Finite-element mesh

The discretization of a problem domain into a finite element mesh consisting of randomly sized triangular elements is shown in Figure 2,1. In the coarse mesh shown there are relatively large gaps between the actual domain boundary and the boundary of the mesh and hence the overall discretization error is expected to be large. 

Consider the integration of a function/(xj, X2) over a quadrilateral element in a finite element mesh expressed as... 

Lagrangian-Eulerian (ALE) method. In the ALE technique the finite element mesh used in the simulation is moved, in each time step, according to a predetermined pattern. In this procedure the element and node numbers and nodal connectivity remain constant but the shape and/or position of the elements change from one time step to the next. Therefore the solution mesh appears to move with a velocity which is different from the flow velocity. Components of the mesh velocity are time derivatives of nodal coordinate displacements expressed in a two-dimensional Cartesian system as... 

Figure 5.2 shows the finite element mesh corresponding to the configuration shown in Figure 5.1. This mesh consists of 225 nine-node bi-quadratic elements and its utihzation in the present model is based on the application of isoparametric mapping, described in Chapter 2.

Figure 5.4 The finite element mesh configurations in the Arbitrary Lagrangian-Eulerian scheme...

Figure 5.8 The finite element mesh used to model free surface flow in example 5.2.1...

GENERAL CONSIDERATIONS RELATED TO FINITE ELEMENT MESH GENERATION... 

Fig. 18 Finite element modeling of steady-state concentration profiles in the human eye[241] from a hypothetical device that releases from one side only, (a) Device releases towards the front (b) device releases towards the back. Arbitrary concentration units (scale, inset a) highest concentration marked x. Contours are shown for x-z plane and for x-y plane through the center, x-z portion of finite element mesh displayed (inset b) device (opaque to diffusion) represented by voided region. (Adapted from Ref. 244.)... 

Figure 16 Representation of a finite-element mesh for the simulation between a fractal, elastic object and a flat substrate. Reproduced with permission from reference 24.

Figure 5.3 Sample two-dimensional simulations of the RTM process. (Top) finite element mesh (bottom) flow front progression, Kyy — 3KXX, Kxy = 0.0...

The finite element mesh used in the computations is shown in the top of Figure 5.6. Similar to the RTM process dP/dn is set to zero on all solid boundaries and the pressure is... 

Figure 5.6 Sample three-dimensional simulations of the IP process. (Top) Finite element mesh. Total length 30 cm (0 < X < 30), total height 1 cm (0 < Z < 1), total width 3 cm (0 < Y < 3). Fluid is injected from both sides through the thickness (i.e., in the Z-direction through a 1 cm x 1 cm square). (Bottom) Flow front progression at the midplane (i.e., Z — 0.5), Ka = Kzz = 2Kyy K, - = 0.0...

Figure 9.8 Finite element mesh with 4 elements and 10 nodes.

Figure 9.13 Finite element mesh using constant strain, or gradient, triangles for the domain presented in Fig. 9.12...

Figure 9.15 Finite element mesh using isoparametric quadrilateral elements for the domain...

Figure 9.19 Four-noded isoparametric finite element mesh for the L-shape charge.

Figure 9.23 Finite element mesh of the cross-section of an SMC charge [12].

In addition to the above formulation, they used two-noded elements to represent the runner system. Figure 9.29 presents the finite element mesh employed by Wang et al. [18] with the dimensions and location of the pressure transducers used to record pressure during mold filling. The fan gates were of variable thickness as pointed out in the figure, and the mold cavity was of constant thickness. 

Figure 9.35 Finite element mesh of one half of the lens geometry and associated boundary conditions [10].

Figure 9.40 Finite element mesh used to simulate the teardrop channel geometry [7].

Figure 1. Navier-Stokes flow through a semipermeable membrane (a) geometry and (b) finite element mesh.

P. Laug and H. Borouchaki, Generation of finite element meshes on molecular surfaces, Int. J. Quantum. Chem., 93 (2003) 131-138. 

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