3 papers
math.NA2026
A Positivity-Preserving Relaxation Algorithm
Thomas Izgin, Hendrik Ranocha, Chi-Wang Shu
We combine Patankar-type methods with suitable relaxation procedures that are capable of ensuring correct dissipation or conservation of functionals such as entropy or energy while…
math.NA2025
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…
math.NA2025
Efficient optimization-based invariant-domain-preserving limiters in solving gas dynamics equations
Chen Liu, Dionysis Milesis, Chi-Wang Shu +1
We introduce effective splitting methods for implementing optimization-based limiters to enforce the invariant domain in gas dynamics in high order accurate numerical schemes. The…