A finite-element method is developed for the two-dimensional advection-diffusion heat equation. The method features up to cubic triangular elements with Lagrange polynomial basis functions and isoparametric elements for curved boundaries. First, test problems show that the error of the method agrees with theoretical estimates. Then the method is used to compute the temperature in the flow around an internally cooled airfoil and in the airfoil itself

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CWI
Modelling, Analysis and Simulation [MAS]
Scientific Computing

Wackers, J. (2004). A finite-element solver for the 2D heat equation with convection.. Modelling, Analysis and Simulation [MAS]. CWI.