Numerical simulation of glacier dynamics in mountainous regions using low-order, shallow ice models is desirable for computational efficiency and their capability of including ice dynamics in estimates of mountain glacier wastage worldwide. However, these models present several difficulties when applied to complex topography. One such problem arises where dynamical mass flux over steep topography produces spurious mass at a grid cell flux boundary if upstream cells receive positive mass balance. This paper describes a vertically integrated, shallow ice model using a second order flux limiting spatial discretization scheme that enforces mass conservation. An exact solution to ice flow over a bedrock step is derived for a given mass balance forcing as a benchmark to evaluate the model performance in such a difficult setting. This benchmark should serve as a useful test for modellers interested in simulating glaciers over complex terrain.