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- Yulong Xing, Chi-Wang Shu
- J. Comput. Physics
- 2006

Hyperbolic balance laws have steady state solutions in which the flux gradients are nonzero but are exactly balanced by the source term. In our earlier work [J. Comput. Phys. 208 (2005) 206-227; J.… (More)

Shallow water equations with a non-flat bottom topography have been widely used to model flows in rivers and coastal areas. An important difficulty arising in these simulations is the appearance of… (More)

- Yulong Xing, Chi-Wang Shu
- 2005

Shallow water equations with nonflat bottom have steady state solutions in which the flux gradients are nonzero but exactly balanced by the source term. It is a challenge to design genuinely high… (More)

- Sebastian Noelle, Yulong Xing, Chi-Wang Shu
- J. Comput. Physics
- 2007

A characteristic feature of hyperbolic systems of balance laws is the existence of non-trivial equilibrium solutions, where the effects of convective fluxes and source terms cancel each other.… (More)

- Yulong Xing, Chi-Wang Shu
- J. Sci. Comput.
- 2013

The gas dynamics equations, coupled with a static gravitational field, admit the hydrostatic balance where the flux produced by the pressure is exactly canceled by the gravitational source term. Many… (More)

- Yulong Xing
- J. Comput. Physics
- 2014

Hyperbolic conservation laws with source terms often admit steady state solutions where the fluxes and source terms balance each other. To capture this balance and near-equilibrium solutions,… (More)

Abstract Superparameterization (SP) is a large-scale modeling system with explicit representation of small-scale and mesoscale processes provided by a cloud-resolving model (CRM) embedded in each… (More)

- Yulong Xing, Xiangxiong Zhang
- J. Sci. Comput.
- 2013

The shallow water equations model flows in rivers and coastal areas and have wide applications in ocean, hydraulic engineering, and atmospheric modeling. In “Xing et al. Adv. Water Resourc. 33:… (More)

- Jerry L. Bona, Hongqiu Chen, Ohannes A. Karakashian, Yulong Xing
- Math. Comput.
- 2013

We construct, analyze and numerically validate a class of conservative, discontinuous Galerkin schemes for the Generalized Korteweg–de Vries equation. Up to round-off error, these schemes preserve… (More)

- Yulong Xing, Chi-Wang Shu
- 2011

The shallow water equations are used to model flows in rivers and coastal areas, and have wide applications in ocean, hydraulic engineering, and atmospheric modeling. These equations have still water… (More)