Background
Ziyao Xu is an assistant professor in the Department of Mathematics and Statistics at Binghamton University. His research interests lie in scientific computing and numerical analysis of partial differential equations (PDEs), with a particular focus on developing robust and efficient high-order numerical methods for flow and transport problems. He has worked extensively in computational fluid dynamics and fluid flow in porous media, designing high-order accurate finite element and finite difference methods, as well as mathematical modeling in these areas.
Before joining Binghamton, Xu was a Robert and Sara Lumpkins Postdoctoral Research Associate in the Department of Applied and Computational Mathematics and Statistics at the University of Notre Dame. He received his PhD in applied mathematics from Brown University.
Select Publications
- X. Wu, H. Guo, Z. Xu, L. Tian & Y. Yang, A reinterpreted discrete fracture model for wormhole propagation in fractured porous media, Journal of Computational Physics, v532 (2025), 113953.
- Z. Xu & Y.-T. Zhang, High-order exponential time differencing multi-resolution alternative finite difference WENO methods for nonlinear degenerate parabolic equations, Journal of Computational Physics, v529 (2025), 113838.
- Z. Xu & C.-W. Shu, A high-order well-balanced alternative finite difference WENO (A-WENO) method with the exact conservation property for the shallow water equations, Advances in Water Resources, v196 (2025), 104898.
- 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, Advances in Water Resources, v195 (2025), 104869.
- 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, v101 (2024), 39.
Education
- PhD, Brown University
Research Interests
- Scientific computing
- Numerical analysis
Teaching Interests
- Real analysis
- Number systems