios UL; Skouras, Eugene; Loukopoulos, Vasilios et al

in Computer Modeling in Engineering & Sciences (2010), 59(1), 31-63

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 ... [more ▼]

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 conjunc- tion with the general framework of the point collocation method. Computations are obtained for regular and irregular nodal distributions, stressing the positivity con- ditions 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 established benchmark problems. The numerical scheme was also applied to a case with irregular geometry for marginally high Reynolds numbers [less ▲]

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See detailAn accurate, stable and efficient domain-type meshless method for the solution of MHD flow problems
Bourantas, Georgios UL; Skouras, Eugene; Loukopoulos, Vasilios et al

in Journal of Computational Physics (2009), 228

The aim of the present paper is the development of an efficient numerical algorithm for the solution of magnetohydrodynamics flow problems for regular and irregular geometries subject to Dirichlet ... [more ▼]

The aim of the present paper is the development of an efficient numerical algorithm for the solution of magnetohydrodynamics flow problems for regular and irregular geometries subject to Dirichlet, Neumann and Robin boundary conditions. Toward this, the meshless point collocation method (MPCM) is used for MHD flow problems in channels with fully insulating or partially insulating and partially conducting walls, having rectangular, circu- lar, elliptical or even arbitrary cross sections. MPC is a truly meshless and computationally efficient method. The maximum principle for the discrete harmonic operator in the mesh- free point collocation method has been proven very recently, and the convergence proof for the numerical solution of the Poisson problem with Dirichlet boundary conditions have been attained also. Additionally, in the present work convergence is attained for Neumann and Robin boundary conditions, accordingly. The shape functions are constructed using the Moving Least Squares (MLS) approximation. The refinement procedure with meshless methods is obtained with an easily handled and fully automated manner. We present results for Hartmann number up to 105 . The numerical evidences of the proposed meshless method demonstrate the accuracy of the solutions after comparing with the exact solution and the conventional FEM and BEM, for the Dirichlet, Neumann and Robin boundary con- ditions of interior problems with simple or complex boundaries. [less ▲]

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