Some Applications of CDL-BIEM

1994 ◽  
Author(s):  
Nhan Phan-Thien ◽  
Sangtae Kim
Keyword(s):  
Analytical Solution ◽  
Numerical Method ◽  
Analytical Solutions ◽  
Spherical Inclusion ◽  
Three Dimensional ◽  
Simple Problem ◽  
Benchmark Problem ◽  
Bounding Surface ◽  
Rigid Displacement ◽  
Particulate Solids

This chapter presents some selected three-dimensional applications of the CDL-BIEM in elasticity and Stokes flows, especially to particulate solids for which the method is devised. It is paramount that any numerical method should be validated against known analytical solutions. The method will therefore be benchmarked against known simple solutions of the type reported in chapters 2 and 5. Some selected nontrivial examples, where no analytical solutions are available, will also be presented. The translating sphere is a simple problem with known analytical solution and smooth bounding surface; it is a popular benchmark problem for boundary element codes. Here a rigid spherical inclusion of radius a, centered at x = 0, is displaced by either (1) a constant vector U or (2) acted on by a force F, and we seek the force in the case of problem (1), or the rigid displacement in problem (2).

Application of the Conservation Element and Solution Element Method in Numerical Modeling of Three-Dimensional Heat Conduction With Melting and/or Freezing

2004 ◽  
Vol 126 (6) ◽  
pp. 937-945 ◽  
Author(s):  
Anahita Ayasoufi ◽  
Theo G. Keith ◽  
Ramin K. Rahmani
Keyword(s):  
Numerical Modeling ◽  
Heat Conduction ◽  
Fluid Mechanics ◽  
Phase Change ◽  
Numerical Method ◽  
Analytical Solutions ◽  
Three Dimensional ◽  
Solution Element ◽  
Explicit Numerical Method ◽  
Element Method

The conservation element and solution element (CE/SE) method, an accurate and efficient explicit numerical method for resolving moving discontinuities in fluid mechanics problems, is used to solve three-dimensional phase-change problems. Several isothermal phase-change cases are studied and comparisons are made to existing analytical solutions. The CE/SE method is found to be accurate, robust, and efficient for the numerical modeling of phase-change problems.

Application of the Conservation Element and Solution Element Method in Numerical Modeling of Three-Dimensional Heat Conduction With Melting and/or Freezing

2003 ◽  
Author(s):  
Anahita Ayasoufi ◽  
Theo G. Keith
Keyword(s):  
Numerical Modeling ◽  
Heat Conduction ◽  
Fluid Mechanics ◽  
Phase Change ◽  
Numerical Method ◽  
Analytical Solutions ◽  
Three Dimensional ◽  
Solution Element ◽  
Explicit Numerical Method ◽  
Element Method

The conservation element and solution element (CE/SE) method, an accurate and efficient explicit numerical method for resolving moving discontinuities in fluid mechanics problems, is used to solve three-dimensional phase change problems. Several isothermal phase change cases are studied and comparisons are made to existing analytical solutions. The CE/SE method is found to be accurate, robust and efficient for the numerical modeling of phase change problems.

Formulation of a three dimensional analytical solution to evaluate stresses in backfilled vertical narrow openings

2005 ◽  
Vol 42 (6) ◽  
pp. 1705-1717 ◽  
Author(s):  
Li Li ◽  
Michel Aubertin ◽  
Tikou Belem
Keyword(s):  
Numerical Modeling ◽  
Analytical Solution ◽  
Analytical Solutions ◽  
Mechanical Response ◽  
Three Dimensional ◽  
Earth Pressure ◽  
The State ◽  
Experimental Results ◽  
State Of Stress ◽  
Earth Pressures

The mechanical response of backfill in narrow openings is significantly influenced by its interaction with the surrounding walls. Previous work conducted on backfilled trenches and mining stopes indicates that the theory of arching can be used to estimate earth pressures in narrow, vertical backfilled openings. In this paper, a 3D analytical solution is proposed to evaluate the state of stress along the boundaries of the openings. The proposed solution, based on a generalized version of the Marston approach, is compared with numerical modeling and laboratory experimental results taken from the literature. A discussion follows on some particular features and limitations of the analytical solutions.Key words: backfill, earth pressure, 3D openings, analytical solutions, trenches, mining stopes.

scholarly journals New Analytical Solutions for Longitudinal Vibration of a Floating Pile in Layered Soils with Radial Heterogeneity

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1294 ◽  
Author(s):  
Zhimeng Liang ◽  
Chunyi Cui ◽  
Kun Meng ◽  
Yu Xin ◽  
Huafu Pei ◽  
...  
Keyword(s):  
Analytical Solution ◽  
Analytical Solutions ◽  
Longitudinal Vibration ◽  
Three Dimensional ◽  
Complex Impedance ◽  
Vibration Characteristics ◽  
Layered Soils ◽  
Transform Method ◽  
Floating Pile ◽  
The Time Domain

Based on the theory of wave propagation in three-dimensional (3D) continuum, a new analytical approach for the longitudinal vibration characteristics of a floating pile in layered soils with radial heterogeneity is developed by employing a viscous-type damping model. Firstly, an analytical solution for the longitudinal complex impedance at the pile head is deduced by employing the Laplace transform and complex stiffness technique with the compatibility conditions of the pile and radially inhomogeneous surrounding soil. Secondly, a semi-analytical solution in the time domain is further acquired by using the inverse Fourier transform method. Furthermore, the corresponding analytical solutions are validated through contrasts with previous solutions. Finally, parametric analyses are underway to investigate the effect of radial heterogeneity of surrounding soils on longitudinal vibration characteristics of floating piles. It is indicated that the proposed approach and corresponding solutions can provide a more wide-ranging application than the simple harmonic vibration for longitudinal vibration analysis of a floating pile in soils.

scholarly journals The Hydromechanical Interplay in the Simplified Three-Dimensional Limit Equilibrium Analyses of Unsaturated Slope Stability

Geosciences ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 73
Author(s):  
Panagiotis Sitarenios ◽  
Francesca Casini
Keyword(s):  
Analytical Solution ◽  
Slope Stability ◽  
Slope Failure ◽  
Failure Modes ◽  
Pore Water Pressure ◽  
Limit Equilibrium ◽  
Water Pressure ◽  
Three Dimensional ◽  
Stability Limit ◽  
Smooth Transition

This paper presents a three-dimensional slope stability limit equilibrium solution for translational planar failure modes. The proposed solution uses Bishop’s average skeleton stress combined with the Mohr–Coulomb failure criterion to describe soil strength evolution under unsaturated conditions while its formulation ensures a natural and smooth transition from the unsaturated to the saturated regime and vice versa. The proposed analytical solution is evaluated by comparing its predictions with the results of the Ruedlingen slope failure experiment. The comparison suggests that, despite its relative simplicity, the analytical solution can capture the experimentally observed behaviour well and highlights the importance of considering lateral resistance together with a realistic interplay between mechanical parameters (cohesion) and hydraulic (pore water pressure) conditions.

scholarly journals The time domain numerical method of three-dimensional conductors including radiation with lumped parameter circuit

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Souma Jinno ◽  
Shuji Kitora ◽  
Hiroshi Toki ◽  
Masayuki Abe
Keyword(s):  
Numerical Method ◽  
Time Domain ◽  
Maxwell Equations ◽  
Three Dimensional ◽  
New Formalism ◽  
Vector Potentials ◽  
Lumped Parameter ◽  
Radiation Theory ◽  
Stable Solutions ◽  
The Time Domain

AbstractWe formulate a numerical method on the transmission and radiation theory of three-dimensional conductors starting from the Maxwell equations in the time domain. We include the delay effect in the integral equations for the scalar and vector potentials rigorously, which is vital to obtain numerically stable solutions for transmission and radiation phenomena in conductors. We provide a formalism to connect the conductors to any passive lumped-parameter circuits. We show one example of numerical calculations, demonstrating that the new formalism provides stable solutions to the transmission and radiation phenomena.

scholarly journals A Fast Two-Dimensional Numerical Method for the Wake Simulation of a Vertical Axis Wind Turbine

Energies ◽  
2020 ◽  
Vol 14 (1) ◽  
pp. 49
Author(s):  
Zheng Yuan ◽  
Jin Jiang ◽  
Jun Zang ◽  
Qihu Sheng ◽  
Ke Sun ◽  
...  
Keyword(s):  
Velocity Distribution ◽  
Numerical Method ◽  
Three Dimensional ◽  
Particle Method ◽  
Vortex Method ◽  
Vertical Axis ◽  
Two Dimensional ◽  
Vertical Axis Wind Turbine ◽  
Wake Effect ◽  
Array Design

In the array design of the vertical axis wind turbines (VAWT), the wake effect of the upstream VAWT on the downstream VAWT needs to be considered. In order to simulate the velocity distribution of a VAWT wake rapidly, a new two-dimensional numerical method is proposed, which can make the array design easier and faster. In this new approach, the finite vortex method and vortex particle method are combined to simulate the generation and evolution of the vortex, respectively, the fast multipole method (FMM) is used to accelerate the calculation. Based on a characteristic of the VAWT wake, that is, the velocity distribution can be fitted into a power-law function, a new correction model is introduced to correct the three-dimensional effect of the VAWT wake. Finally, the simulation results can be approximated to the published experimental results in the first-order. As a new numerical method to simulate the complex VAWT wake, this paper proves the feasibility of the method and makes a preliminary validation. This method is not used to simulate the complex three-dimensional turbulent evolution but to simulate the velocity distribution quickly and relatively accurately, which meets the requirement for rapid simulation in the preliminary array design.

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