10 papers
Fully Discrete Multi-Entropy Stability of High-Order Schemes for Compressible MHD: A Weak-to-Strong Framework
Huihui Cao, Kailiang Wu, Caiyou Yuan
We establish a fully discrete weak-to-strong (W2S) multi-entropy stability theory for arbitrarily high-order finite-volume and discontinuous Galerkin (DG) approximations of the ide…
Runge--Kutta-Aligned Oscillation Elimination: Restoring Superconvergence for Fully Discrete Shock-Capturing DG Schemes
Manting Peng, Zhuoyun Li, Kailiang Wu
Nonlinear stabilization is indispensable for discontinuous Galerkin (DG) discretizations of hyperbolic conservation laws, yet it typically disrupts the delicate error structure req…
Compact Finite-Average-Moment Schemes with Single-Step Oscillation Elimination for Hyperbolic Conservation Laws
Chuan Fan, Kailiang Wu
High-order shock-capturing schemes often face severe computational bottlenecks due to wide stencils, stagewise nonlinear weights, and expensive local characteristic decompositions.…
Hidden Accuracy and Superconvergence Analysis of Central Discontinuous Galerkin Methods on Overlapping Meshes
Manting Peng, Kailiang Wu
This paper establishes the first rigorous superconvergence theory for semidiscrete and fully discrete central discontinuous Galerkin (CDG) methods for linear hyperbolic equations o…
Constraint-Preserving High-Order Compact OEDG Method for Spherically Symmetric Einstein-Euler System
Yuchen Huang, Manting Peng, Kailiang Wu
Numerical simulation of the spherically symmetric Einstein--Euler (EE) system faces severe challenges due to the stringent physical admissibility constraints of relativistic fluids…
An active-flux-type scheme for ideal MHD with provable positivity and discrete divergence-free property
Mengqing Liu, Dongwen Pang, Remi Abgrall +1
We develop a positivity-preserving (PP) PAMPA (Point-Average-Moment PolynomiAl-interpreted) scheme that enforces a discrete divergence-free (DDF) magnetic field for ideal MHD on Ca…
Provably realizability-preserving finite volume method for quadrature-based moment models of kinetic equations
Chuan Fan, Qian Huang, Kailiang Wu
Quadrature-based moment methods (QBMM) provide tractable closures for multiscale kinetic equations, with diverse applications across aerosols, sprays, and particulate flows, etc. H…
Provably positivity-preserving, globally divergence-free central DG methods for ideal MHD system
Ruifang Yan, Huihui Cao, Kailiang Wu
This paper proposes a numerical method, termed PosDiv-CDG, that provably preserves both positivity and the globally divergence-free (DF) condition at arbitrarily high order in mult…
Provably Positivity-Preserving Constrained Transport (PPCT) Second-Order Scheme for Ideal Magnetohydrodynamics
Dongwen Pang, Kailiang Wu
This paper proposes and analyzes a robust and efficient second-order positivity-preserving constrained transport (PPCT) scheme for ideal magnetohydrodynamics (MHD) on non-staggered…
Robust Discontinuous Galerkin Methods Maintaining Physical Constraints for General Relativistic Hydrodynamics
Huihui Cao, Manting Peng, Kailiang Wu
Simulating general relativistic hydrodynamics (GRHD) presents challenges such as handling curved spacetime, achieving high-order shock-capturing accuracy, and preserving key physic…