Constraint propagation of C2-adjusted formulation. II. Another recipe for robust Baumgarte-Shapiro-Shibata-Nakamura evolution system

In order to obtain an evolution system which is robust against the violation of constraints, we present a new set of evolution systems based on the so-called Baumgarte-Shapiro-Shibata-Nakamura equations. The idea is to add functional derivatives of the norm of constraints, C2, to the evolution equations, which was proposed by Fiske (2004) and was applied to the ADM formulation in our previous study. We derive the constraint propagation equations, discuss the behavior of constraint damping, and present the results of numerical tests using the gauge-wave and polarized Gowdy wave spacetimes. The construction of the C2-adjusted system is straightforward. However, in BSSN, there are two kinetic constraints and three algebraic constraints; thus, the definition of C2 is a matter of concern. By analyzing constraint propagation equations, we conclude that C2 should include all the constraints, which is also confirmed numerically. By tuning the parameters, the lifetime of the simulations can be increased 2-10 times longer than those of the standard Baumgarte-Shapiro-Shibata-Nakamura evolutions.