Summary A novel method for simulating multi‐phase flow in porous media is presented. The approach is based on a control volume finite element mixed formulation and new force‐balanced finite element pairs. The novelty of the method lies in (i) permitting both continuous and discontinuous description of pressure and saturation between elements; (ii) the use of arbitrarily high‐order polynomial representation for pressure and velocity and (iii) the use of high‐order flux‐limited methods in space and time to avoid introducing non‐physical oscillations while achieving high‐order accuracy where and when possible. The model is initially validated for two‐phase flow. Results are in good agreement with analytically obtained solutions and experimental results. The potential of this method is demonstrated by simulating flow in a realistic geometry composed of highly permeable meandering channels.
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Gomes et al. (2016) studied this question.
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