Adaptive finite element approximation of coupled flow and transport problems with applications in heat transfer

Abstract

SUMMARYIn this paper we develop an adaptive finite element method for heat transfer in incompressible fluid flow. The adaptive method is based on an a posteriori error estimate for the coupled problem, which identifies how accurately the flow and heat transfer problems must be solved in order to achieve overall accuracy in a specified goal quantity. The a posteriori error estimate is derived using duality techniques and is of dual weighted residual type. We consider, in particular, an a posteriori error estimate for a variational approximation of the integrated heat flux through the boundary of a hot object immersed into a cooling fluid flow. We illustrate the method on some test cases involving three-dimensional time-dependent flow and transport.

Adaptive finite element approximation of multiphysics problems: A fluid–structure interaction model problem

“…A general methodology for a posteriori error estimation in segregated multiphysics finite element solvers is presented by the authors in [2], where an application to micro-electro-mechanical systems involving electrostatics, heat conduction, and elasticity is studied. In [3] these results are extended to heat transfer in time-dependent incompressible flow. Closely related results are presented by Estep and coworkers [4] in the context of multiscale operator decomposition for elliptic problems.…”

Error Assessment in Structural Transient Dynamics

“…where the data λ O and λ O N are weighting functions allowing to localize the average of displacements in some sub-domains in Ω and Γ N respectively, is neither directly included in (25). In this case, an auxiliary problem is introduced: find…”

“…It is worth noting that the quantity of interest associated to the energy consistent double field formulation CGA is the equivalent to the single field quantity of interest defined in (25). This is because the definition of…”

“…For instance, quasi-steady-state non-linear problems are addressed in references [15,16,17,18], estimates for advection-diffusion-reaction equation are discussed in [19], similar approaches for the Stokes problem are presented in [20], and extension to parabolic time-dependent problems is introduced in [21,22,23]. Moreover, the same type of tools for coupled problems have been recently discussed in [24,25,26,27,28].…”

14th International Conference on Finite Elements in Flow Problems

“…The topic of adaptivity and a posteriori error estimation for coupled heat-transfer fluid flow is treated in the work by Larson et al [17]. The error estimator is based on a duality technique and applied to the heat flux at an immersed boundary.…”