Particle Strength Exchange Method Research Articles

Integrating discrete sub-grid filters with discretization-corrected particle strength exchange method for high Reynolds number flow simulations

Integrating discrete sub-grid filters with discretization-corrected particle strength exchange method for high Reynolds number flow simulations

Wall-bounded flow simulation on vortex dynamics

Vortical flow animation has attracted considerable attention within the realm of computer graphics. Given that boundaries are the source of vorticity, we introduce a novel approach for the wall-bounded flow simulation in the vortex dynamics framework. We enhance the traditional Lagrangian vortex particle method in terms of boundary treatment and viscosity computation for boundary layer to furnish support for the simulation of the vortex shedding phenomenon behind the moving solids. We extend the boundary treatment strategy based on the idea of vortex generation with a reasonable placement algorithm for the generated vortex element to better satisfy the impermeability of solids. Furthermore, we modify the particle strength exchange method at solid boundaries to capture momentum transfer of moving solids. We demonstrate the efficacy of our approach by simulating a series of wall-bounded flows, such as the wake behind a delta wing and the vortex shedding behind the rotating sphere.

Entropically damped artificial compressibility for the discretization corrected particle strength exchange method in incompressible fluid mechanics

We present a consistent mesh-free numerical scheme for solving the incompressible Navier–Stokes equations. Our method is based on entropically damped artificial compressibility for imposing the incompressibility constraint explicitly, and the Discretization-Corrected Particle Strength Exchange (DC-PSE) method to consistently discretize the differential operators on mesh-free particles. We further couple our scheme with Brinkman penalization to solve the Navier–Stokes equations in complex geometries. The method is validated using the 3D Taylor–Green vortex flow and the lid-driven cavity flow problem in 2D and 3D, where we also compare our method with hr-SPH and report better accuracy for DC-PSE. In order to validate DC-PSE Brinkman penalization, we study flow past obstacles, such as a cylinder, and report excellent agreement with previous studies.

An immersed boundary vector potential‐vorticity meshless solver of the incompressible Navier–Stokes equation

AbstractWe present a strong form meshless solver for numerical solution of the nonstationary, incompressible, viscous Navier–Stokes equations in two (2D) and three dimensions (3D). We solve the flow equations in their stream function‐vorticity (in 2D) and vector potential‐vorticity (in 3D) formulation, by extending to 3D flows the boundary condition‐enforced immersed boundary method, originally introduced in the literature for 2D problems. We use a Cartesian grid, uniform or locally refined, to discretize the spatial domain. We apply an explicit time integration scheme to update the transient vorticity equations, and we solve the Poisson type equation for the stream function or vector potential field using the meshless point collocation method. Spatial derivatives of the unknown field functions are computed using the discretization‐corrected particle strength exchange method. We verify the accuracy of the proposed numerical scheme through commonly used benchmark and example problems. Excellent agreement with the data from the literature was achieved. The proposed method was shown to be very efficient, having relatively large critical time steps.

A Ship Firefighting Training Simulator with Physics-Based Smoke

Under the current background of navigation education, students generally lack a comprehensive grasp of ship firefighting equipment’s operation. Therefore, we develop a novel ship firefighting training simulator with a multi-sensory human–computer interaction function for teaching and training marine students. In the simulator, we consider a container ship of 1.8w containers as the prototype ship, and the entire ship models are built using three-dimensional modeling technology. We design various interactive modes and realize a full-process operation simulation of several standard ship firefighting equipment. Furthermore, we propose a purely Lagrangian vortex dynamics framework to simulate smoke and flame in fire scenarios. In this framework, we model fluids using velocity and vorticity fields discretized on discrete vortex segments. The main components of the framework include a stable geometric stretching solution and particle strength exchange method for solving the diffusion term. The simulation results show that the simulator has good behavioral realism and scene immersion and can be applied to ship firefighting training. To the best of our knowledge, this is the first study on real-time smoke simulation using a physics-based method in a firefighting training simulator.

A Particle Strength Exchange Method for Metal Removal in Laser Drilling

A meshfree Particle Strength Exchange (PSE) method is developed for metal removal in a simplified laser drilling problem. To this end, the problem of transient state heat transfer is solved by exerting a static laser beam with a Gaussian intensity distribution, as the external heat source. The proposed PSE scheme is a fully Lagrangian approach, which is straightforward to implement as compared to alternative meshfree methods currently adopted in the state of the art. The performance of the PSE method in solving the heat transfer problem at hand is assessed through a case-study on single-pulse laser heating of a metal workpiece. The simulation results are finally verified against both numerical and experimental data available in the literature, demonstrating the suitability of the proposed approach in addressing the thermal issues of complex manufacturing processes.

A self-regularising DVM–PSE method for the modelling of diffusion in particle methods

The modelling of diffusive terms in particle methods is a delicate matter and several models have been proposed in the literature. The Diffusion Velocity Method (DVM) consists in rewriting these terms in an advective way, thus defining a so-called diffusion velocity. In addition to the actual velocity, it is used to compute the particles displacement. On the other hand, the well-known and commonly used Particle Strength Exchange method (PSE) uses an approximation of the Laplacian operator in order to model diffusion. This approximation is based on an exchange of particles strength.Although DVM is particularly well suited to particle methods since it preserves their Lagrangian aspect, its major drawback stems in the fact that it suffers from severe singular behaviours. This paper intends to give insights and ideas for coping with these issues, based on an exact decomposition of the diffusion coefficient allowing a hybrid DVM–PSE treatment of diffusive terms.

A model to simulate the oxygen distribution in hypoxic tumors for different vascular architectures

As hypoxic cells are more resistant to photon radiation, it is desirable to obtain information about the oxygen distribution in tumors prior to the radiation treatment. Noninvasive techniques are currently not able to provide reliable oxygenation maps with sufficient spatial resolution; therefore mathematical models may help to simulate microvascular architectures and the resulting oxygen distributions in the surrounding tissue. Here, the authors present a new computer model, which uses the vascular fraction of tumor voxels, in principle measurable noninvasively in vivo, as input parameter for simulating realistic PO2 histograms in tumors, assuming certain 3D vascular architectures. Oxygen distributions were calculated by solving a reaction-diffusion equation in a reference volume using the particle strength exchange method. Different types of vessel architectures as well as different degrees of vascular heterogeneities are considered. Two types of acute hypoxia (ischemic and hypoxemic) occurring additionally to diffusion-limited (chronic) hypoxia were implemented as well. No statistically significant differences were observed when comparing 2D- and 3D-vessel architectures (p>0.79 in all cases) and highly heterogeneously distributed linear vessels show good agreement, when comparing with published experimental intervessel distance distributions and PO2 histograms. It could be shown that, if information about additional acute hypoxia is available, its contribution to the hypoxic fraction (HF) can be simulated as well. Increases of 128% and 168% in the HF were obtained when representative cases of ischemic and hypoxemic acute hypoxia, respectively, were considered in the simulations. The presented model is able to simulate realistic microscopic oxygen distributions in tumors assuming reasonable vessel architectures and using the vascular fraction as macroscopic input parameter. The model may be used to generate PO2 histograms, which are needed as input in models predicting the radiation response of hypoxic tumors.

Evaluation of Grid-Based and Grid-Free Methods to Model Microchannel Transport-Reaction

The goal of this paper is to investigate the spectral element method (SEM), a grid-based computational approach, and the grid-free particle strength exchange method (PSEM) for solving the advection-diffusion-reaction equation in a microfluidic channel. We identify the dimensionless parameter regimes at which each algorithm provides a satisfactory solution in terms of accuracy and computational time. We also compare the velocity field computed in microchannel geometries for nonzero and zero Reynolds numbers by solving the full Navier--Stokes equations with the SEM and solving the inertia-free Stokes equations with the boundary element method, which does not require an internal mesh. The methods discussed may be utilized in any appropriate combination to solve high and low Peclet number and zero and nonzero Reynolds number transport problems to allow fast, accurate evaluation of a binding reaction between two species. We show that the grid-free particle and boundary element methods are suitable for solving ...

An assessment of particle methods for approximating anisotropic dispersion

SUMMARYWe derive a smoothed particle hydrodynamics (SPH) approximation for anisotropic dispersion that only depends upon the first derivative of the kernel function and study its numerical properties. In addition, we compare the performance of the newly derived SPH approximation versus an implementation of the particle strength exchange (PSE) method and a standard finite volume method for simulating multiple scenarios defined by different combinations of physical and numerical parameters. We show that, for regularly spaced particles, given an adequate selection of numerical parameters such as kernel function and smoothing length, the new SPH approximation is comparable with the PSE method in terms of convergence and accuracy and similar to the finite volume method. On other hand, the performance of both particle methods (SPH and PSE) decreases as the degree of disorder of the particle increases. However, we demonstrate that in these situations the accuracy and convergence properties of both particle methods can be improved by an adequate choice of some numerical parameters such as kernel core size and kernel function. Copyright © 2012 John Wiley & Sons, Ltd.

Analysis of Reynolds number effects on bridge deck sections by the PSE method

ABSTRACT Reynolds numbers play an important role in fluid dynamics, because flow separations and reattachments are often Reynolds-number dependent, even if the bodies have sharp edges. To satisfy Reynolds scaling in experiments, the model scale can be very large. Computational fluid dynamics (CFD) provides an interesting alternative to wind tunnel tests, especially when Reynolds effects have to be assessed for a design stage. In this paper, the particle strength exchange (PSE) of vortex methods is introduced for assessing Reynolds number effects on bridge deck cross-sections. For this purpose, this study analyses how the aerodynamic forces of two different bridges sections are influenced by these effects. The computation results with PSE are compared with wind tunnel tests. The relation between Strouhal numbers and Reynolds numbers are also analyzed and compared with experimental results. All the results show that the particle strength exchange method can be efficiently used to calculate Reynolds effects on 2-dimensional bridge deck sections.

Analysis of Reynolds number effects on bridge deck sections by the PSE method

ABSTRACT Reynolds numbers play an important role in fluid dynamics, because flow separations and reattachments are often Reynolds-number dependent, even if the bodies have sharp edges. To satisfy Reynolds scaling in experiments, the model scale can be very large. Computational fluid dynamics (CFD) provides an interesting alternative to wind tunnel tests, especially when Reynolds effects have to be assessed for a design stage. In this paper, the particle strength exchange (PSE) of vortex methods is introduced for assessing Reynolds number effects on bridge deck cross-sections. For this purpose, this study analyses how the aerodynamic forces of two different bridges sections are influenced by these effects. The computation results with PSE are compared with wind tunnel tests. The relation between Strouhal numbers and Reynolds numbers are also analyzed and compared with experimental results. All the results show that the particle strength exchange method can be efficiently used to calculate Reynolds effects on 2-dimensional bridge deck sections.

Study of water waves with submerged obstacles using a vortex method with Helmholtz decomposition

AbstractThe present study develops a 2‐D numerical scheme that combines the vortex method and the boundary integral method by a Helmholtz decomposition to investigate the interaction of water waves with submerged obstacles. Viscous effects and generation of vorticity on the free surface are neglected. The second kind of Fredholm integral equations that govern the strengths of vortex sheets along boundaries are solved iteratively. Vorticity is convected and diffused in the fluid via a Lagrangian vortex (blob) method with varying cores, using the particle strength exchange method for diffusion, with particle redistribution. A grid‐convergence study of the numerical method is reported. The inviscid part of the method and the simulation of the free‐surface motion are tested using two calculations: solitary wave propagation in a uniform channel and a moving line vortex in the fluid. Finally, the full model is verified by simulating periodic waves travelling over a submerged rectangular obstacle using nonuniform vortex blobs with a mapping of the redistribution lattice. Overall, the numerical model predicts the vortices' evolution and the free‐surface motion reasonably well. Copyright © 2008 John Wiley & Sons, Ltd.

Simulation of anisotropic diffusion by means of a diffusion velocity method

An alternative method to the Particle Strength Exchange method for solving the advection–diffusion equation in the general case of a non-isotropic and non-uniform diffusion is proposed. This method is an extension of the diffusion velocity method. It is shown that this extension is quite straightforward due to the explicit use of the diffusion flux in the expression of the diffusion velocity. This approach is used to simulate pollutant transport in groundwater and the results are compared to those of the PSE method presented in an earlier study by Zimmermann et al.

Comparisons of Two Viscous Models for Vortex Methods in Parallel Computation.

A parallel implementation of vortex methods dealing with unsteady viscous flows on a distributed computing environment through Parallel Virtual Machine (PVM) is reported in this paper. We test the recently developed diffusion schemes of vortex methods. We directly compare the particle strength exchange method with the vorticity distribution method in terms of their accuracy and computational efficiency. Comparisons between both viscous models described are presented for the impulsively started flows past a circular cylinder at Reynolds number 60. We also present the comparisons of both methods in their parallel computation efficiency and speed-up ratio.

Simulation of Pollutant Transport Using a Particle Method

A Lagrangian scheme is presented for the two-dimensional simulation of pollutant transport in a porous medium. The anisotropic extension of the particle strength exchange method is implemented to describe the diffusive–dispersive process. By applying the scheme to a benchmark problem with an analytical solution, the method is shown to be accurate and stable even in the limiting cases of vanishing diffusion–dispersion coefficients and high anisotropy ratios. The scheme is shown to perform well with spatially variable velocity fields also.

Treatment of a Neumann boundary condition by a Particle Strength Exchange method

Particle Methods with an integral approximation of the diusion operator have been successfully developed among others by G.H. Cottet, P. Degond, S. Mas-Gallic and P.A. Raviart for a domain without boundary condition and by S. Mas-Gallic with a planar boundary. We extend in this paper the designing of the integral approximation of the diusion operator that can be used in a straightforward way for a wider class of domain geometries. In such methods the fluid is represented by a combination of Dirac measures or particles which travel according to the fluid velocity. The problem was then to nd an approximation of the second order dierential operator in a way that could be treated by a Lagrangian method. This gave rise to the work of Raviart’s team (4, 5, 6, 13) where the second order dierential operator is approximated by an integral operator. To include the treatment of the diusion, we allocate each particle a weight which varies according to a rst order dierential equation in time. In the Particle Strength Exchange Method onR 2 , the Laplacian operator is approximated by an integral