High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments
CW Shu - Journal of Computational Physics, 2016 - Elsevier
For solving time-dependent convection-dominated partial differential equations (PDEs),
which arise frequently in computational physics, high order numerical methods, including …
which arise frequently in computational physics, high order numerical methods, including …
Geometric quasilinearization framework for analysis and design of bound-preserving schemes
K Wu, CW Shu - SIAM Review, 2023 - SIAM
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 the …
example, the density and pressure are positive for equations of fluid dynamics, and in the …
Provably positive high-order schemes for ideal magnetohydrodynamics: analysis on general meshes
K Wu, CW Shu - Numerische Mathematik, 2019 - Springer
This paper proposes and analyzes arbitrarily high-order discontinuous Galerkin (DG) and
finite volume methods which provably preserve the positivity of density and pressure for the …
finite volume methods which provably preserve the positivity of density and pressure for the …
Bound-preserving high-order schemes for hyperbolic equations: Survey and recent developments
CW Shu - Theory, Numerics and Applications of Hyperbolic …, 2018 - Springer
Solutions to many hyperbolic equations have convex invariant regions, for example,
solutions to scalar conservation laws satisfy the maximum principle, solutions to …
solutions to scalar conservation laws satisfy the maximum principle, solutions to …
Explicit discontinuous spectral element method with entropy generation based artificial viscosity for shocked viscous flows
A spatio-temporal adaptive artificial viscosity (AV) based shock-capturing scheme is
proposed for the solution of both inviscid and viscous compressible flows using a high-order …
proposed for the solution of both inviscid and viscous compressible flows using a high-order …
Bound-preserving modified exponential Runge–Kutta discontinuous Galerkin methods for scalar hyperbolic equations with stiff source terms
In this paper, we develop bound-preserving modified exponential Runge–Kutta (RK)
discontinuous Galerkin (DG) schemes to solve scalar hyperbolic equations with stiff source …
discontinuous Galerkin (DG) schemes to solve scalar hyperbolic equations with stiff source …
Unstructured Cartesian refinement with sharp interface immersed boundary method for 3D unsteady incompressible flows
A novel numerical method is developed for solving the 3D, unsteady, incompressible Navier–
Stokes equations on locally refined fully unstructured Cartesian grids in domains with …
Stokes equations on locally refined fully unstructured Cartesian grids in domains with …
The numerical error of the Xinanjiang model
The numerical error of the Xinanjiang (XAJ) model has long been ignored, despite its wide
application in China. Separating the mathematically formulated model from the …
application in China. Separating the mathematically formulated model from the …
Positivity-preserving finite difference weighted ENO schemes with constrained transport for ideal magnetohydrodynamic equations
In this paper, we utilize the maximum-principle-preserving flux limiting technique, originally
designed for high-order weighted essentially nonoscillatory (WENO) methods for scalar …
designed for high-order weighted essentially nonoscillatory (WENO) methods for scalar …
A new locally divergence-free WLS-ENO scheme based on the positivity-preserving finite volume method for ideal MHD equations
M Liu, M Zhang, C Li, F Shen - Journal of Computational Physics, 2021 - Elsevier
In this paper, the WLS-ENO (Weighted-Least-Squares based Essentially Non-Oscillatory)
reconstruction is modified to maintain the conservation of the cell average values …
reconstruction is modified to maintain the conservation of the cell average values …