Asymptotic justification of the treatment of a metallostatic pressure type boundary condition in an aluminium casting

摘要

We present an asymptotic analysis to justify the treatment of a metallostatic pressure type boundary condition on a thermal free boundary arising from the thermomechanical modelling of aluminium. alloy castings. The problem is solved by means of a fictitious domain method. Using the Saint-Venant's principle we shall justify that for a suitable choice of the Lame coefficients in the fictitious domain, the solution obtained with this methodology approaches the initial problem solution "far" from the free boundary. [References: 18]