  In \cite{ZH2019}, we developed a boundary treatment method for
implicit-explicit (IMEX) Runge-Kutta (RK) methods for solving hyperbolic
systems with source terms. Since IMEX RK methods include explicit ones as
special cases, this boundary treatment method naturally applies to explicit
methods as well. In this paper, we examine this boundary treatment method for
the case of explicit RK schemes of arbitrary order applied to hyperbolic
conservation laws. We show that the method not only preserves the accuracy of
explicit RK schemes but also possesses good stability. This compares favourably
to the inverse Lax-Wendroff method in \cite{TS2010,TWSN2012} where analysis and
numerical experiments have previously verified the presence of order reduction
\cite{TS2010,TWSN2012}. In addition, we demonstrate that our method performs
well for strong-stability-preserving (SSP) RK schemes involving negative
coefficients and downwind spatial discretizations. It is numerically shown that
when boundary conditions are present and the proposed boundary treatment is
used, that SSP RK schemes with negative coefficients still allow for larger
time steps than schemes with all non-negative coefficients. In this regard, our
boundary treatment method is an effective supplement to SSP RK schemes
with/without negative coefficients for initial-boundary value problems for
hyperbolic conservation laws.
