High Speed Inviscid Compressible Flow by the Finite Element Method

Zienkiewicz, O. C.; Loehner, Rainald; Morgan, K.

doi:10.1016/b978-0-12-747255-3.50006-x

Cited by 19 publications

(26 citation statements)

References 14 publications

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“…Which would be the best depends on the physical conditions of the problem. Continuative boundary conditions comprise zero normal derivatives at the 'open' boundary and are intended to represent a smooth continuation of the flow through the boundary, and is used for example in studies by Zienkiewicz et al (1985) and Peraire (1986). However, this type of boundary conditions has no strong physical basis, but rather is a mathematical statement which in some situations provides the desired flow behaviour.…”

Section: Nonlocal Continuum Plasticitymentioning

confidence: 99%

Bending of a single crystal: discrete dislocation and nonlocal crystal plasticity simulations

Yefimov¹,

Giessen²,

Groma³

2004

Modelling Simul. Mater. Sci. Eng.

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We have recently proposed a nonlocal continuum crystal plasticity theory that is based on a statistical-mechanics description of the collective behaviour of dislocations. Kinetic equations for the dislocation density fields have been derived from the equation of motion of individual dislocations and have been coupled to a continuum description of single slip. Dislocation nucleation, the material resistance to dislocation glide and dislocation annihilation are included in the formulation. The theory is applied, in this paper, to the problem of bending of a single-crystal strip in plane strain, using parameter values obtained previously from fitting to discrete dislocation results of a different boundary value problem. A numerical solution of the problem is obtained using a finite element method. The bending moment versus rotation angle and the evolution of the dislocation structure are analysed for different orientations and specimen sizes with due consideration of the role of geometrically necessary dislocations. The results are compared to those of discrete dislocation simulations of the same problem. Without any additional fitting of the parameters, the continuum theory is able to describe the dependence on slip plane orientation and on specimen size.

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Section: Nonlocal Continuum Plasticitymentioning

confidence: 99%

Bending of a single crystal: discrete dislocation and nonlocal crystal plasticity simulations

Yefimov¹,

Giessen²,

Groma³

2004

Modelling Simul. Mater. Sci. Eng.

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“…It will be assumed that the discretization employs p nodes, which need not be numbered sequentially and are such that node J is located at x 1 = x 1J . Elements, joining neighbouring nodes, are also numbered and the standard linear finite-element shape function associated with node J is denoted by N J (x 1 ) [26]. Finite-dimensional subspaces T (p) and W (p) of the trial and weighting function spaces, respectively, are defined by…”

Section: Galerkin Approximationmentioning

confidence: 99%

“…Both integrals are evaluated using the standard finite-element approach of summing the contributions from the individual elements [26]. On the left-hand side, the resulting element integrals are evaluated exactly.…”

Section: Galerkin Approximationmentioning

confidence: 99%

“…the numbers of the ordered nodes belonging to each element are prescribed. The discrete equations are then formed by looping over all the elements in the grid and sending element contributions to the respective nodes [26]. This grid data structure is widely employed in finite-element solvers, over a wide range of disciplines, and is the format which has been assumed in the construction of the right-hand sides in equations ( 60) and (110).…”

Section: Unstructured Gridsmentioning

confidence: 99%

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Unstructured grid finite-element methods for fluid mechanics

Morgan¹,

Peraire²

1998

Rep. Prog. Phys.

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The development of unstructured grid-based, finite-element methods for the simulation of fluid flows is reviewed. The review concentrates on solution techniques for the compressible Euler and Navier-Stokes equations, employing methods which are based upon a Galerkin discretization in space together with an appropriate finite-difference representation in time. It is assumed that unstructured assemblies of triangles are used to achieve the spatial discretization in two dimensions, with unstructured assemblies of tetrahedra employed in the three-dimensional case. Adaptive grid procedures are discussed and methods for accelerating the iterative solution convergence are considered. The areas of incompressible flow modelling and optimization are also included.

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“…The finite element method for (13), ( 14), (15) leads to the approximation ψ(x, y) ≈ ψ h (x, y) = j ψ h j u h j (x, y). Here ψ h j are the approximate values of the solution in the nodes of the triangular mesh, u h j (x, y) are the basic functions of piecewise-linear interpolation [9] on the mesh, ψ h (x, y) the finite element approximation of the solution. The summation is over all nodes of the mesh, including boundary nodes with the values of the solution prescribed by ( 14) and (15).…”

Section: Finite Element Methodsmentioning

confidence: 99%

Extraction of inductances of plane thin film superconducting circuits

Khapaev

1997

Supercond. Sci. Technol.

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The problem of extraction of the matrix of self-and mutual inductances of a thin plane superconducting film of arbitrary shape is considered. The accurate definition of the problem based on the London model of superconducting current is presented. An exact potential representation (stream function) is used for the current density. A new computational technique, based on the finite element method using triangular mesh, is suggested. An effective program is developed and results of calculations are presented. The computational method and the program can be used for the extraction of inductances of realistic superconducting circuits.

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High Speed Inviscid Compressible Flow by the Finite Element Method

Cited by 19 publications

References 14 publications

Bending of a single crystal: discrete dislocation and nonlocal crystal plasticity simulations

Bending of a single crystal: discrete dislocation and nonlocal crystal plasticity simulations

Unstructured grid finite-element methods for fluid mechanics

Extraction of inductances of plane thin film superconducting circuits

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