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Transient thermal conduction with variable conductivity using the Meshless Local Petrov–Galerkin method ; Bourantas, Georgios ; et al in Applied Mathematics and Computation (2015) A numerical solution of the transient heat conduction problem with spatiotemporally vari- able conductivity in 2D space is obtained using the Meshless Local Petrov–Galerkin (MLPG) method. The ... [more ▼] A numerical solution of the transient heat conduction problem with spatiotemporally vari- able conductivity in 2D space is obtained using the Meshless Local Petrov–Galerkin (MLPG) method. The approximation of the field variables is performed using Moving Least Squares (MLS) interpolation. The accuracy and the efficiency of the MLPG schemes are investigated through variation of (i) the domain resolution, (ii) the order of the basis functions, (iii) the shape of the integration site around each node, (iv) the conductivity range, and (v) the volumetric heat capacity range. Steady-state boundary conditions of the essential type are assumed. The results are compared with those calculated by a typical Finite Element method. Specific rectangular-type integration sites are introduced during both steady-state and transient MLPG integration, in order to provide complete surface coverage of the domain without overlapping, and the accuracy of the method is demonstrated in all cases studied. Computational efficiency is also investigated with this MLPG method and found to be slower than FE methods during construction stage, but it clearly surpasses that of FEM approaches during the solution stage on a wide parameter range. [less ▲] Detailed reference viewed: 126 (3 UL)Localized meshless point collocation method for time-dependent magnetohydrodynamics flow through pipes under a variety of wall conductivity conditions ; Bourantas, Georgios ; in Computational Mechanics (2011), 47(2), 137-159 In this article a numerical solution of the time dependent, coupled system equations of magnetohydrody- namics (MHD) flow is obtained, using the strong-form local meshless point collocation (LMPC) method ... [more ▼] In this article a numerical solution of the time dependent, coupled system equations of magnetohydrody- namics (MHD) flow is obtained, using the strong-form local meshless point collocation (LMPC) method. The approxima- tion of the field variables is obtained with the moving least squares (MLS) approximation. Regular and irregular nodal distributions are used. Thus, a numerical solver is developed for the unsteady coupled MHD problems, using the collo- cation formulation, for regular and irregular cross sections, as are the rectangular, triangular and circular. Arbitrary wall conductivity conditions are applied when a uniform mag- netic field is imposed at characteristic directions relative to the flow one. Velocity and induced magnetic field across the section have been evaluated at various time intervals for sev- eral Hartmann numbers (up to 105) and wall conductivities. The numerical results of the strong-form MPC method are compared with those obtained using two weak-form mesh- less methods, that is, the local boundary integral equation (LBIE) meshless method and the meshless local Petrov– Galerkin (MLPG) method, and with the analytical solutions, where they are available. Furthermore, the accuracy of the method is assessed in terms of the error norms L 2 and L ∞ , the number of nodes in the domain of influence and the time step length depicting the convergence rate of the method. Run time results are also presented demonstrating the efficiency and the applicability of the method for real world problems. [less ▲] Detailed reference viewed: 90 (0 UL)Numerical Solution of Non-Isothermal Fluid Flows Using Local Radial Basis Functions (LRBF) Interpolation and a Velocity-Correction Method Bourantas, Georgios ; ; et al in Computer Modeling in Engineering & Sciences (2010), 64(2), 187-212 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 ... [more ▼] 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 sta- bility of the proposed scheme are demonstrated through three representative, well known and established benchmark problems. Results are presented for high values of the characteristics non-dimensional numbers of the flow, that is, the Reynolds, the Rayleigh and the Richardson number [less ▲] Detailed reference viewed: 72 (0 UL)Meshfree Point Collocation Schemes for 2D Steady State Incompressible Navier-Stokes Equations in Velocity-Vorticity Formulation for High Values of Reynolds Number Bourantas, Georgios ; ; 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 ▲] Detailed reference viewed: 128 (7 UL)Adaptive support domain implementation on the Moving Least Squares approximation for Mfree methods applied on elliptic and parabolic PDE problems using strong-form description Bourantas, Georgios ; ; in Computer Modeling in Engineering & Sciences (2009), 43 The extent of application of meshfree methods based on point collocation (PC) techniques with adaptive support domain for strong form Partial Differential Equations (PDE) is investigated. The basis ... [more ▼] The extent of application of meshfree methods based on point collocation (PC) techniques with adaptive support domain for strong form Partial Differential Equations (PDE) is investigated. The basis functions are constructed using the Moving Least Square (MLS) approximation. The weak-form description of PDEs is used in most MLS methods to circumvent problems related to the increased level of resolution necessary near natural (Neumann) boundary conditions (BCs), dislocations, or regions of steep gradients. Alternatively, one can adopt Radial Basis Function (RBF) approximation on the strong-form of PDEs using meshless PC methods, due to the delta function behavior (exact solution on nodes). The present approach is one of the few successful attempts of using MLS approximation [Atluri, Liu, and Han (2006), Han, Liu, Rajendran and Atluri (2006), Atluri and Liu (2006)] instead of RBF approximation for the meshless PC method using strong-form description. To increase the accuracy of the MLS interpolation method and its robustness in problems with natural BCs, a suitable support domain should be chosen in order to ensure an optimized area of coverage for interpolation. To this end, the basis functions are constructed using two different approaches, pertinent to the dimension of the support domain. On one hand, a compact form for the support domain is retained by keeping its radius constant. On the other hand, one can control the number of neighboring nodes as the support domain of each point. The results show that some inaccuracies are present near the boundaries using the first approach, due to the limited number of nodes belonging to the support domain, which results in failed matrix inversion. Instead, the second approach offers capability for fully matrix inversion under many (if not all) circumstances, resulting in basis functions of increased accuracy and robustness. This PC method, applied along with an intelligent adaptive refinement, is demonstrated for elliptic and for parabolic PDEs, related to many flow and mass transfer problems. [less ▲] Detailed reference viewed: 132 (4 UL)An accurate, stable and efficient domain-type meshless method for the solution of MHD flow problems Bourantas, Georgios ; ; 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 ▲] Detailed reference viewed: 90 (1 UL)Computational representation and hemodynamic characterization of in vivo acquired severe stenotic renal artery geometries using turbulence modeling ; ; Bourantas, Georgios et al in Medical Engineering & Physics (2008), 30(5), 647-660 The present study reports on computational fluid dynamics in the case of severe renal artery stenosis (RAS). An anatomically realistic model of a renal artery was reconstructed from CT scans, and used to ... [more ▼] The present study reports on computational fluid dynamics in the case of severe renal artery stenosis (RAS). An anatomically realistic model of a renal artery was reconstructed from CT scans, and used to conduct CFD simulations of blood flow across RAS. The recently developed Shear Stress Transport turbulence model was pivotally applied in the simulation of blood flow in the region of interest. Blood flow was studied in vivo under the presence of RAS and subsequently in simulated cases before the development of RAS, and after endovascular stent implantation. The pressure gradients in the RAS case were many orders of magnitude larger than in the healthy case. The presence of RAS increased flow resistance, which led to considerably lower blood flow rates. A simulated stent in place of the RAS decreased the flow resistance at levels proportional to, and even lower than, the simulated healthy case without the RAS. The wall shear stresses, differential pressure profiles, and net forces exerted on the surface of the atherosclerotic plaque at peak pulse were shown to be of relevant high distinctiveness, so as to be considered potential indicators of hemodynamically significant RAS. [less ▲] Detailed reference viewed: 115 (1 UL) |
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