Publications

Rao, Rekha R.; Noble, David R.; Schunk, Randy; Wilkes, Edward D.; Baer, Thomas A.; Rao, Rekha R.; Notz, Patrick N.

Solidification and blood flow seemingly have little in common, but each involves a fluid in contact with a deformable solid. In these systems, the solid-fluid interface moves as the solid advects and deforms, often traversing the entire domain of interest. Currently, these problems cannot be simulated without innumerable expensive remeshing steps, mesh manipulations or decoupling the solid and fluid motion. Despite the wealth of progress recently made in mechanics modeling, this glaring inadequacy persists. We propose a new technique that tracks the interface implicitly and circumvents the need for remeshing and remapping the solution onto the new mesh. The solid-fluid boundary is tracked with a level set algorithm that changes the equation type dynamically depending on the phases present. This novel approach to coupled mechanics problems promises to give accurate stresses, displacements and velocities in both phases, simultaneously.

Salinger, Andrew G.; Pawlowski, Roger P.; Lehoucq, Richard B.; Romero, L.A.; Wilkes, Edward D.

LOCA, the Library of Continuation Algorithms, is a software library for performing stability analysis of large-scale applications. LOCA enables the tracking of solution branches as a function of a system parameter, the direct tracking of bifurcation points, and, when linked with the ARPACK library, a linear stability analysis capability. It is designed to be easy to implement around codes that already use Newton's method to converge to steady-state solutions. The algorithms are chosen to work for large problems, such as those that arise from discretizations of partial differential equations, and to run on distributed memory parallel machines. This manual presents LOCA's continuation and bifurcation analysis algorithms, and instructions on how to implement LOCA with an application code. The LOCA code is being made publicly available at www.cs.sandia.gov/loca.