Assessment of Cell-centered and Cell-vertex Finite Volume Approaches for Computation of 2D Structural Dynamics on Arbitrary Quadrilateral Grids
Kazem Hejranfar and Mohammad-Hadi Azampour

Source CMES: Computer Modeling in Engineering & Sciences, Vol. 106, No. 6, pp. 395-439, 2015
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Keywords Cell-centered and cell-vertex finite volume approaches, Structural dynamics, Arbitrary quadrilateral grids

In this study, cell-centered (CC) and cell-vertex (CV) finite volume (FV) approaches are applied and assessed for the simulation of two-dimensional structural dynamics on arbitrary quadrilateral grids. For the calculation of boundary nodes’ displacement in the CC FV approach, three methods are employed. The first method is a simple linear regression of displacement of boundary nodes from the displacement of interior cell centers. In the second method, an extrapolation technique is applied for this purpose and, in the third method; the line boundary cell technique is incorporated into the solution algorithm in an explicit manner. To study the effects of grid irregularity on the results of CC and CV FV approaches, different grid types are used ranging from regular square grids to irregular ones, including random perturbations of the grid nodes. A comparison between the CC and CV FV approaches is made in terms of accuracy and performance by simulating some benchmark test cases in structural dynamics on different grid types. The present study demonstrates the suitability of using CC FV approach for the simulation of structural dynamics problems and that the results obtained by careful implementation of the CC FV can be comparable with those of the CV FV. On irregular grids, the CC FV approach employing the extrapolation technique fails to obtain accurate results in the most cases studied, however, two other techniques, namely the linear regression and boundary cell methods provide reasonable results. It is indicated that the CV and CC approaches are equivalent in terms of accuracy and convergence rate on regular grids, though, the CV approach is more efficient in term of computational costs. The results obtained by these two approaches for the problems considered here are in good agreement with the analytical solutions.

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