scholarly journals On modelling of thermodynamic interaction of particles suspended in two-dimensional medium

2021 ◽  
Vol 23 (4) ◽  
pp. 444-460
Author(s):  
Aleksei O. Syromyasov ◽  
Yulia V. Ponkratova ◽  
Tatyana V. Menshakova
Keyword(s):  
Heterogeneous Media ◽  
Domain Size ◽  
Analytical Description ◽  
Particle Method ◽  
Numerical Approach ◽  
Multipole Expansion ◽  
Multipole Expansions ◽  
Approximate Boundary Conditions ◽  
Complicated Geometry ◽  
Thermodynamic Processes

Analytical description of temperature distribution in a medium with foreign inclusions is difficult due to the complicated geometry of the problem, so asymptotic and numerical methods are usually used to model thermodynamic processes in heterogeneous media. To be convinced in convergence of these methods the authors consider model problem about two identical round particles in infinite planar medium with temperature gradient which is constant at infinity. Authors refine multipole expansion of the solution obtained earlier by continuing it up to higher powers of small parameter, that is nondimensional radius of thermodynamically interacting particles. Numerical approach to the problem using ANSYS software is described; in particular, appropriate choice of approximate boundary conditions is discussed. Authors ascertain that replacement of infinite medium by finite-sized domain is important source of error in FEM. To find domain boundaries in multiple inclusions’ problem the authors develop “fictituous particle” method; according to it the cloud of particles far from the center of the cloud acts approximately as a single equivalent particle of greater size and so may be replaced by it. Basing on particular quantitative data the dependence of domain size that provides acceptable accuracy on thermal conductivities of medium and of particles is explored. Authors establish series of numerical experiments confirming convergence of multipole expansions method and FEM as well; proximity of their results is illustrated, too.

scholarly journals Lagrangian meshfree finite difference particle method with variable smoothing length for solving wave equations

2018 ◽  
Vol 10 (7) ◽  
pp. 168781401878924 ◽  
Author(s):  
Sheng Wang ◽  
Yong Ou Zhang ◽  
Jing Ping Wu
Keyword(s):  
Finite Difference ◽  
Wave Equations ◽  
Time Integration ◽  
Simple Wave ◽  
Domain Size ◽  
Particle Method ◽  
Computational Time ◽  
Integration Scheme ◽  
Smoothed Particle ◽  
Support Domain

In a Lagrangian meshfree particle-based method, the smoothing length determines the size of the support domain for each particle. Since the particle distribution is irregular and uneven in most cases, a fixed smoothing length sometime brings too much or insufficient neighbor particles for the weight function which reduces the numerical accuracy. In this work, a Lagrangian meshfree finite difference particle method with variable smoothing length is proposed for solving different wave equations. This pure Lagrangian method combines the generalized finite difference scheme for spatial resolution and the time integration scheme for time resolution. The new method is tested via the simple wave equation and the Burgers’ equation in Lagrangian form. These wave equations are widely used in analyzing acoustic and hydrodynamic waves. In addition, comparison with a modified smoothed particle hydrodynamics method named the corrective smoothed particle method is also presented. Numerical experiments show that two kinds of Lagrangian wave equations can be solved well. The variable smoothing length updates the support domain size appropriately and allows the finite difference particle method results to be more accurate than the constant smoothing length. To obtain the same level of accuracy, the corrective smoothed particle method needs more particles in the computation which requires more computational time than the finite difference particle method.

scholarly journals Model of a bilateral Brown-type central pattern generator for symmetric and asymmetric locomotion

2018 ◽  
Vol 119 (3) ◽  
pp. 1071-1083 ◽  
Author(s):  
Anton Sobinov ◽  
Sergiy Yakovenko
Keyword(s):  
Analytical Solution ◽  
Central Pattern Generators ◽  
Analytical Description ◽  
Numerical Approach ◽  
Pattern Generation ◽  
Neural Element ◽  
Steering Control ◽  
Velocity Signal ◽  
Robust Model ◽  
Order Of Magnitude

The coordinated activity of muscles is produced in part by spinal rhythmogenic neural circuits, termed central pattern generators (CPGs). A classical CPG model is a system of coupled oscillators that transform locomotor drive into coordinated and gait-specific patterns of muscle recruitment. The network properties of this conceptual model can be simulated by a system of ordinary differential equations with a physiologically inspired coupling locus of interactions capturing the timing relationship for bilateral coordination of limbs in locomotion. Whereas most similar models are solved numerically, it is intriguing to have a full analytical description of this plausible CPG architecture to illuminate the functionality within this structure and to expand it to include steering control. Here, we provided a closed-form analytical solution contrasted against the previous numerical method. The evaluation time of the analytical solution was decreased by an order of magnitude when compared with the numerical approach (relative errors, <0.01%). The analytical solution tested and supported the previous finding that the input to the model can be expressed in units of the desired limb locomotor speed. Furthermore, we performed parametric sensitivity analysis in the context of controlling steering and documented two possible mechanisms associated with either an external drive or intrinsic CPG parameters. The results identify specific propriospinal pathways that may be associated with adaptations within the CPG structure. The model offered several network configurations that may generate the same behavioral outcomes. NEW & NOTEWORTHY Using a simple process of leaky integration, we developed an analytical solution to a robust model of spinal pattern generation. We analyzed the ability of this neural element to exert locomotor control of the signal associated with limb speeds and tested the ability of this simple structure to embed steering control using the velocity signal in the model’s inputs or within the internal connectivity of its elements.

scholarly journals Coda-wave decorrelation sensitivity kernels in 2-D elastic media: a numerical approach

2020 ◽  
Vol 223 (2) ◽  
pp. 934-943
Author(s):  
Alejandro Duran ◽  
Thomas Planès ◽  
Anne Obermann
Keyword(s):  
Analytical Solution ◽  
Numerical Simulations ◽  
Heterogeneous Media ◽  
Synthetic Data ◽  
Numerical Approach ◽  
Coda Waves ◽  
Coda Wave ◽  
Elastic Media ◽  
S Wave ◽  
Velocity Changes

SUMMARY Probabilistic sensitivity kernels based on the analytical solution of the diffusion and radiative transfer equations have been used to locate tiny changes detected in late arriving coda waves. These analytical kernels accurately describe the sensitivity of coda waves towards velocity changes located at a large distance from the sensors in the acoustic diffusive regime. They are also valid to describe the acoustic waveform distortions (decorrelations) induced by isotropically scattering perturbations. However, in elastic media, there is no analytical solution that describes the complex propagation of wave energy, including mode conversions, polarizations, etc. Here, we derive sensitivity kernels using numerical simulations of wave propagation in heterogeneous media in the acoustic and elastic regimes. We decompose the wavefield into P- and S-wave components at the perturbation location in order to construct separate P to P, S to S, P to S and S to P scattering sensitivity kernels. This allows us to describe the influence of P- and S-wave scattering perturbations separately. We test our approach using acoustic and elastic numerical simulations where localized scattering perturbations are introduced. We validate the numerical sensitivity kernels by comparing them with analytical kernel predictions and with measurements of coda decorrelations on the synthetic data.

A New Particle Method for Two-Phase Flows With Large Density Difference

2014 ◽  
Author(s):  
C. G. Koh ◽  
M. Luo ◽  
M. Gao ◽  
W. Bai
Keyword(s):  
Potential Problem ◽  
Taylor Series Expansion ◽  
Particle Method ◽  
Numerical Approach ◽  
Coefficient Matrix ◽  
Fluid Interfaces ◽  
Two Phase Flows ◽  
Two Phase ◽  
Selection Scheme ◽  
Spatial Derivatives

A new numerical approach for solving two-phase flows is presented in the framework of the recently developed Consistent Particle Method (CPM). The spatial derivatives along fluid interfaces where abrupt discontinuity of fluid density exists are computed by including neighbor particles of another fluid and applying Taylor series expansion on specific pressure energy. In addition, a new h-adaptive particle selection scheme is proposed to overcome the potential problem of ill-conditioned coefficient matrix of PPE when particles are sparse and non-uniformly spaced. Using this method, water-air sloshing in a closed rectangular tank is studied with experimental validation.

A NUMERICALLY CONSISTENT MULTIPHASE POISEUILLE FLOW COMPUTATION BY A NEW PARTICLE METHOD

2015 ◽  
Vol 76 (8) ◽  
Author(s):  
K. C. Ng ◽  
Y. H. Hwang ◽  
T. W. H. Sheu ◽  
M. Z. Yusoff
Keyword(s):  
Fluid Flow ◽  
Poiseuille Flow ◽  
Particle Method ◽  
Numerical Approach ◽  
Particle Methods ◽  
Diffusion Term ◽  
Flow Solver ◽  
Mesh Free ◽  
Consistent Method ◽  
Moving Particle

Recently, there is a rising interest in simulating fluid flow by using particle methods, which are mesh-free. However, the viscous stresses (or diffusion term) appeared in fluid flow governing equations are commonly expressed as the second-order derivatives of flow velocities, which are usually discretized by an inconsistent numerical approach in a particle-based method. In this work, a consistent method in discretizing the diffusion term is implemented in our particle-based fluid flow solver (namely the Moving Particle Pressure Mesh (MPPM) method). The new solver is then used to solve a multiphase Poiseuille flow problem. The error is decreasing while the grid is refined, showing the consistency of our current numerical implementation.

scholarly journals Model of a bilateral Brown-type central pattern generator for symmetric and asymmetric locomotion

2017 ◽  
Author(s):  
Anton Sobinov ◽  
Sergiy Yakovenko
Keyword(s):  
Analytical Solution ◽  
Central Pattern Generators ◽  
Analytical Description ◽  
Numerical Approach ◽  
Pattern Generation ◽  
Neural Element ◽  
Steering Control ◽  
Velocity Signal ◽  
Robust Model ◽  
Order Of Magnitude

AbstractThe coordinated activity of muscles is produced in part by spinal rhythmogenic neural circuits, termed central pattern generators (CPGs). A classical CPG model is a system of coupled oscillators that transform locomotor drive into coordinated and gait-specific patterns of muscle recruitment. The network properties of this conceptual model can be simulated by a system of ordinary differential equations with a physiologically-inspired coupling locus of interactions capturing the timing relationship for bilateral coordination of limbs in locomotion. While most similar models are solved numerically, it is intriguing to have a full analytical description of this plausible CPG architecture to illuminate the functionality within this structure and to expand it to include steering control. Here, we provided a closed-form analytical solution contrasted against the previous numerical method. The computational load of the analytical solution was decreased by order of magnitude when compared to the numerical approach (relative errors, <0.01%). The analytical solution tested and supported the previous finding that the input to the model can be expressed in units of the desired limb locomotor speed. Furthermore, we performed parametric sensitivity analysis in the context of controlling steering and documented two possible mechanisms associated with either an external drive or intrinsic CPG parameters. The results identify specific propriospinal pathways that may be associated with adaptations within the CPG structure. The model offered several network configurations that may generate the same behavioral outcomes.New & NoteworthyUsing a simple process of leaky integration, we developed an analytical solution to a robust model of spinal pattern generation. We analyzed the ability of this neural element to exert locomotor control of the signal associated with limb speeds and tested the ability of this simple structure to embed steering control using the velocity signal in the model’s inputs or within the internal connectivity of its elements.

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