Interdisciplinary Applied Mathematics

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bJ


101


Г



Mesh A


8



Mesh B


10-3



Mesh C


8



Mesh D



Mesh E


10-5


<


Mesh F


8


О


Mesh G


о


Mesh H


10-7


— 8

10-9


8


10



10-13



J.


5


O О


8


8


_i_i_i_i_i_i_i_i_i_i_i


10    15    20


Expansion Order


FIGURE 14.6. Convergence in the L2 norm for modal projection of the function u = sin(^®) sin(^y) on meshes A through H shown in Figure 14.5.


has a concentration of в = 0. The zero-flux boundary conditions for the species are used on the channel side-walls and on the cylinder surface. At the channel exit fully developed conditions are assumed, and the pressure is set to zero (gauge pressure) at the outflow.


The computational domain and the corresponding spectral/hp element discretization are shown in Figure 14.7. Here a 6th-order modal expansion is employed in each direction inside each element with 32 quadrilateral and 314 triangular    elements.    The    total    number    of    elements    is    fixed    during a


simulation. The elemental discretization is shown by the thick lines, and quadrature points are shown by the thin lines (a). Figure 14.7 (b) shows the deformed mesh at the cylinder minimum position, caused by the cylinder oscillation. The dashed-dotted line shows the center of the channel. The elements near the cylinder experience large deformations. Based on the test results in Figures 14.5 and 14.6, we expect the unstructured hp mesh to sustain high-order accuracy under large deformations. Thus, we do not have to remesh the computational domain for most practical applications.

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