Numerical studies of magnetic particles concentration in biofluid (blood) under the influence of high gradient magnetic field in microchannel

Scientific Conference (2016, July 15)

Hybrid mesh/particle meshless method for modeling geological flows with discontinuous transport properties

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 ▲]

A hybrid particle-mesh method for incompressible active polar viscous gels

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 ▲]

Hybrid mesh/particle meshless method for geological flows with discontinuous transport properties

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 ▲]

MHD natural-convection flow in an inclined square enclosure filled with a micropolar-nanofluid

in International Journal of Heat and 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 ▲]

Real-time tumor ablation simulation based on the dynamic mode decomposition method

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 ▲]

Numerical Solution of Non-Isothermal Fluid Flows Using Local Radial Basis Functions (LRBF) Interpolation and a Velocity-Correction Method

in Computer Modeling in Engineering and 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 ▲]

Adaptive support domain implementation on the Moving Least Squares approximation for Mfree methods applied on elliptic and parabolic PDE problems using strong-form description

in Computer Modeling in Engineering and 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 ▲]

Computational representation and hemodynamic characterization of in vivo acquired severe stenotic renal artery geometries using turbulence modeling

in Medical Engineering and 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 ▲]