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8th Thermal and Fluids Engineering Conference (TFEC)
March, 26-29, 2023, College Park, MD, USA

ON DEMAND FORMULATION OF THE GRADIENT ADAPTIVE TRANSFINITE ELEMENTS FOR FLOWFIELD PROBLEMS

Get access (open in a dialog) pages 461-477
DOI: 10.1615/TFEC2023.cmd.046433

Abstract

In the computational simulation of flows, multiple field variables must be approximated simultaneously, which necessitates a mixed finite element formulation. It has been shown that when discretizing using conventional finite elements that interpolate the field variables at discrete points, spurious pressure oscillations can result if the mesh is not sufficiently refined. The required mesh size to avoid such issues can become extremely small, hence resulting in excessive computational cost and inaccurate flow field predictions. Therefore, conventional finite elements, such as those contained in commercial finite element packages, are not well suited for the simulation of flows overs complex domains in presence of steep gradients.
It is the goal of this paper to detail our new development which is based "on demand element formulation" framework to match the minimum required order of approximation in domain and flow field variables without needing to regenerate discretization to achieve convergence. Unlike traditional finite elements, these elements interpolate the desired field and domain variables along the sides, (or surfaces if three-dimensional, of subdomains and provide a smooth interpolating function through the subdomain. This paper first details the new framework "Elements on demand formulation" of the gradient adaptive transfinite elements. Then, convergence results are presented for a linear problem and an incompressible flow problem. A case study involving flow over cylinder is also presented.