Maximum-principle-satisfying and positivity-preserving high-order schemes for conservation laws: survey and new developments
In an earlier study (Zhang & Shu 2010 b J. Comput. Phys. 229, 3091–3120 (doi: 10.1016/j.
jcp. 2009.12. 030)), genuinely high-order accurate finite volume and discontinuous Galerkin …
jcp. 2009.12. 030)), genuinely high-order accurate finite volume and discontinuous Galerkin …
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 …
A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws
M Dumbser, O Zanotti, R Loubère, S Diot - Journal of Computational …, 2014 - Elsevier
The purpose of this work is to propose a novel a posteriori finite volume subcell limiter
technique for the Discontinuous Galerkin finite element method for nonlinear systems of …
technique for the Discontinuous Galerkin finite element method for nonlinear systems of …
[图书][B] Strong stability preserving Runge-Kutta and multistep time discretizations
Strong Stability Preserving Explicit Runge—Kutta Methods | Strong Stability Preserving
Runge-Kutta and Multistep Time Discretizations World Scientific Search This Book Anywhere …
Runge-Kutta and Multistep Time Discretizations World Scientific Search This Book Anywhere …
[图书][B] Proper orthogonal decomposition methods for partial differential equations
Z Luo, G Chen - 2018 - books.google.com
Proper Orthogonal Decomposition Methods for Partial Differential Equations evaluates the
potential applications of POD reduced-order numerical methods in increasing computational …
potential applications of POD reduced-order numerical methods in increasing computational …
A 2D well-balanced shallow flow model for unstructured grids with novel slope source term treatment
Within the framework of the Godunov-type cell-centered finite volume (CCFV) scheme, this
paper proposes a 2D well-balanced shallow water model for unstructured grids. In this …
paper proposes a 2D well-balanced shallow water model for unstructured grids. In this …
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 …
[HTML][HTML] An efficient unstructured MUSCL scheme for solving the 2D shallow water equations
The aim of this paper is to present a novel monotone upstream scheme for conservation law
(MUSCL) on unstructured grids. The novel edge-based MUSCL scheme is devised to …
(MUSCL) on unstructured grids. The novel edge-based MUSCL scheme is devised to …
A new class of fully nonlinear and weakly dispersive Green–Naghdi models for efficient 2D simulations
We introduce a new class of two-dimensional fully nonlinear and weakly dispersive Green–
Naghdi equations over varying topography. These new Green–Naghdi systems share the …
Naghdi equations over varying topography. These new Green–Naghdi systems share the …
Exactly well-balanced discontinuous Galerkin methods for the shallow water equations with moving water equilibrium
Y Xing - Journal of Computational Physics, 2014 - Elsevier
Hyperbolic conservation laws with source terms often admit steady state solutions where the
fluxes and source terms balance each other. To capture this balance and near-equilibrium …
fluxes and source terms balance each other. To capture this balance and near-equilibrium …