The modifications required to apply Roe's Riemann solver to the Euler equat
ions with source terms are developed and demonstrated. The generalized quas
i-one-dimensional Row including the effects of friction, secondary mass add
ition, and energy addition has been considered, The modifications require e
xtensions of the expressions for the strengths of the characteristic waves,
The modified expressions for the wave strengths in Roe's Riemann solver ar
e obtained from the theory of characteristics using the compatibility relat
ions that depend on the specific source terms present. It is also shown tha
t appropriate discretization of the source terms is required to obtain the
correct solution. It is demonstrated that the compatibility relations in th
e presence of source terms can be used to modify not only Roe's Riemann sol
ver but also characteristic-based boundary conditions. The validity of the
proposed approach is illustrated by comparing the exact analytical solution
s and the numerical solutions with and without the proposed corrections for
two examples involving steady Bow and one involving unsteady Bow.