Steamflooding is a tertiary oil recovery mechanism with proven economic potential. Reliable numerical simulations of candidate injection schemes can aid in the optimization of process parameters. State-of-the-art numerical models exhibit varying degrees of grid effects which affect their reliability with respect to the modeling of pattern floods. This paper presents a numerical steamflood model which does not exhibit a significant amount of grid orientation. This model utilizes a numerical discretization technique which is an admixture of finite difference and finite element methods. Fluid properties are determined as a function of primary variables in a manner that allows a straightforward implementation of Newton's method for solving the nonlinear system of discretized equations. Fractional flows are defined using mass rather than volumetric mobilities, and are used to upwind the convective flow terms.