Insight into the flow‐condition‐based interpolation finite element approach: solution of steady‐state advection–diffusion problems

Abstract

SUMMARYThe flow-condition-based interpolation (FCBI) finite element approach is studied in the solution of advection-diffusion problems. Two FCBI procedures are developed and tested with the original FCBI method: in the first scheme, a general solution of the advection-diffusion equation is embedded into the interpolation, and in the second scheme, the link-cutting bubbles approach is used in the interpolation. In both procedures, as in the original FCBI method, no artificial parameters are included to reach stability for high Péclet number flows. The procedures have been implemented for two-dimensional analysis and the results of some test problems are presented. These results indicate good stability and accuracy characteristics and the potential of the FCBI solution approach.

A flow‐condition‐based interpolation finite element procedure for triangular grids

“…Figure 4 shows the analytical model of the temperature problem considered with the boundary conditions and the mesh of 30 × 30 × 2 elements used in this study (see also Reference [7]). When a unit velocity is prescribed in the x direction over the whole domain, …”

“…The speciÿc aim in the FCBI 674 H. KOHNO AND K. J. BATHE solution approach is to reach procedures that are stable, accurate and e cient for any Reynolds number ow, even when rather coarse meshes are used for solution. The aims of our developments have been presented in detail in References [5][6][7].…”

“…The requirements that we have set for our developments within the FCBI solution approach are [5][6][7][8]10]:…”

Finite element developments for general fluid flows with structural interactions

“…Such a scheme does not exist yet, but we are developing the FCBI approach to obtain a method closer to the ideal scheme. The current FCBI procedure can already be used for complex fluid flow problems with structural interactions, and we see considerable potential to further increase its effectiveness [32], in particular when used with goal-oriented error estimations [33,34].…”

An unstructured finite volume approach for structural dynamics in response to fluid motions

“…The efforts to bridge the differences between them have been attempted. In particular, Bathe et al [2][3][4][5] proposed a flow-condition-based interpolation (FCBI) finite element scheme for incompressible fluid flows to achieve local mass and momentum conservation which was considered the unique property of the FV method. The FCBI finite element procedure was applied to solve multi-physics problems in a consistent FE framework and its accuracy was assessed by the goal-oriented error estimation technique [6,7].…”