A level set based method for the optimization of cast part

A cast part is formed via casting process in which molten liquid is poured into and solidifies in a cavity enclosed by molds. Then, one obtains the cast part when the molds are removed. An important issue in the casting process is that a cast part should have a proper geometry so that the molds can actually be removed. Accordingly, in the optimization of a cast part one not only needs to optimize the performance of the cast part but also needs to ensure the cast part have a proper geometry. With these goals, a level set based method is proposed for the optimization of cast part. A molding condition and a performance condition on the design velocity are derived for the optimization. Numerical examples are provided in 2D and 3D.