A SECOND-ORDER ACCURATE, LINEARITY-PRESERVING VOLUME TRACKING ALGORITHM FOR FREE SURFACE FLOWS ON 3-D UNSTRUCTURED MESHES

The design of an optimal casting process begins with a fundamental understanding of the free surface flow dynamics brought about by the discharge of molten metal into a mold cavity. For the foundries at the Los Alamos National Laboratory (LANL), this discharge is initiated by a gravity pour process which results in a turbulent and topologically complex 3-D flow as the mold cavity is filled. To better understand the moldfilling portion of LANL casting processes, a new casting simulation tool 1 has been recently developed. A key method embodied in this tool is a novel volume tracking algorithm capable of faithfully replicating the kinematics of free surfaces moving within 3D domains partitioned by generalized unstructured meshes. The method exhibits several desirable properties: robustness, secondorder temporal and spatial accuracy, and a suitability for any unstructured mesh comprised of elements bounded by ruled surface faces. Details necessary for algorithm implementation, e.g., exact volume truncation expressions, are given along with several illustrative numerical simulations.