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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, Georgios ; ; et al in Engineering Analysis with Boundary Elements (2017), 77 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 ... [more ▼] 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. [less ▲] Detailed reference viewed: 31 (2 UL)Numerical studies of magnetic particles concentration in biofluid (blood) under the influence of high gradient magnetic field in microchannel ; Bourantas, Georgios ; et al Scientific Conference (2016, July 15) Detailed reference viewed: 97 (9 UL)Numerical study of magnetic particles concentration in biofluid (blood) under the influence of high gradient magnetic field in microchannel ; Bourantas, Georgios ; et al Scientific Conference (2016, June) A meshless numerical scheme [1] is developed in order to simulate the magnetically mediated separation of biological mixture used in lab-on-chip devices as solid carriers for capturing, transporting and ... [more ▼] A meshless numerical scheme [1] is developed in order to simulate the magnetically mediated separation of biological mixture used in lab-on-chip devices as solid carriers for capturing, transporting and detecting biological magnetic labeled entities [2], as well as for drug delivering, magnetic hyperthermia treatment, magnetic resonance imaging, magnetofection, etc. A modified one-way particle-fluid coupling analysis is considered to model the interaction of the base fluid of the mixture with the distributed particles motion. In details, bulk flow influences particle motion (through a simplified Stokes drag relation), while it is strongly dependent on particle motion through (particle) concentration. Due to the imposed magnetic field stagnation regions are developed, leading to the accumulation of the magnetic labeled species and finally to their collection from the heterogeneous mixture. The role of (i) the intensity of magnetic field and its gradient, (ii) the position of magnetic field, (iii) the magnetic susceptibility of magnetic particles, (iv) the volume concentration of magnetic particles (nanoparticles) and their size, (v) the flow velocity in the magnetic- fluidic interactions and interplay between the magnetophoretic mass transfer and molecular diffusion are thoroughly investigated. Both Newtonian and non-Newtonian blood flow models are considered, along with different expressions for the concentration and numerical results are presented for a wide range of physical parameters (Hartmann number (Ha), Reynolds number (Re)). A comprehensive study investigates their impact on the biomagnetic separation. For verification purposes, the numerical results obtained by the proposed meshless scheme were compared with established numerical results from the literature, being in excellent agreement. [less ▲] Detailed reference viewed: 248 (11 UL)Discretization Correction Particle Strength Exchange (DC PSE) method for Linear Elasticity Bourantas, Georgios ; Bordas, Stéphane Report (2016) Detailed reference viewed: 127 (3 UL)Hybrid mesh/particle meshless method for modeling geological flows with discontinuous transport properties Bourantas, Georgios ; ; van Dam, Tonie et al E-print/Working paper (2016) In the present paper, we introduce the Finite Difference Method-Meshless Method (FDM-MM) in the context of geodynamical simulations. The proposed numerical scheme relies on the well-established FD method ... [more ▼] In the present paper, we introduce the Finite Difference Method-Meshless Method (FDM-MM) in the context of geodynamical simulations. The proposed numerical scheme relies on the well-established FD method along with the newly developed “meshless” method and, is considered as a hybrid Eulerian/Lagrangian scheme. Mass, momentum, and energy equations are solved using an FDM method, while material properties are distributed over a set of markers (particles), which represent the spatial domain, with the solution interpolated back to the Eulerian grid. The proposed scheme is capable of solving flow equations (Stokes flow) in uniform geometries with particles, “sprinkled” in the spatial domain and is used to solve convection- diffusion problems avoiding the oscillation produced in the Eulerian approach. The resulting algebraic linear systems were solved using direct solvers. Our hybrid approach can capture sharp variations of stresses and thermal gradients in problems with a strongly variable viscosity and thermal conductivity as demonstrated through various benchmarking test cases. The present hybrid approach allows for the accurate calculation of fine thermal structures, offering local type adaptivity through the flexibility of the particle method. [less ▲] Detailed reference viewed: 201 (15 UL)A hybrid particle-mesh method for incompressible active polar viscous gels ; Bourantas, Georgios ; et al in Journal of Computational Physics (2015), 291 We present a hybrid particle-mesh method for numerically solving the hydrodynamic equations of incompressible active polar viscous gels. These equations model the dynamics of polar active agents, embedded ... [more ▼] We present a hybrid particle-mesh method for numerically solving the hydrodynamic equations of incompressible active polar viscous gels. These equations model the dynamics of polar active agents, embedded in a viscous medium, in which stresses are induced through constant consumption of energy. The numerical method is based on Lagrangian particles and staggered Cartesian finite-difference meshes. We show that the method is second-order and first-order accurate with respect to grid and time-step sizes, respectively. Using the present method, we simulate the hydrodynamics in rectangular geometries, of a passive liquid crystal, of an active polar film and of active gels with topological defects in polarization. We show the emergence of spontaneous flow due to Fréedericksz transition, and transformation in the nature of topological defects by tuning the activity of the system. [less ▲] Detailed reference viewed: 68 (1 UL)Control of Flame Spray Pyrolysis synthesis of Li4Ti5O12: Experimental and Computational study ; ; Bourantas, Georgios et al Poster (2015, May 14) Lithium titanate (Li4Ti5O12, LTO) is a promising anode material for the next generation of lithium ion batteries. Its physical properties and morphology (which consequently affect its electrochemical ... [more ▼] Lithium titanate (Li4Ti5O12, LTO) is a promising anode material for the next generation of lithium ion batteries. Its physical properties and morphology (which consequently affect its electrochemical performance) highly depend on its synthesis method. Flame spray pyrolysis (FSP) is an attractive process for the controlled one-step synthesis of functional multicomponent oxides from low cost precursors. The main aim of this study is to control the growth process of LTO by FSP in order to maintain the desired particle properties. LTO nanoparticles of different sizes are synthesized by variation of the FSP processing conditions and characterized accordingly. Numerical simulations based on Population Balance Models are also implemented in order to investigate the evolution of primary and agglomerate particle growth. [less ▲] Detailed reference viewed: 261 (1 UL)Hybrid mesh/particle meshless method for geological flows with discontinuous transport properties Bourantas, Georgios ; ; et al Scientific Conference (2015, April 12) Geodynamic modeling is an important branch of Earth Sciences. Direct observation of geodynamic processes is limited in both time and space, while on the other hand numerical methods are capable of ... [more ▼] Geodynamic modeling is an important branch of Earth Sciences. Direct observation of geodynamic processes is limited in both time and space, while on the other hand numerical methods are capable of simulating millions of years in a matter of days on a desktop computer. The model equations can be reduced to a set of Partial Differential Equations with possibly discontinuous coefficients, governing mass, momentum and heat transfer over the domain. Some of the major challenges associated with such simulations are (1) geological time scales, which require long (in physical time) simulations using small time steps; (2) the presence of localization zones over which large gradients are present and which are much smaller than the overall physical dimensions of the computational domain and require much more refined discretization than for the rest of the domain, much like in fracture or shear band mechanics. An added difficulty is that such structures in the solution may appear after long periods of stagnant behaviour; (3) the definition of boundary conditions, material parameters and that of a suitable computational domain in terms of size; (4) a posteriori error estimation, sensitivity analysis and discretization adaptivity for the resulting coupled problem, including error propagation between different unknown fields. Consequently, it is arguable that any suitable numerical methods aimed at the solution of such problems on a large scale must be able to (i) provide ease of discretization refinement, including possible partition of unity enrichment; (ii) offer a large stability domain, so that “large” time steps can be chosen; (iii) ease of parallelization and good scalability. Our approach is to rely on “meshless” methods based on a point collocation strategy for the discretization of the set of PDEs. The method is hybrid Eulerian/Lagrangian, which enables to switch easily between stagnant periods and periods of localization. Mass and momentum equations are solved using a meshless point collocation Eulerian method, while energy equation are solved using a set of particles, distributed over the spatial domain, with the solution interpolated back to the Eulerian grid at every time step. This hybrid approach allows for the accurate calculation of fine thermal structures, through the ease of adaptivity offered by the flexibility of the particle method. The approximation space is constructed using the Discretization Correction Particle Strength Exchange (DC PSE) method. The proposed scheme gives the capability of solving flow equations (Stokes flow) in fully irregular geometries while particles, “sprinkled” in the spatial domain, are used to solve convection-diffusion problems avoiding the oscillation produced in the Eulerian approach. The resulting algebraic linear systems were solved using direct solvers. Our hybrid approach can capture sharp variations of stresses and thermal gradients in problems with a strongly variable viscosity and thermal conductivity as demonstrated through various benchmarking test cases such as the development of Rayleigh-Taylor instabilities, viscous heating and flows with non-Newtonian rheology. [less ▲] Detailed reference viewed: 545 (25 UL)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: 89 (2 UL)MHD natural-convection flow in an inclined square enclosure filled with a micropolar-nanofluid Bourantas, Georgios ; in International Journal of Heat & Mass Transfer (2014) Transient, laminar, natural-convection flow of a micropolar-nanofluid (Al2O3/water) in the presence of a magnetic field in an inclined rectangular enclosure is considered. A meshless point collocation ... [more ▼] Transient, laminar, natural-convection flow of a micropolar-nanofluid (Al2O3/water) in the presence of a magnetic field in an inclined rectangular enclosure is considered. A meshless point collocation method utilizing a velocity-correction scheme has been developed. The governing equations in their velocity–vorticity formulation are solved numerically for various Rayleigh (Ra) and Hartman (Ha) numbers, different nanoparticles volume fractions (φ) and considering different inclination angles and magnetic field directions. The results show that, both, the strength and orientation of the magnetic field significantly affect the flow and temperature fields. For the cases considering herein, experimentally given forms of dynamic viscosity, thermal conductivity and electrical conductivity are utilized. [less ▲] Detailed reference viewed: 86 (0 UL)Solution of Two-dimensional Linear and Nonlinear Unsteady Schrödinger Equation using “Quantum Hydrodynamics” Formulation with a MLPG Collocation Method ; Bourantas, Georgios in Computer Modeling in Engineering & Sciences (2014), 103(1), 49-70 A numerical solution of the linear and nonlinear time-dependent Schrödinger equation is obtained, using the strong form MLPG Collocation method. Schrödinger equation is replaced by a system of coupled ... [more ▼] A numerical solution of the linear and nonlinear time-dependent Schrödinger equation is obtained, using the strong form MLPG Collocation method. Schrödinger equation is replaced by a system of coupled partial differential equa tions in terms of particle density and velocity potential, by separating the real and imaginary parts of a general solution, called a quantum hydrodynamic (QHD) equa tion, which is formally analogous to the equations of irrotational motion in a classical fluid. The approximation of the field variables is obtained with the Moving Least Squares (MLS) approximation and the implicit Crank-Nicolson scheme is used for time discretization. For the two-dimensional nonlinear Schrödinger equation, the lagging of coefficients method has been utilized to eliminate the non-linearity of the corresponding examined problem. A Type-I nodal distribution is used in order to provide convergence for the discrete Laplacian operator used at the governing equation. Numerical results are validated, comparing them with analyti cal and numerical solutions. [less ▲] Detailed reference viewed: 84 (0 UL)Real-time tumor ablation simulation based on the dynamic mode decomposition method Bourantas, Georgios ; ; et al in Medical Physics (2014), 41(5), The Dynamic Mode Decomposition (DMD) method is used to provide a reliable forecasting of tumor ablation treatment simulation in real time, which is quite needed in medical practice. To achieve this, an ... [more ▼] The Dynamic Mode Decomposition (DMD) method is used to provide a reliable forecasting of tumor ablation treatment simulation in real time, which is quite needed in medical practice. To achieve this, an extended Pennes bioheat model must be employed, taking into account both the water evaporation phenomenon and the tissue damage during tumor ablation. [less ▲] Detailed reference viewed: 77 (1 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: 51 (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: 62 (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: 113 (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: 114 (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: 51 (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: 55 (1 UL) |
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