A phase-field-lattice-Boltzmann method, coupled with parallel computing and adaptive mesh refinement (Para-AMR), was employed to study the effect of forced flow on permeability of the mushy zone during solidification. Accuracy of the method was testified by comparing with predictions of conventional models, as well as other numerical investigations in literature. Results showed that the permeability of the mushy zone changed as the forced flow was imposed. For columnar dendritic networks, the permeability decreased exponentially either parallel or normal to the dendritic growth direction due to impinging and interlocking of secondary arms. The permeability of equiaxed dendritic networks decreased significantly when the flow was present. The permeability changed as a result of morphological transformation of the dendritic network, which became more columnar-like under a higher incoming velocity. Based on the numerical results and theoretical analysis, a new model was proposed for predicting permeability under the forced flow. Results showed that the model was suitable for describing the permeability of both columnar and equiaxed dendritic structures under a moderate forced flow, and could be used as a viable alternative to determine the permeability in a wide range of solid fraction during solidification. (C) 2018 Elsevier Ltd. All rights reserved.