7 papers
High-order fully discrete multi-entropy-stable and bound-preserving schemes for relativistic Euler equations
Linfeng Xu, Kailiang Wu
A discrete entropy inequality is the principal nonlinear stability estimate available for systems of conservation laws, and evaluating it presupposes a physically admissible state.…
GQL-Based Physical-Constraint-Preserving High-Order Finite Difference Schemes for Special Relativistic Hydrodynamics in Arbitrary Dimensions
Linfeng Xu, Shengrong Ding, Kailiang Wu
High-order accurate simulations of special relativistic hydrodynamics (RHD) are prone to numerical breakdown if intrinsic physical constraints (positive rest-mass density/pressure…
EPO: A Unified Framework for Entropy Stability, Positivity, and Oscillation Suppression
Kailiang Wu
High-order finite volume and discontinuous Galerkin methods are often stabilized by separate nonlinear devices for admissibility, entropy control, and oscillation suppression. This…
High Order Numerical Methods Preserving Invariant Domain for Hyperbolic and Related Systems
Kailiang Wu, Xiangxiong Zhang, Chi-Wang Shu
Admissible states in hyperbolic systems and related equations often form a convex invariant domain. Numerical violations of this domain can lead to loss of hyperbolicity, resulting…
Bound-Preserving WENO Schemes for Temple-class systems
Wei Chen, Shumo Cui, Kailiang Wu +2
This paper explores numerical schemes for Temple-class systems, which are integral to various applications including one-dimensional two-phase flow, elasticity, traffic flow, and s…
Oscillation-eliminating central DG schemes for hyperbolic conservation laws
Manting Peng, Kailiang Wu, Caiyou Yuan
This paper proposes and analyzes a class of essentially non-oscillatory central discontinuous Galerkin (CDG) methods for general hyperbolic conservation laws. First, we introduce a…