# Publications

## Preprints

X. Wu, H. Guo,

**Z. Xu**, L. Tian & Y. Yang, A reinterpreted discrete fracture model for wormhole propagation in fractured porous media, submitted to Journal of Computational Physics.**Z. Xu**& Y.-T. Zhang, High-order exponential time differencing multi-resolution alternative finite difference WENO methods for nonlinear degenerate parabolic equations, arXiv:2406.05237, submitted to Journal of Computational Physics.Y. Liu &

**Z. Xu**, An interior penalty discontinuous Galerkin method for an interface model of flow in fractured porous media, arXiv:2405.06874, submitted to Journal of Computational Physics.**Z. Xu**& D. Gläser, An extension of the box method discrete fracture model (Box-DFM) to include low-permeable barriers with minimal additional degrees of freedom, arXiv:2404.18338, submitted to Advances in Water Resources.**Z. Xu**& C.-W. Shu, A high-order well-balanced alternative finite difference WENO (A-WENO) method with the exact conservation property for systems of hyperbolic balance laws, submitted to Advances in Water Resources.

## Journal Papers

**Z. Xu**& C.-W. Shu, A high-order well-balanced discontinuous Galerkin method for hyperbolic balance laws based on the Gauss-Lobatto quadrature rules, Journal of Scientific Computing, to appear.**Z. Xu**& C.-W. Shu, Local characteristic decomposition–free high-order finite difference WENO schemes for hyperbolic systems endowed with a coordinate system of Riemann invariants, SIAM Journal on Scientific Computing, v46 (2024), pp.A1352-A1372.X. Wu, H. Guo,

**Z. Xu**& Y. Yang, A reinterpreted discrete fracture model for Darcy-Forchheimer flow in fractured porous media, Advances in Water Resources, (2023), 104504.**Z. Xu**& C.-W. Shu, On the conservation property of positivity-preserving discontinuous Galerkin methods for stationary hyperbolic equations, Journal of Computational Physics, v490 (2023), 112304.**Z. Xu**, Z. Huang & Y. Yang, The hybrid-dimensional Darcy’s law: A non-conforming reinterpreted discrete fracture model (RDFM) for single-phase flow in fractured media, Journal of Computational Physics, v473 (2022), 111749.**Z. Xu**& C.-W. Shu, Third order maximum-principle-satisfying and positivity-preserving Lax-Wendroff discontinuous Galerkin methods for hyperbolic conservation laws, Journal of Computational Physics, v470 (2022), 111591.**Z. Xu**& C.-W. Shu, High order conservative positivity-preserving discontinuous Galerkin method for stationary hyperbolic equations, Journal of Computational Physics, v466 (2022), 111410.H. Guo, W. Feng,

**Z. Xu**& Y. Yang, Conservative numerical methods for the reinterpreted discrete fracture model on non-conforming meshes and their applications in contaminant transportation in fractured porous media, Advances in Water Resources, v153 (2021), 103951.**Z. Xu**& Y. Yang, The hybrid dimensional representation of permeability tensor: A reinterpretation of the discrete fracture model and its extension on nonconforming meshes, Journal of Computational Physics, v415(2020), 109523.**Z. Xu**, Y. Yang & H. Guo, High-order bound-preserving discontinuous Galerkin methods for wormhole propagation on triangular meshes, Journal of Computational Physics, v390 (2019), pp.323-341.N. Chuenjarern,

**Z. Xu**& Y. Yang, High-order bound-preserving discontinuous Galerkin methods for compressible miscible displacements in porous media on triangular meshes, Journal of Computational Physics,v378 (2019), pp.110-128H. Guo, L. Tian,

**Z. Xu**, Y. Yang & N. Qi, High-order local discontinuous Galerkin method for simulating wormhole propagation, Journal of Computational and Applied Mathematics, v350 (2019), pp.247-261.

## Conference Papers

**Z. Xu**& Y. Yang, The hybrid-dimensional Darcy’s law: A non-conforming reinterpreted discrete fracture model (RDFM) for the compressible miscible displacement and multicomponent gas flow in fractured media, Paper presented at the SPE Reservoir Simulation Conference, (2023), SPE-212164-MS.