  Flood front is the jump interface where fluids distribute discontinuously,
whose interface condition is the theoretical basis of a mathematical model of
the multiphase flow in porous medium. The conventional interface condition at
the jump interface is expressed as the continuous Darcy velocity and fluid
pressure (named CPVCM). This paper has inspected it via the studying the
water-oil displacement in one dimensional reservoir with considering capillary
pressure but ignoring the compressibility and gravity. It is proved
theoretically that the total Darcy velocity and total pressure (defined by
Antoncev etc.), instead of the Darcy velocities and pressures of water and oil,
are continuous at the flood front without considering the compressibility of
fluid and porous media. After that, new interface conditions for the pressures
and Darcy velocity of each fluid are established, which are collectively named
as Jump Pressures and Velocities Conditions Model (JPVCM) because the model has
shown the jump pressures and jump Darcy velocities at the flood front. Finally,
three application-examples are proposed and the results show JPVCM is more
reasonable than CPVCM. Keywords: Flood front; Jump Condition; Two phase;
numerical flux; mathematical model
