  Different formulations of Einstein's equations used in numerical relativity
can affect not only the stability but also the accuracy of numerical
simulations. In the original Baumgarte-Shapiro-Shibata-Nakamura (BSSN)
formulation, the loss of the angular momentum, $J$, is non-negligible in highly
spinning single black hole evolutions. This loss also appears, usually right
after the merger, in highly spinning binary black hole simulations, The loss of
$J$ may be attributed to some unclear numerical dissipation. Reducing
unphysical dissipation is expected to result in more stable and accurate
evolutions. In the previous work \cite{yhlc12} we proposed several
modifications which are able to prevent black hole evolutions from the
unphysical dissipation, and the resulting simulations are more stable than in
the traditional BSSN formulation. Specifically, these three modifications (M1,
M2, and M3) enhance the effects of stability, hyperbolicity, and dissipation of
the formulation. We experiment further in this work with these modifications,
and demonstrate that these modifications improve the accuracy and also
effectively suppress the loss of $J$, particularly in the black hole
simulations with the initially large ratio of $J$ and the square of the ADM
mass.
