A mathematical framework of high-order surface stresses in three-dimensional configurations

2014 ◽  
Vol 225 (4-5) ◽  
pp. 1043-1060 ◽  
Author(s):  
Tungyang Chen ◽  
Min-Sen Chiu
Keyword(s):  
Three Dimensional ◽  
High Order ◽  
Mathematical Framework ◽  
Surface Stresses ◽  
Order Surface

Timoshenko Beam Model for Buckling of Nanowires with High-Order Surface Stresses Effects

2012 ◽  
Vol 528 ◽  
pp. 281-284 ◽  
Author(s):  
Min Sen Chiu ◽  
Tung Yang Chen
Keyword(s):  
Timoshenko Beam ◽  
Surface Stress ◽  
Surface Effect ◽  
High Order ◽  
Mathematical Framework ◽  
Beam Model ◽  
Axial Buckling ◽  
Surface Stresses ◽  
Wide Range ◽  
Order Surface

High-order surface effects can have a significant effect in the mechanical behavior of micro- and nano-sized materials and structures. In the literature the mathematical framework of surface/interface stresses are generally described by generalized Young-Laplace equations based on membrane theory. A refined model of surface stress, counting into surface stresses as well as surface moments, collectively referred to as high-order surface stress, was recently derived by the authors. This framework allows us to simulate the interface between two neighboring media which may have varying in-plane stress through the thickness of the thin membrane. To illustrate surface stress effects, we consider the critical force of axial buckling of nanowires by accounting various degrees of surface stresses. Using the refined Timoshenko beam theory, we incorporate the high-order surface effect in the simulation of axial buckling of nanowires. The results are compared with the solutions based on conventional surface stress model as well as existing experimental data. This study might be helpful to characterize the mechanical properties of nanowires in a wide range of applications.

scholarly journals High-Order Finite-Element Framework for the Efficient Simulation of Multifluid Flows

Mathematics ◽  
2018 ◽  
Vol 6 (10) ◽  
pp. 203 ◽  
Author(s):  
Thibaut Metivet ◽  
Vincent Chabannes ◽  
Mourad Ismail ◽  
Christophe Prud’homme
Keyword(s):  
Finite Elements ◽  
Level Set ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Time Discretization ◽  
High Order ◽  
Navier Stokes ◽  
Mathematical Framework ◽  
Navier Stokes Equations ◽  
Coupling Approach

In this paper, we present a comprehensive framework for the simulation of Multifluid flows based on the implicit level-set representation of interfaces and on an efficient solving strategy of the Navier-Stokes equations. The mathematical framework relies on a modular coupling approach between the level-set advection and the fluid equations. The space discretization is performed with possibly high-order stable finite elements while the time discretization features implicit Backward Differentation Formulae of arbitrary order. This framework has been implemented within the Feel++ library, and features seamless distributed parallelism with fast assembly procedures for the algebraic systems and efficient preconditioning strategies for their resolution. We also present simulation results for a three-dimensional Multifluid benchmark, and highlight the importance of using high-order finite elements for the level-set discretization for problems involving the geometry of the interfaces, such as the curvature or its derivatives.

Optimization of the Navy’s three-dimensional mine impact burial prediction simulation model, Impact35, using high-order numerical methods

2021 ◽  
pp. 154851292110286
Author(s):  
Athanasios Donas ◽  
Ioannis Famelis ◽  
Peter C Chu ◽  
George Galanis
Keyword(s):  
Numerical Analysis ◽  
Numerical Methods ◽  
Prediction Model ◽  
Simulation Model ◽  
Three Dimensional ◽  
Simulation System ◽  
High Order ◽  
Alternative Methodology ◽  
Runge Kutta ◽  
Fifth Order

The aim of this paper is to present an application of high-order numerical analysis methods to a simulation system that models the movement of a cylindrical-shaped object (mine, projectile, etc.) in a marine environment and in general in fluids with important applications in Naval operations. More specifically, an alternative methodology is proposed for the dynamics of the Navy’s three-dimensional mine impact burial prediction model, Impact35/vortex, based on the Dormand–Prince Runge–Kutta fifth-order and the singly diagonally implicit Runge–Kutta fifth-order methods. The main aim is to improve the time efficiency of the system, while keeping the deviation levels of the final results, derived from the standard and the proposed methodology, low.

scholarly journals High-order compact LOD methods for solving high-dimensional advection equations

2021 ◽  
Vol 40 (3) ◽  
Author(s):  
Bo Hou ◽  
Yongbin Ge
Keyword(s):  
Truncation Error ◽  
Three Dimensional ◽  
Taylor Series Expansion ◽  
High Order ◽  
High Dimensional ◽  
Analysis Method ◽  
Order Accuracy ◽  
Von Neumann ◽  
One Dimensional ◽  
Von Neumann Analysis

AbstractIn this paper, by using the local one-dimensional (LOD) method, Taylor series expansion and correction for the third derivatives in the truncation error remainder, two high-order compact LOD schemes are established for solving the two- and three- dimensional advection equations, respectively. They have the fourth-order accuracy in both time and space. By the von Neumann analysis method, it shows that the two schemes are unconditionally stable. Besides, the consistency and convergence of them are also proved. Finally, numerical experiments are given to confirm the accuracy and efficiency of the present schemes.

scholarly journals Visualizing High-Order Surface Geometry

2009 ◽  
Vol 6 (2) ◽  
pp. 263-268
Author(s):  
Pushkar P. Joshi ◽  
Carlo H. Séquin
Keyword(s):  
High Order ◽  
Surface Geometry ◽  
Order Surface

VERY HIGH-ORDER SPATIALLY IMPLICIT SCHEMES FOR COMPUTATIONAL ACOUSTICS ON CURVILINEAR MESHES

2001 ◽  
Vol 09 (04) ◽  
pp. 1259-1286 ◽  
Author(s):  
MIGUEL R. VISBAL ◽  
DATTA V. GAITONDE
Keyword(s):  
Three Dimensional ◽  
Radiation Condition ◽  
Higher Order ◽  
High Order ◽  
High Frequencies ◽  
Decomposition Strategies ◽  
The Impact ◽  
Spurious Modes ◽  
Very High ◽  
Computational Strategy

A high-order compact-differencing and filtering algorithm, coupled with the classical fourth-order Runge–Kutta scheme, is developed and implemented to simulate aeroacoustic phenomena on curvilinear geometries. Several issues pertinent to the use of such schemes are addressed. The impact of mesh stretching in the generation of high-frequency spurious modes is examined and the need for a discriminating higher-order filter procedure is established and resolved. The incorporation of these filtering techniques also permits a robust treatment of outflow radiation condition by taking advantage of energy transfer to high-frequencies caused by rapid mesh stretching. For conditions on the scatterer, higher-order one-sided filter treatments are shown to be superior in terms of accuracy and stability compared to standard explicit variations. Computations demonstrate that these algorithmic components are also crucial to the success of interface treatments created in multi-domain and domain-decomposition strategies. For three-dimensional computations, special metric relations are employed to assure the fidelity of the scheme in highly curvilinear meshes. A variety of problems, including several benchmark computations, demonstrate the success of the overall computational strategy.

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