we introduce semiclassical eulerian methods that are efficient in computing high frequency waves through heterogeneous media. the method is based on the classical liouville equation in phase space, with discontinous hamiltonians due to the barriers or material interfaces. we provide physically relevant interface conditions consistent with the correct transmissions and reflections, and then build the interface conditions into the numerical fluxes. this method allows the resolution of high frequency waves without numerically resolving the small wave lengths, and capture the correct transmissions and reflections at the interface. this method can also be extended to deal with diffraction and quantum barriers.