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arbitrary Lagrangian-Euler equation

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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
...-fluids systems geometry arbitrary Lagrangian-Euler equation SIMULATION OF CASTING is motivated by the need to minimize casting defects by understanding and controlling the fluid flow and thermal processes throughout the casting process. However, modeling of casting processes is difficult because...
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 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...
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
... 3 , when calculating compressible flows. The previous equations are expressed in Eulerian form; that is, the time derivative is taken at a fixed point in space. This contrasts with the Lagrangian form, in which the time derivative is taken following a fluid element ( Ref 14 ). Although...
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
... energy or enthalpy equations, in place of Eq 3 , when calculating compressible flows. The above equations are expressed in Eulerian form; that is, the time derivative is taken at a fixed point in space. This contrasts with the Lagrangian form, in which the time derivative is taken following...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005422
EISBN: 978-1-62708-196-2
... their triple junctions, called vertices, in a manner similar to the approaches of Fullman ( Ref 7 ) and Soares et al. ( Ref 10 ). However, in the approach of Kawasaki et al., the velocities of the triple junctions resulted from the solution of a system of Lagrangian equations for the dissipation...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005450
EISBN: 978-1-62708-196-2
... Concept of the Control Volume Eulerian and Lagrangian Views In analyzing problems in mechanics, two approaches have evolved. In the Lagrangian method, equations of motion are written for a moving particle. Variations in a fluid property are monitored for each individual particle as it moves...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005435
EISBN: 978-1-62708-196-2
.... For the free energy in Eq 2 , the Euler-Lagrange variation of [ F − Λ G ] with respect to the nonorder parameter strains, e 1 , e 3 is then ( Ref 9 , 12 ) δ( F c – Σ r Λ G )/δ e i = 0, where i = 1,3, and G denotes the constraint equation ( Eq 6 ), Λ is a Lagrangian multiplier, and F...