scholarly journals Fast and Accurate Numerical Solution of Allen–Cahn Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Yongho Kim ◽  
Gilnam Ryu ◽  
Yongho Choi
Keyword(s):  
Mean Curvature ◽  
Three Dimensional ◽  
Fast Computation ◽  
Simulation Code ◽  
Convolution Operation ◽  
Cahn Equation ◽  
Simulation Speed ◽  
Explicit Finite Difference ◽  
Accurate Numerical Solution ◽  
Explicit Finite Difference Method

Simulation speed depends on code structures. Hence, it is crucial how to build a fast algorithm. We solve the Allen–Cahn equation by an explicit finite difference method, so it requires grid calculations implemented by many for-loops in the simulation code. In terms of programming, many for-loops make the simulation speed slow. We propose a model architecture containing a pad and a convolution operation on the Allen–Cahn equation for fast computation while maintaining accuracy. Also, the GPU operation is used to boost up the speed more. In this way, the simulation of other differential equations can be improved. In this paper, various numerical simulations are conducted to confirm that the Allen–Cahn equation follows motion by mean curvature and phase separation in two-dimensional and three-dimensional spaces. Finally, we demonstrate that our algorithm is much faster than an unoptimized code and the CPU operation.

A Nonlinear Rail Vehicle Dynamics Computer Program SAMS/Rail: Part 1—Theory and Formulations

2009 ◽  
Author(s):  
Khaled E. Zaazaa ◽  
Brian Whitten ◽  
Brian Marquis ◽  
Erik Curtis ◽  
Magdy El-Sibaie ◽  
...  
Keyword(s):  
High Speed ◽  
Dynamic Performance ◽  
Three Dimensional ◽  
Contact Element ◽  
Contact Forces ◽  
Simulation Code ◽  
Vehicle Performance ◽  
Normal Contact ◽  
Advantages And Disadvantages ◽  
High Speed Trains

Accurate prediction of railroad vehicle performance requires detailed formulations of wheel-rail contact models. In the past, most dynamic simulation tools used an offline wheel-rail contact element based on look-up tables that are used by the main simulation solver. Nowadays, the use of an online nonlinear three-dimensional wheel-rail contact element is necessary in order to accurately predict the dynamic performance of high speed trains. Recently, the Federal Railroad Administration, Office of Research and Development has sponsored a project to develop a general multibody simulation code that uses an online nonlinear three-dimensional wheel-rail contact element to predict the contact forces between wheel and rail. In this paper, several nonlinear wheel-rail contact formulations are presented, each using the online three-dimensional approach. The methods presented are divided into two contact approaches. In the first Constraint Approach, the wheel is assumed to remain in contact with the rail. In this approach, the normal contact forces are determined by using the technique of Lagrange multipliers. In the second Elastic Approach, wheel/rail separation and penetration are allowed, and the normal contact forces are determined by using Hertz’s Theory. The advantages and disadvantages of each method are presented in this paper. In addition, this paper discusses future developments and improvements for the multibody system code. Some of these improvements are currently being implemented by the University of Illinois at Chicago (UIC). In the accompanying “Part 2” and “Part 3” to this paper, numerical examples are presented in order to demonstrate the results obtained from this research.

Thermal Analysis of Expressway Considering Wind Effect

2013 ◽  
Vol 419 ◽  
pp. 895-904
Author(s):  
X. Cao ◽  
H. Miyashita ◽  
T. Kako ◽  
Z. Zhang ◽  
B. Song
Keyword(s):  
Mathematical Model ◽  
Thermal Analysis ◽  
Thermal Conduction ◽  
Computer Calculation ◽  
Basic Mechanism ◽  
Weather Data ◽  
Wind Effect ◽  
Fortran Language ◽  
Explicit Finite Difference ◽  
Explicit Finite Difference Method

This paper reports a method of thermal analysis of expressway and the results of analysis of four expressways currently used in Japan. The authors built a mathematical model based on the principle of thermal conduction. For the boundary conditions in this mathematical model the influence of solar radiation, wind and air temperature etc. are taken into consideration. Explicit finite difference method is used in the analysis. The authors made an analysis program in Fortran language. Four main expressways distributing from the northern to the southern in Japan are chosen as the objects of this study. The observed weather data of the hottest days experienced by these expressways during the past 30 years is input into the computer calculation. The basic mechanism of expressway temperature change and effect factors are illuminated. The results are reported and discussed.

Multiple Ship Motion Simulation Code Correlation with Model Test Results

2017 ◽  
Author(s):  
James A. Coller ◽  
Andrew Silver ◽  
Okey Nwogu ◽  
Benjamin S.H. Connell
Keyword(s):  
Real Time ◽  
Model Test ◽  
Three Dimensional ◽  
Angle Measurement ◽  
Ship Motion ◽  
Ship Motions ◽  
Simulation Code ◽  
Forecasting System ◽  
Scale Experiment ◽  
Response Amplitude Operators

The US Nav has developed a real-time multi-ship ship motion forecasting system which combines forecast wave conditions with ship motion simulations to produce a prediction of the relative motions between two ships operating in a skin-to-skin configuration. The system utilizes two different simulation methods for predicting ship motions: MotionSim and Reduced Order Model (ROM) based on AEGIR. MotionSim is a fast three-dimensional panel method that is used to estimate the Response Amplitude Operators (RAOs) necessary for multi-ship motion predictions. The ROM works to maximize the accuracy of high fidelity ship motion prediction methods while maintaining the computational speed required for real-time forecasting. A model scale experiment was performed in 2015 on two Navy ships conventionally moored together. The predicted relative ship motions from MotionSim and ROM were compared to the model data using three different metrics: RMS (root mean square) ratio, correlation coefficient, and average angle measurement (AAM).This paper provides an overview of the two methods for predicting the multi-ship motions, a description of the model test, challenges faced during testing, and a discussion on the methodology of the evaluation and the results of each code correlation.

scholarly journals Three-dimensional multispecies hybrid simulation of Titan's highly variable plasma environment

2007 ◽  
Vol 25 (1) ◽  
pp. 117-144 ◽  
Author(s):  
S. Simon ◽  
A. Boesswetter ◽  
T. Bagdonat ◽  
U. Motschmann ◽  
J. Schuele
Keyword(s):  
Plasma Flow ◽  
Flow Direction ◽  
Three Dimensional ◽  
Hybrid Simulation ◽  
Slight Modification ◽  
Magnetospheric Plasma ◽  
Particle Model ◽  
Tail Region ◽  
Simulation Code ◽  
Ion Species

Abstract. The interaction between Titan's ionosphere and the Saturnian magnetospheric plasma flow has been studied by means of a three-dimensional (3-D) hybrid simulation code. In the hybrid model, the electrons form a mass-less, charge-neutralizing fluid, whereas a completely kinetic approach is retained to describe ion dynamics. The model includes up to three ionospheric and two magnetospheric ion species. The interaction gives rise to a pronounced magnetic draping pattern and an ionospheric tail that is highly asymmetric with respect to the direction of the convective electric field. Due to the dependence of the ion gyroradii on the ion mass, ions of different masses become spatially dispersed in the tail region. Therefore, Titan's ionospheric tail may be considered a mass-spectrometer, allowing to distinguish between ion species of different masses. The kinetic nature of this effect is emphasized by comparing the simulation with the results obtained from a simple analytical test-particle model of the pick-up process. Besides, the results clearly illustrate the necessity of taking into account the multi-species nature of the magnetospheric plasma flow in the vicinity of Titan. On the one hand, heavy magnetospheric particles, such as atomic Nitrogen or Oxygen, experience only a slight modification of their flow pattern. On the other hand, light ionospheric ions, e.g. atomic Hydrogen, are clearly deflected around the obstacle, yielding a widening of the magnetic draping pattern perpendicular to the flow direction. The simulation results clearly indicate that the nature of this interaction process, especially the formation of sharply pronounced plasma boundaries in the vicinity of Titan, is extremely sensitive to both the temperature of the magnetospheric ions and the orientation of Titan's dayside ionosphere with respect to the corotating magnetospheric plasma flow.

Integral criteria for closed surfaces with constant mean curvature

2007 ◽  
Vol 463 (2081) ◽  
pp. 1199-1210
Author(s):  
Luca Guzzardi ◽  
Epifanio G Virga
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Three Dimensional ◽  
Dimensional Euclidean Space ◽  
Second Variation ◽  
Closed Surfaces ◽  
Area Functional ◽  
Symmetric Surface ◽  
The Second Variation ◽  
Integral Identities

We propose three integral criteria that must be satisfied by all closed surfaces with constant mean curvature immersed in the three-dimensional Euclidean space. These criteria are integral identities that follow from requiring the second variation of the area functional to be invariant under rigid displacements. We obtain from them a new proof of the old result by Delaunay, to the effect that the sphere is the only closed axis-symmetric surface.

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