Method for Treating Hourglass Patterns

摘要

Hourglassing is a problem frequently encountered in numerical simulations of fluid and solid dynamics. The problem arises because certain volume-preserving distortions of cell shape produce no restoring forces. The result is an unrestricted drifting mode in the velocity field that leads to severe distortions of the computational mesh. These distortions cause large errors in the numerical approximations of the equations of motion. The drift may also allow adjacent vertices to get very close to each other. This results in the computational time step based on a Courant stability condition to become very small, effectively halting the calculation. We describe a mathematical formalism that identifies and selectively damps the hourglass patterns. The damping is constructed to preserve the physical aspects of the solution while maintaining a reasonable computational mesh. We further describe the implementation of our scheme in a 2D hydro code, and show the relative improvement in the results of six different test problems that we calculated. (ERA citation 12:034068)