Just another WordPress site - Ruhr-Universität Bochum
A control volume treatment of finite elements and its applications to a solidification problem
he control volume method (CVM) is of particular interest for the numerical solution of instationary non-linear partial differential equations. It is superior to the finite element method (EM) as regards the physical interpretation and the simplicity of integrating special features such as upwinding methods. The numerical accuracy of both methods is similar for a wide range of problems. However, the integration of different types of elements into an unstructured mesh is a severe limitation of the CVM. This presentation describes a finite element based control volume method and its application to solidification problems. Starting FEM with first-order approximations, the transient problem is localized by lumping masses in nodes, respectively the control volumes. The exchange integrals between the nodes – representing the control volumes – are determined by standard FE integration and adding up the conditions of connected elements. The exchange integrals are then identified with those of a 1-dimensional problem localized on an individual link between the two control volumes. This formal CVM has been implemented into the FE-code CASTS  for the simulation of casting processes. Numerical calculations are presented that examine the influence of fluid flow on the solidification front. The advantages of the new FE-based CV-method are discussed with respect to their application to industrial scale solidification simulation of complex shaped castings.