Simple modifications of monotonicity-preserving limiters

We present simple modifications of standard monotonicity-preserving limiter s that provide either sign preservation or alternative bounding values for the resulting numerical schemes (e.g., that the solution remain between zer o and one rather than preserving monotonicity). These limiters can be easil y implemented in Godunov-type methods by modifying the reconstruction step of the algorithm. These modifications allow methods to achieve greater form al accuracy, for example by improving the first-order accuracy in the L-inf inity norm. The greatest advantage of our approach is its natural extension to more than one spatial dimension, and to systems of equations without op erator splitting.