numerical solutions
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Materials ◽  
2022 ◽  
Vol 15 (2) ◽  
pp. 641
Wang Huang ◽  
Jianjun Yang ◽  
Jan Sladek ◽  
Vladimir Sladek ◽  
Pihua Wen

The modulus of elasticity of some materials changes under tensile and compressive states is simulated by constructing a typical material nonlinearity in a numerical analysis in this paper. The meshless Finite Block Method (FBM) has been developed to deal with 3D semi-infinite structures in the bimodular materials in this paper. The Lagrange polynomial interpolation is utilized to construct the meshless shape function with the mapping technique to transform the irregular finite domain or semi-infinite physical solids into a normalized domain. A shear modulus strategy is developed to present the nonlinear characteristics of bimodular material. In order to verify the efficiency and accuracy of FBM, the numerical results are compared with both analytical and numerical solutions provided by Finite Element Method (FEM) in four examples.

2022 ◽  
Vol 2022 ◽  
pp. 1-9
Mine Aylin Bayrak ◽  
Ali Demir ◽  
Ebru Ozbilge

The task of present research is to establish an enhanced version of residual power series (RPS) technique for the approximate solutions of linear and nonlinear space-time fractional problems with Dirichlet boundary conditions by introducing new parameter λ . The parameter λ allows us to establish the best numerical solutions for space-time fractional differential equations (STFDE). Since each problem has different Dirichlet boundary conditions, the best choice of the parameter λ depends on the problem. This is the major contribution of this research. The illustrated examples also show that the best approximate solutions of various problems are constructed for distinct values of parameter λ . Moreover, the efficiency and reliability of this technique are verified by the numerical examples.

Vladimir Kolobov ◽  
Juan Alonso Guzmán ◽  
R R Arslanbekov

Abstract A self-consistent hybrid model of standing and moving striations was developed for low-current DC discharges in noble gases. We introduced the concept of surface diffusion in phase space (r,u) (where u denotes the electron kinetic energy) described by a tensor diffusion in the nonlocal Fokker-Planck kinetic equation for electrons in the collisional plasma. Electrons diffuse along surfaces of constant total energy ε=u-eφ(r) between energy jumps in inelastic collisions with atoms. Numerical solutions of the 1d1u kinetic equation for electrons were obtained by two methods and coupled to ion transport and Poisson solver. We studied the dynamics of striation formation in Townsend and glow discharges in Argon gas at low discharge currents using a two-level excitation-ionization model and a “full-chemistry” model, which includes stepwise and Penning ionization. Standing striations appeared in Townsend and glow discharges at low currents, and moving striations were obtained for the discharge currents exceeding a critical value. These waves originate at the anode and propagate towards the cathode. We have seen two types of moving striations with the 2-level and full-chemistry models, which resemble the s and p striations previously observed in the experiments. Simulations indicate that processes in the anode region could control moving striations in the positive column plasma. The developed model helps clarify the nature of standing and moving striations in DC discharges of noble gases at low discharge currents and low gas pressures.

Xueying Yu ◽  
Yanlin Shao ◽  
David R. Fuhrman

Abstract It is essential for a Navier-Stokes equations solver based on a projection method to be able to solve the resulting Poisson equation accurately and efficiently. In this paper, we present numerical solutions of the 2D Navier-Stokes equations using the fourth-order generalized harmonic polynomial cell (GHPC) method as the Poisson equation solver. Particular focus is on the local and global accuracy of the GHPC method on non-uniform grids. Our study reveals that the GHPC method enables use of more stretched grids than the original HPC method. Compared with a second-order central finite difference method (FDM), global accuracy analysis also demonstrates the advantage of applying the GHPC method on stretched non-uniform grids. An immersed boundary method is used to deal with general geometries involving the fluid-structure-interaction problems. The Taylor-Green vortex and flow around a smooth circular cylinder and square are studied for the purpose of verification and validation. Good agreement with reference results in the literature confirms the accuracy and efficiency of the new 2D Navier-Stokes equation solver based on the present immersed-boundary GHPC method utilizing non-uniform grids. The present Navier-Stokes equations solver uses second-order FDM for the discretization of the diffusion and advection terms, which may be replaced by other higher-order schemes to further improve the accuracy.

Elliot J Carr ◽  
Daniel J VandenHeuvel ◽  
Joshua M Wilson ◽  
Matthew J Simpson

Abstract Calculating the mean exit time (MET) for models of diffusion is a classical problem in statistical physics, with various applications in biophysics, economics and heat and mass transfer. While many exact results for MET are known for diffusion in simple geometries involving homogeneous materials, calculating MET for diffusion in realistic geometries involving heterogeneous materials is typically limited to repeated stochastic simulations or numerical solutions of the associated boundary value problem (BVP). In this work we derive exact solutions for the MET in irregular annular domains, including some applications where diffusion occurs in heterogenous media. These solutions are obtained by taking the exact results for MET in an annulus, and then constructing various perturbation solutions to account for the irregular geometries involved. These solutions, with a range of boundary conditions, are implemented symbolically and compare very well with averaged data from repeated stochastic simulations and with numerical solutions of the associated BVP. Software to implement the exact solutions is available on \href{}{GitHub}.

Nabil T. Eldabe ◽  
Mohamed Y. Abou zeid ◽  
Sami M. El Shabouri ◽  
Tarek N. Salama ◽  
Aya M. Ismael

Inclined uniform magnetic field and mixed convention effects on micropolar non-Newtonian nanofluid Al2O3 flow with heat transfer are studied. The heat source, both viscous and ohmic dissipation and temperature micropolarity properties are considered. We transformed our system of non-linear partial differential equations into ordinary equations by using suitable similarity transformations. These equations are solved by making use of Rung–Kutta–Merson method in a shooting and matching technique. The numerical solutions of the tangential velocity, microtation velocity, temperature and nanoparticle concentration are obtained as functions of the physical parameters of the problem. Moreover, we discussed the effects of these parameters on the numerical solutions and depicted graphically. It is obvious that these parameters control the fluid flow. It is noticed that the tangential velocity magnifies with an increase in the value of Darcy number. Meanwhile, the value of the tangential velocity reduces with the elevation in the value of the magnetic field parameter. On the other hand, the elevation in the value of Brownian motion parameter leads to a reduction in the value of fluid temperature. Furthermore, increasing in the value of heat source parameter makes an enhancement in the value of nanoparticles concentration. The current study has many accomplishments in several scientific areas like medical industry, medicine, and others. Therefore, it represents the depiction of gas or liquid motion over a surface. When particles are moving from areas of high concentration to areas of low concentration.

2022 ◽  
pp. 1-12
Nastran Khodabandehloo ◽  
Kosar Mozaffari ◽  
Liping Liu ◽  
Pradeep Sharma

Abstract Electrolyte in a rechargeable Li-ion battery plays a critical role in determining its capacity and efficiency. While the typically used electrolytes in Li-ion batteries are liquid, soft solid electrolytes are being increasingly explored as an alternative due to their advantages in terms of increased stability, safety and potential applications in the context of flexible and stretchable electronics. However, ionic conductivity of solid polymer electrolytes is significantly lower compared to liquid electrolytes. In a recent work, we developed a theoretical framework to model the coupled deformation, electrostatics and diffusion in heterogeneous electrolytes and also established a simple homogenization approach for the design of microstructures to enhance ionic conductivity of composite solid electrolytes. Guided by the insights from the theoretical framework, in this paper, we ex- amine specific microstructures that can potentially yield significant improvement in the effective ionic conductivity. We numerically implement our theory in the open source general purpose finite element package FEniCS to solve the governing equations and present numerical solutions and insights on the effect of microstructure on the enhancement of ionic conductivity. Specifically, we investigate the effect of shape by considering ellipsoidal inclusions. We also propose an easily manufacturable microstructure that increases the ionic conductivity of the composite electrolyte by forty times, simply by the addition of dielectric columns parallel to the solid electrolyte phase.

Seif Bayoumi ◽  
Erkan Oterkus ◽  
Hassan El-Gamal ◽  
Atilla Incecik

The prompt estimation of power and geometrical aspects enables faster and more accurate financial assessment of wave energy converters to be deployed. This may lead to better commercialisation of wave energy technologies, as they require location-based customisation, unlike the mature wind energy technologies with developed benchmark. The adopted approach provides simple and efficient modelling tool allowing the study of the system from different perspective. The aim of this study is to select the optimum dynamic model to predict the captured power of a spar-buoy Oscillating Water Column (OWC) wave energy converter. Four dynamic models were developed to predict the system dynamics and results were validated experimentally. In-depth investigations on the effect of the mass and damping ratios of the oscillating bodies on the accuracy of the adopted models were performed. Such investigations included the proposed one-way coupling model and three two-degree of freedom models and three reduced-scale models, in addition to analytical and numerical solutions. Pneumatic power was calculated for the reduced-scale model where orifices’ covers simulated the power take-off mechanism damping experimentally. Analysis and comparisons between the adopted models are finally provided.

Trifce Sandev ◽  
Viktor Domazetoski ◽  
Ljupco Kocarev ◽  
Ralf Metzler ◽  
Alexei Chechkin

Abstract We study a heterogeneous diffusion process with position-dependent diffusion coefficient and Poissonian stochastic resetting. We find exact results for the mean squared displacement and the probability density function. The nonequilibrium steady state reached in the long time limit is studied. We also analyze the transition to the non-equilibrium steady state by finding the large deviation function. We found that similarly to the case of the normal diffusion process where the diffusion length grows like $t^{1⁄2}$ while the length scale ξ(t) of the inner core region of the nonequilibrium steady state grows linearly with time t, in the heterogeneous diffusion process with diffusion length increasing like $t^{p⁄2}$ the length scale ξ(t) grows like $t^{p}$. The obtained results are verified by numerical solutions of the corresponding Langevin equation.

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