This paper is concerned with numerical methods for compressible multicomponent fluids. The fluid components are assumed immiscible, and are
separated by material interfaces, each endowed with its own equation of state (EOS). Cell averages of computational cells that are occupied
by several fluid components require a “mixed-cell” EOS, which may not always be physically meaningful, and often leads to spurious
oscillations. We present a new interface tracking algorithm, which avoids using mixed-cell information by solving the Riemann problem
between its single-fluid neighboring cells. The resulting algorithm is oscillation-free for isolated material interfaces, conservative, and
tends to produce almost perfect jumps across material fronts. The computational framework is general and may be used in conjunction with
one's favorite finite-volume method. The robustness of the method is illustrated on shock-interface interaction in one space dimension,
oscillating bubbles with radial symmetry and shock-bubble interaction in two space dimensions.