  In this work we study the solution of the Riemann problem for the barotropic
version of the conservative symmetric hyperbolic and thermodynamically
compatible (SHTC) two-phase flow model introduced in
\cite{Romenski2007,Romenski2009}. All characteristic fields are carefully
studied and explicit expressions are derived for the Riemann invariants and the
Rankine-Hugoniot conditions. Due to the presence of multiple characteristics in
the system under consideration, non-standard wave phenomena can occur.
Therefore we briefly review admissibility conditions for discontinuities and
then discuss possible wave interactions. In particular we will show that
overlapping rarefaction waves are possible and moreover we may have shocks that
lie inside a rarefaction wave. In contrast to nonconservative two phase flow
models, such as the Baer-Nunziato system, we can use the advantage of the
conservative form of the model under consideration. Furthermore, we show the
relation between the considered conservative SHTC system and the corresponding
barotropic version of the nonconservative Baer-Nunziato model. Additionally, we
derive the reduced four equation Kapila system for the case of instantaneous
relaxation, which is the common limit system of both, the conservative SHTC
model and the non-conservative Baer-Nunziato model. Finally, we compare exact
solutions of the Riemann problem with numerical results obtained for the
conservative two-phase flow model under consideration, for the non-conservative
Baer-Nunziato system and for the Kapila limit. The examples underline the
previous analysis of the different wave phenomena, as well as differences and
similarities of the three systems.
