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finite difference method

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Series: ASM Handbook
Volume: 4C
Publisher: ASM International
Published: 09 June 2014
DOI: 10.31399/asm.hb.v04c.a0005876
EISBN: 978-1-62708-167-2
...-element method, finite difference method, boundary-element method or volume-integral method, and direct-solution method. The article also discusses the typical structure of commercial codes (preprocessor, solver, and postprocessor) to solve field problems mainly in finite-element method. computer...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005431
EISBN: 978-1-62708-196-2
... Abstract Several methods are developed for the numerical solution of partial differential equations, namely, meshed-solution methods such as the finite-element method (FEM), finite-difference method, and boundary-element method; and numerical algorithms consisting of so-called meshed-solution...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005426
EISBN: 978-1-62708-196-2
... techniques. It introduces some common techniques for discretizing the fluid-flow equations and methods for solving the discrete equations. These include finite-difference methods, finite-element methods, spectral methods, and computational particle methods. The article describes the approaches for grid...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005533
EISBN: 978-1-62708-197-9
... of metals, including normalizing, annealing, hardening, and tempering and stress relieving. It discusses the simulation techniques of the electromagnetic and thermal processes that occur during induction heat treating. The article explains the finite-difference method, finite-element method, mutual...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005506
EISBN: 978-1-62708-197-9
... and boundary conditions. The article discusses approximate and advanced solution techniques that can be employed in practice for simulation of residual stress relief: finite-difference method and finite-element method. It also describes advanced techniques applicable to transient creep, advanced constitutive...
Series: ASM Handbook
Volume: 4C
Publisher: ASM International
Published: 09 June 2014
DOI: 10.31399/asm.hb.v04c.a0005897
EISBN: 978-1-62708-167-2
... Abstract Estimation of process parameters for selective heating and heat treating of simple- and complex-shaped workpieces in induction hardening can be accurately carried out using numerical simulation techniques such as the finite-element analysis and the finite-different method. Along...
Series: ASM Desk Editions
Publisher: ASM International
Published: 01 December 1998
DOI: 10.31399/asm.hb.mhde2.a0003176
EISBN: 978-1-62708-199-3
..., and the molding method used. Designers can predict the effect of the design on the structure of the final part using solidification simulation models, namely finite element and finite difference models, and rapid prototyping. The article concludes with a short note on how the quality is assured in the foundry...
Series: ASM Handbook
Volume: 20
Publisher: ASM International
Published: 01 January 1997
DOI: 10.31399/asm.hb.v20.a0002444
EISBN: 978-1-62708-194-8
... an important role. This article presents the governing equations of fluid dynamics and an introduction to the CFD techniques for their solution. It introduces discretization techniques that are used by finite-difference, finite-volume, finite-element, spectral, and some particle methods. Associated concepts...
Series: ASM Handbook
Volume: 4A
Publisher: ASM International
Published: 01 August 2013
DOI: 10.31399/asm.hb.v04a.a0005789
EISBN: 978-1-62708-165-8
... Curve Fitting Based on Local Procedures , J. Assoc. Comput. Mach. , Vol 17 ( No. 4 ), 1970 , p 589 – 602 10.1145/321607.321609 19. Mitchell A.R. and Griffiths D.F. , The Finite Difference Method in Partial Differential Equations , John Wiley & Sons Ltd. , Chichester...
Book Chapter

Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003544
EISBN: 978-1-62708-180-1
... Abstract This article describes three design-life methods or philosophies of fatigue, namely, infinite-life, finite-life, and damage tolerant. It outlines the three stages in the process of fatigue fracture: the initial fatigue damage leading to crack initiation, progressive cyclic growth...
Series: ASM Handbook
Volume: 18
Publisher: ASM International
Published: 31 December 2017
DOI: 10.31399/asm.hb.v18.a0006385
EISBN: 978-1-62708-192-4
... of extrusion as well as thermodynamics. The finite-element method suitable for simulation of metal forming processes is explained. The article examines the extrusion defects that are divided into three different categories including surface, subsurface, and internal type. It includes information on friction...
Series: ASM Handbook
Volume: 24
Publisher: ASM International
Published: 15 June 2020
DOI: 10.31399/asm.hb.v24.a0006546
EISBN: 978-1-62708-290-7
... regions in the vat, known as the Jacobs model, and a high-fidelity, continuum approach that uses finite-element methods. The final section is devoted to material jetting, focusing on simulations used to study droplet generation at the nozzle and droplet impact. References 1. Turner B.N...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005543
EISBN: 978-1-62708-197-9
... International , 1992 • DoD Modeling and Simulation (M&S) Glossary , U.S. Department of Defense, (DoD 5000.59-M), Jan 1998 • Introduction to Finite-Difference Methods for Numerical Fluid Dynamics , Los Alamos National Laboratories, released to OSTI, 1996 • Dictionary of Scientific...
Book Chapter

Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005454
EISBN: 978-1-62708-196-2
... and Simulation (M&S) Glossary , U.S. Department of Defense, (DoD 5000.59-M), Jan 1998 • Introduction to Finite-Difference Methods for Numerical Fluid Dynamics , Los Alamos National Laboratories , released to OSTI, 1996 • Dictionary of Scientific and Technical Terms , 5th ed. , McGraw-Hill...
Series: ASM Handbook
Volume: 20
Publisher: ASM International
Published: 01 January 1997
DOI: 10.31399/asm.hb.v20.a0002446
EISBN: 978-1-62708-194-8
... as: (Eq 6) d F d b i ≈ F ( b + Δ b i ) − F ( b ) Δ b i where Δ b i is a zero vector with the exception of the i th location that contains Δ b i . Significant disadvantages of the finite difference method exist when it is used with CAE...
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005233
EISBN: 978-1-62708-187-0
... description of CFD, but it is necessary to speak in general terms when introducing a subject that encompasses such a wide variety of solution techniques. There are several numerical methods for solving CFD equations, and this overview focuses on the most common: finite difference, finite volume, and finite...
Series: ASM Handbook
Volume: 14B
Publisher: ASM International
Published: 01 January 2006
DOI: 10.31399/asm.hb.v14b.a0005169
EISBN: 978-1-62708-186-3
...; F b is the tensile force/yield force fcc face-centered cubic FDM finite-difference method FEA finite-element analysis FEM finite-element method/model Fig. figure FLD forming limit diagram FR functional requirements FRP fiber-reinforced plastic...
Series: ASM Handbook
Volume: 13A
Publisher: ASM International
Published: 01 January 2003
DOI: 10.31399/asm.hb.v13a.a0003596
EISBN: 978-1-62708-182-5
... such as finite-element methods, finite-difference methods, or boundary-element methods are applied to analyze the ECM process. A single equation has been derived ( Ref 6 ) for numerical methods analysis. It is applicable simultaneously to both the cases, that is, for f = 0 and f ≠ 0. Equation 10 can...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005503
EISBN: 978-1-62708-197-9
... method for Eq 2 , while a finite-difference method is used in the z -direction (thickness), making use of the same finite elements in the x - y plane for solving Eq 3 . The finite-difference method (FDM) is a relatively efficient and simple numerical method for solving differential equations...
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005348
EISBN: 978-1-62708-187-0
... solid fraction FC furnace cool fcc face-centered cubic FCAW flux cored arc welding FDM finite difference method FEM finite element method FG flake graphic Fig. figure FM full mold FM (process) fnote mince (thin iron) process FRC free radical...