In a fast neutron reactor severe accident, hot corium-cold sodium interaction may result in vapor explosions. This kind of interaction is commonly modeled by shock wave propagation using multiphase Navier-Stokes equations. Two main multiphase models are the Baer-Nunziato and isobaric formulations. These models can be discretized using finite volume staggered grids, as implemented in the multiphase incompressible PolyMAC scheme from the CFD solver TRUST, which solves the internal energy formulation of the isobaric model. This formulation does not automatically guarantee total energy conservation, leading to the violation of jump conditions, and hence to inaccurate solutions for compressible flows. Consequently, the corium-sodium interaction code SCONE (based on TRUST) is limited to low-compressibility flows. The purpose of this work is to develop a fully conservative staggered scheme that solves the Euler internal energy formulation. A comparative study was conducted on several schemes solving the single-phase internal energy formulation of Euler equations on uniform and non-uniform meshes. Specifically, we analyzed schemes that ensure discrete total energy conservation by introducing a corrective term in the internal energy equation. To evaluate both shock-capturing accuracy and total energy conservation, the comparison is based on standard shock-tube benchmark tests from the literature as well as on the intense shock Leblanc test-case. Corrected schemes demonstrated overall great shock-capturing precision, stability, convergence, and robustness. We are currently extending the correction term to multiphase flows to develop a conservative scheme for the internal energy isobaric multiphase model. Few studies provide a multiphase correction term. Since the isobaric model is not hyperbolic, elliptic instabilities may arise and must be stabilized using Bestion drag. Our study will employ various numerical and engineering techniques including implicit pressure treatment, MUSCL reconstruction, flux limitation and artificial viscosity for oscillation stabilization. The final objective is to select a conservative staggered scheme suitable for simulating all-Mach multiphase flows.