293 citations · 1.2k across the 39 of their papers we have counts for
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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…
High order asymptotic preserving finite difference WENO schemes with constrained transport for MHD equations in all sonic Mach numbers
Wei Chen, Kailiang Wu, Tao Xiong
In this paper, a high-order semi-implicit (SI) asymptotic preserving (AP) and divergence-free finite difference weighted essentially nonoscillatory (WENO) scheme is proposed for ma…
Positivity-Preserving Well-Balanced Central Discontinuous Galerkin Schemes for the Euler Equations under Gravitational Fields
Haili Jiang, Huazhong Tang, Kailiang Wu
This paper designs and analyzes positivity-preserving well-balanced (WB) central discontinuous Galerkin (CDG) schemes for the Euler equations with gravity. A distinctive feature of…
A Physical-Constraint-Preserving Finite Volume WENO Method for Special Relativistic Hydrodynamics on Unstructured Meshes
Yaping Chen, Kailiang Wu
This paper presents a highly robust third-order accurate finite volume weighted essentially non-oscillatory (WENO) method for special relativistic hydrodynamics on unstructured tri…
Is the Classic Convex Decomposition Optimal for Bound-Preserving Schemes in Multiple Dimensions?
Shumo Cui, Shengrong Ding, Kailiang Wu
Since proposed in [X. Zhang and C.-W. Shu, J. Comput. Phys., 229: 3091--3120, 2010], the Zhang--Shu framework has attracted extensive attention and motivated many bound-preserving…
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…