Using DC PSE operator discretization in Eulerian meshless collocation methods improves their robustness in complex geometries

Bourantas, George C.; Cheeseman, Bevan L.; Ramaswamy, Rajesh; Sbalzarini, Ivo F.

doi:10.1016/j.compfluid.2016.06.010

Cited by 33 publications

(38 citation statements)

References 45 publications

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“…The intermediate velocity, U * , computed from the Poisson equations for the velocity components (Equations (28) and 29), did not satisfy the continuity equation. Therefore, the velocity field was updated, using the velocity correction method [47,48]. Assuming that the velocity correction (∂U) is irrotational, a correction potential, ψ n+1 , can be defined as ∇ψ n+1 = ∂U n+1 .…”

Section: Methodsmentioning

confidence: 99%

“…DC PSE was originally introduced as a Lagrangian particle-based solution method. The method has been reformulated [47] to numerically solve partial differential equations in Eulerian frameworks. The DC PSE interpolation method relies on Particle Strength Exchange (PSE) operators, i.e., kernel functions that approximate differential operators which conserve particle strength in particle-particle interactions.…”

mentioning

confidence: 99%

“…The PSE method was first introduced by Degond and Mas-Gallic [50] for diffusion and convection-diffusion problems, while Eldredge et al [51] extended the method to compute approximations of arbitrary derivatives. Details on the DC PSE method can be found in [47].…”

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confidence: 99%

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Modeling the Natural Convection Flow in a Square Porous Enclosure Filled with a Micropolar Nanofluid under Magnetohydrodynamic Conditions

et al. 2020

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The laminar, natural convective flow of a micropolar nanofluid in the presence of a magnetic field in a square porous enclosure was studied. The micropolar nanofluid is considered to be an electrically conductive fluid. The governing equations of the flow problem are the conservation of mass, energy, and linear momentum, as well as the angular momentum and the induction equations. In the proposed model, the Darcy–Brinkman momentum equations with buoyancy and advective inertia are used. Experimentally obtained forms of the dynamic viscosity, the thermal conductivity, and the electric conductivity are employed. A meshless point collocation method has been applied to numerically solve the flow and transport equations in their vorticity-stream function formulation. The effects of characteristic dimensionless parameters, such as the Rayleigh and Hartmann numbers, for a range of porosity and solid volume fraction of Al2O3 particles in a water-based micropolar nanofluid on the flow and heat transfer in the cavity are investigated. The results indicate that the intensity of the magnetic field significantly affects both the flow and the temperature distributions. Moreover, the addition of nanoparticles deteriorates the heat-transfer efficiency under specific conditions.

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Section: Methodsmentioning

confidence: 99%

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confidence: 99%

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Modeling the Natural Convection Flow in a Square Porous Enclosure Filled with a Micropolar Nanofluid under Magnetohydrodynamic Conditions

et al. 2020

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“…A number of interpolating/approximating methods are described in the meshless literature [14,15]. Among them, the most widely used are the Moving Least Squares (MLS) [16], Modified Moving Least Squares (MMLS) [17], Radial Basis Functions (RBF) [15], Discretization Corrected Particle Strength Exchange (DC PSE) [18] and Smoothed Particle Hydrodynamics (SPH) [14]. Each one of these approximation methods can be used for projecting field values from markers to Eulerian grid nodes.…”

Section: Meshless Approximation Methodsmentioning

confidence: 99%

A Flux-Conservative Finite Difference Scheme for the Numerical Solution of the Nonlinear Bioheat Equation

Bourantas

Joldes

Wittek

et al. 2018

Computational Biomechanics for Medicine

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We present a flux-conservative finite difference (FCFD) scheme for solving the nonlinear (bio)heat transfer in living tissue. The proposed scheme deals with steep gradients in the material properties for malignant and healthy tissues. The method applies directly on the raw medical image data without the need for sophisticated image analysis algorithms to define the interface between tumour and healthy tissues.We extend the classical finite difference (FD) method to cases with high discontinuities in the material properties. We apply meshless kernels, widely used in Smoothed Particle Hydrodynamics (SPH) method, to approximate properties in the off-grid points introduced by the flux conservative differential operators. The meshless kernels can accurately capture the steep gradients and provide accurate approximations. We solve the governing equations by using an explicit solver. The relatively small time-step applied is counterbalanced by the small computation effort required at each time step of the proposed scheme. The FCFD method can accurately compute the numerical solution of the bioheat equation even when noise from the image acquisition is present.Results highlight the applicability of the method and its ability to solve tumor ablation simulations directly on the raw image data, without the need to define the interface between malignant and healthy tissues (segmentation) or meshing.

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“…The DC PSE method originated as a Lagrangian particle-based numerical method [34] and is based on Particle Strength Exchange (PSE) operators. To solve PDEs using the DC PSE meshless method, the authors in [35] reformulated the Lagrangian DC PSE method to work in the Eulerian framework. For completion, the PSE operators and the DC PSE method are described below.…”

Section: Discretization Corrected Particle Strength Exchange (Dc Pse)mentioning

confidence: 99%

An Explicit Meshless Point Collocation Solver for Incompressible Navier-Stokes Equations

Bourantas

Zwick

Joldes

et al. 2019

Fluids

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We present a strong form, meshless point collocation explicit solver for the numerical solution of the transient, incompressible, viscous Navier-Stokes (N-S) equations in two dimensions. We numerically solve the governing flow equations in their stream function-vorticity formulation. We use a uniform Cartesian embedded grid to represent the flow domain. We compute the spatial derivatives using the Meshless Point Collocation (MPC) method. We verify the accuracy of the numerical scheme for commonly-used benchmark problems including lid-driven cavity flow, flow over a backward-facing step and vortex shedding behind a cylinder. We have examined the applicability of the proposed scheme by considering flow cases with complex geometries, such as flow in a duct with cylindrical obstacles, flow in a bifurcated geometry, and flow past complex-shaped obstacles. Our method offers high accuracy and excellent computational efficiency as demonstrated by the verification examples, while maintaining a stable time step comparable to that used in unconditionally stable implicit methods.

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Using DC PSE operator discretization in Eulerian meshless collocation methods improves their robustness in complex geometries

Cited by 33 publications

References 45 publications

Modeling the Natural Convection Flow in a Square Porous Enclosure Filled with a Micropolar Nanofluid under Magnetohydrodynamic Conditions

Modeling the Natural Convection Flow in a Square Porous Enclosure Filled with a Micropolar Nanofluid under Magnetohydrodynamic Conditions

A Flux-Conservative Finite Difference Scheme for the Numerical Solution of the Nonlinear Bioheat Equation

An Explicit Meshless Point Collocation Solver for Incompressible Navier-Stokes Equations

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