3 citations · 7 across the 9 of their papers we have counts for
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High-order accurate structure-preserving finite volume schemes on adaptive moving meshes for shallow water equations: Well-balancedness and positivity
Zhihao Zhang, Huazhong Tang, Kailiang Wu
This paper develops high-order accurate, well-balanced (WB), and positivity-preserving (PP) finite volume schemes for shallow water equations on adaptive moving structured meshes.…
On Optimal Cell Average Decomposition for High-Order Bound-Preserving Schemes of Hyperbolic Conservation Laws
Shumo Cui, Shengrong Ding, Kailiang Wu
This paper presents the first systematic study on the fundamental problem of seeking optimal cell average decomposition (OCAD), which arises from constructing efficient high-order…
A New Locally Divergence-Free Path-Conservative Central-Upwind Scheme for Ideal and Shallow Water Magnetohydrodynamics
Alina Chertock, Alexander Kurganov, Michael Redle +1
We develop a new second-order unstaggered path-conservative central-upwind (PCCU) scheme for ideal and shallow water magnetohydrodynamics (MHD) equations. The new scheme possesses…
Provably Positive Central DG Schemes via Geometric Quasilinearization for Ideal MHD Equations
Kailiang Wu, Haili Jiang, Chi-Wang Shu
In the numerical simulation of ideal MHD, keeping the pressure and density positive is essential for both physical considerations and numerical stability. This is a challenge, due…
On Energy Laws and Stability of Runge--Kutta Methods for Linear Seminegative Problems
Zheng Sun, Yuanzhe Wei, Kailiang Wu
This paper presents a systematic theoretical framework to derive the energy identities of general implicit and explicit Runge--Kutta (RK) methods for linear seminegative systems. I…
Geometric Quasilinearization Framework for Analysis and Design of Bound-Preserving Schemes
Kailiang Wu, Chi-Wang Shu
Solutions to many partial differential equations satisfy certain bounds or constraints. For example, the density and pressure are positive for equations of fluid dynamics, and in t…