Mini-Workshop on Variational Multiscale Methods and Stabilized Finite Elements

for the Mini-Workshop “VMS and Stabilized FE” Stabilized Methods for Free-Surface Flow Simulations Marek Behr Chair for Computational Analysis of Technical Systems Center for Computational Engineering Science RWTH Aachen University Steinbachstr. 53B, 52074 Aachen, Germany [email protected] Free-surface flow simulations are an important design and analysis tool in many areas of engineering, including civil engineering, marine and coating industries, and off-shore exploration. Two alternative computational approaches—interface-tracking and interface-capturing—are commonly considered. While interface-capturing offers unmatched flexibility for complex free-surface motion, the interface-tracking approach is very attractive due to its excellent mass conservation properties at low resolution. This provides motivation for expanding the reach of the interface-tracking methods. The fundamentals of interface-tracking free-surface flow simulations—stabilized discretizations of NavierStokes equations, ALE and space-time formulations on moving grids, general mesh update mechanisms based on solid mechanics—are widely known and adopted. Challenges still exist, and we discuss some of the issues that are limiting the success of interface-tracking approach. The generalized form of the kinematic condition, in the form of an elevation equation, as well as its stabilized GLS formulation, has been derived for cases where surface nodes move along prescribed straight lines. This method was then used to simulate water motion in trapezoidal tanks and channels. A further generalization is proposed for cases where surface nodes move along prescribed curvilinear spines. This allows for robust representation of the kinematic condition in an even wider set geometries, such as cylindrical vessels and channels. In a benchmark problem, the role of the stabilization of the kinematic condition is demonstrated, including the influence of discontinuity-capturing. Other aspects of stabilized finite element methodology relevant to moving-boundary flow simulations are also discussed.