A force‐balanced control volume finite element method for multi‐phase porous media flow modelling. (4th August 2016) - Gomes, J. L. M. A.; Pavlidis, D.; Salinas, P.; Xie, Z.; Percival, J. R.; Melnikova, Y.; Pain, C. C.; Jackson, M. D.
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. © 2016 The Authors International Journal for Numerical Methods in Fluids Published by John Wiley & Sons Ltd Abstract : Multi‐phase flow through highly permeable underground channels (the flow is from the left). The novel method presented and validated in this paper allows for discontinuous description of pressure and saturation between elements which results in minimal numerical dispersion. In addition, the method is high‐order accurate and uses fully unstructured meshes as shown in thefigure.