scholarly journals Random Finite-Difference Discretizations of the Ambrosio--Tortorelli Functional with Optimal Mesh-Size

2021 ◽  
Vol 53 (2) ◽  
pp. 2275-2318
Author(s):  
Annika Bach ◽  
Marco Cicalese ◽  
Matthias Ruf
Keyword(s):  
Finite Difference ◽  
Mesh Size ◽  
Optimal Mesh

DEVELOPMENT OF NEW HARMONIC EULER USING NONSTANDARD FINITE DIFFERENCE TECHNIQUE FOR SOLVING STIFF PROBLEMS

2015 ◽  
Vol 77 (20) ◽  
Author(s):  
Nurhafizah Moziyana Mohd Yusop ◽  
Mohammad Khatim Hasan
Keyword(s):  
Finite Difference ◽  
Numerical Algorithm ◽  
Mesh Size ◽  
High Accuracy ◽  
Euler Method ◽  
Stiff Problems ◽  
Harmonic Mean ◽  
Stiff Problem ◽  
Finite Difference Technique ◽  
Nonstandard Finite Difference

Solving stiff problem always required very tiny size of meshes if it is solved via traditional numerical algorithm. Using insufficient of mesh size, will triggered instabilities. In this paper, we develop an algorithm applying Harmonic Mean on Euler method to solve the stiff problems. The main purpose of this paper is to discuss the improvement of Harmonic Euler using Nonstandard Finite Difference (NSFD). The combination of these methods can provide new advantages that Euler method could offer. Four set of stiff problems are solved via three schemes, i.e. Harmonic Euler, Nonstandard Harmonic Euler and Nonstandard EO with Harmonic Euler. Findings show that both nonstandard schemes produce high accuracy results.

Non-Newtonian Fluid Flow Analysis with Finite Difference and Finite Volume Numerical Models

2001 ◽  
Vol 11 (6) ◽  
pp. 325-335
Author(s):  
Jure Marn ◽  
Marjan Delic ◽  
Zoran Zunic
Keyword(s):  
Finite Difference ◽  
Finite Volume ◽  
Numerical Models ◽  
Flow Analysis ◽  
Mesh Size ◽  
Newtonian Flow ◽  
Driven Cavity ◽  
Commercial Code ◽  
Fluid Flow Analysis ◽  
Volume Method

Abstract Suitability of finite difference method and finite volume method for computation of incompressible non newtonian flow is analyzed. In addition, accuracy of numerical results depending of mesh size is assessed. Both methods are tested for driven cavity and compared to each other, to results from available literature and to results obtained using commercial code CFX 4.3.

Determining an optimal mesh size for use in the lampara net fishery for eastern sea garfish, Hyporhamphus australis

2004 ◽  
Vol 11 (6) ◽  
pp. 403-410 ◽  
Author(s):  
J. Stewart ◽  
C. Walsh ◽  
D. Reynolds ◽  
B. Kendall ◽  
C. Gray
Keyword(s):  
Mesh Size ◽  
Optimal Mesh

Accuracy of three-point finite difference approximations for optical waveguides with step-wise refractive index discontinuities

2011 ◽  
Vol 19 (2) ◽  
Author(s):  
S. Sujecki
Keyword(s):  
Refractive Index ◽  
Finite Difference ◽  
Error Analysis ◽  
Optical Waveguides ◽  
Light Propagation ◽  
Truncation Error ◽  
Mesh Size ◽  
Refractive Index Profile ◽  
Finite Difference Approximations ◽  
Difference Approximations

AbstractA rigorous truncation error analysis of three-point finite difference approximations for optical waveguides with step-wise refractive index discontinuities is given. As the basis for the analysis we use the exact coefficients of the series that expresses the field value at a given finite difference node in terms of the field value and its derivatives at a neighbouring node. This series is applied to develop a rigorous formalism for the truncation error analysis of the three-point finite difference approximations used in the numerical modelling of light propagation in optical waveguides with step-wise discontinuities of the refractive index profile. The results show that the approximations reach O(h2) truncation error only asymptotically for sufficiently small values of the mesh size.

scholarly journals Analysis of Blast Wave Parameters Depending on Air Mesh Size

2018 ◽  
Vol 2018 ◽  
pp. 1-18 ◽  
Author(s):  
Hrvoje Draganić ◽  
Damir Varevac
Keyword(s):  
Numerical Simulations ◽  
Blast Wave ◽  
Large Scale ◽  
Wave Interaction ◽  
Mesh Size ◽  
Blast Waves ◽  
3D Environment ◽  
Close Range ◽  
Blast Wave Propagation ◽  
Optimal Mesh

Results of numerical simulations of explosion events greatly depend on the mesh size. Since these simulations demand large amounts of processing time, it is necessary to identify an optimal mesh size that will speed up the calculation and give adequate results. To obtain optimal mesh sizes for further large-scale numerical simulations of blast wave interactions with overpasses, mesh size convergence tests were conducted for incident and reflected blast waves for close range bursts (up to 5 m). Ansys Autodyn hydrocode software was used for blast modelling in axisymmetric environment for incident pressures and in a 3D environment for reflected pressures. In the axisymmetric environment only the blast wave propagation through the air was considered, and in 3D environment blast wave interaction and reflection of a rigid surface were considered. Analysis showed that numerical results greatly depend on the mesh size and Richardson extrapolation was used for extrapolating optimal mesh size for considered blast scenarios.

scholarly journals Optimal Mesh Size for Inverse Medium Scattering Problems

2020 ◽  
Vol 58 (1) ◽  
pp. 733-756
Author(s):  
Habib Ammari ◽  
Yat Tin Chow ◽  
Keji Liu
Keyword(s):  
Mesh Size ◽  
Scattering Problems ◽  
Inverse Medium ◽  
Inverse Medium Scattering ◽  
Optimal Mesh

scholarly journals A 3D FEM-Based Numerical Analysis of the Sheet Metal Strip Flowing Through Drawbead Simulator

Metals ◽  
2019 ◽  
Vol 10 (1) ◽  
pp. 45 ◽  
Author(s):  
Tomasz Trzepiecinski ◽  
Romuald Fejkiel
Keyword(s):  
Sheet Metal ◽  
Material Flow ◽  
Three Dimensional ◽  
Mesh Size ◽  
Experimental Tests ◽  
Metal Strip ◽  
3D Fem ◽  
Stamping Die ◽  
The Coefficient Of Friction ◽  
Optimal Mesh

Drawbeads are elements of the stamping die and they are used to compensate material flow resistance around the perimeter of the drawpiece or to change the stress state in specific regions of the drawpiece. This paper presents the results of experimental and numerical analyses of tests of sheet metal flowing through a drawbead. The tests have been carried out using a special tribological simulator of the drawbead. Experimental tests to determine the coefficient of friction (COF) have been carried out for three widths of sheet metal strip and two drawbead heights. The three-dimensional (3D) elastic-plastic numerical computations were performed using the MSC. Marc program. Special attention was given to the effect of material flow through the drawbead on the distribution of the normal stress on the tool-sheet interface. The mesh sensitivity analysis based on the value of the drawing force of the specimen being pulled through the drawbead allowed an optimal mesh size to be determined. The errors between the numerically predicted values of the COF and the values experimentally determined ranged from about 0.95% to 7.1% in the cases analysed. In the case of a drawbead height of 12 mm, the numerical model overestimated the value of the COF for all specimen widths analysed. By contrast, in the case of a drawbead height of 18 mm, all experimentally determined friction coefficients are underestimated by Finite Element Method (FEM). This was explained by the different character of sheet deformation under friction and frictionless conditions. An increase in the drawbead height, with the same sheet width, increases the value of the COF.

Computer simulation of thermoeconomic optimization of periodic-flow heat exchangers

2003 ◽  
Vol 217 (5) ◽  
pp. 559-570 ◽  
Author(s):  
R. K. Jassim ◽  
A. A K. Mohammed Ali
Keyword(s):  
Computer Simulation ◽  
Heat Exchanger ◽  
Finite Difference ◽  
Unit Cost ◽  
Mesh Size ◽  
Computational Time ◽  
Design Parameters ◽  
Periodic Flow ◽  
Unit Costs ◽  
Flow Heat

A computer simulation of heat transfer by the finite difference technique is presented for calculating the fluid and matrix temperature distributions and their effect on periodic-flow heat exchanger performance. The governing differential equations have been formulated in terms of characteristic dimensionless groups. In order both to secure a high degree of accuracy of the results and to save computational time, three modifications have been made to evaluate the finite difference mesh size for regenerator length, hot period and cold period. The geometry of the matrix of a periodic-flow heat exchanger is optimized using the unit cost of the exergy of the warm delivered air as the objective function. The running cost is determined using unit costs for the pressure component of exergy and for the thermal component of exergy. The ratio of the two unit costs is obtained from an air conditioning plant and a power station in which the regenerator is used. The effect of variation in the principle design parameters on the unit cost of the warm air and on the heat exchange effectiveness are examined, and recommendations are made for the selection of the most appropriate parameters for a regenerator of a given capacity.

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