A new high-resolution spatial discretization scheme is presented for use within the volume-ofluid (VOF) method. This scheme is an adaptation of the previously published boundary gradient maximization (BGM) scheme, with an extension for time-dependent solutions. The scheme does not explicitly reconstruct the interface, but rather resolves the values of the volume fraction in the area of the interface. The scheme is upwind biased to provide numerical stability, and the face values are limited to meet boundedness criteria and prevent variable overshoot. Unlike most other high-resolution schemes found in the literature, the proposed scheme does not use upwind-biased and downwind-biased “switching” to maintain stability. This thesis presents a number of test cases including 2-D and 3-D cases on both structured and unstructured grids. The results display the method’s ability to predict good shape of the volume fraction interface and resolve the volume fraction discontinuity.