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 …
Maximum-principle-satisfying second order discontinuous Galerkin schemes for convection–diffusion equations on triangular meshes
We propose second order accurate discontinuous Galerkin (DG) schemes which satisfy a
strict maximum principle for general nonlinear convection–diffusion equations on …
strict maximum principle for general nonlinear convection–diffusion equations on …
A positivity-preserving implicit-explicit scheme with high order polynomial basis for compressible Navier–Stokes equations
In this paper, we are interested in constructing a scheme solving compressible Navier–
Stokes equations, with desired properties including high order spatial accuracy …
Stokes equations, with desired properties including high order spatial accuracy …
Third order maximum-principle-satisfying direct discontinuous Galerkin methods for time dependent convection diffusion equations on unstructured triangular meshes
We develop 3rd order maximum-principle-satisfying direct discontinuous Galerkin methods
[8],[9],[19],[21] for convection diffusion equations on unstructured triangular mesh. We …
[8],[9],[19],[21] for convection diffusion equations on unstructured triangular mesh. We …
Discrete maximum principle of a high order finite difference scheme for a generalized Allen-Cahn equation
We consider solving a generalized Allen-Cahn equation coupled with a passive convection
for a given incompressible velocity field. The numerical scheme consists of the first order …
for a given incompressible velocity field. The numerical scheme consists of the first order …
Positivity-preserving high order finite difference WENO schemes for compressible Navier-Stokes equations
In this paper, we construct a high order weighted essentially non-oscillatory (WENO) finite
difference discretization for compressible Navier-Stokes (NS) equations, which is rendered …
difference discretization for compressible Navier-Stokes (NS) equations, which is rendered …
Positivity-preserving high order finite volume hybrid Hermite WENO schemes for compressible Navier-Stokes equations
In this paper, we construct a positivity-preserving high order accurate finite volume hybrid
Hermite Weighted Essentially Non-oscillatory (HWENO) scheme for compressible Navier …
Hermite Weighted Essentially Non-oscillatory (HWENO) scheme for compressible Navier …
Is the classic convex decomposition optimal for bound-preserving schemes in multiple dimensions?
S Cui, S Ding, K Wu - Journal of Computational Physics, 2023 - Elsevier
Since proposed in Zhang and Shu (2010)[1], the Zhang–Shu framework has attracted
extensive attention and motivated many bound-preserving (BP) high-order discontinuous …
extensive attention and motivated many bound-preserving (BP) high-order discontinuous …
High order maximum-principle-preserving discontinuous Galerkin method for convection-diffusion equations
In this paper, we propose to apply the parametrized maximum-principle-preserving (MPP)
flux limiter in [T. Xiong, J.-M. Qiu, and Z. Xu, J. Comput. Phys., 252 (2013), pp. 310--331] to …
flux limiter in [T. Xiong, J.-M. Qiu, and Z. Xu, J. Comput. Phys., 252 (2013), pp. 310--331] to …
Maximum-principle-satisfying third order discontinuous Galerkin schemes for Fokker--Planck equations
H Liu, H Yu - SIAM Journal on Scientific Computing, 2014 - SIAM
We design and analyze up to third order accurate discontinuous Galerkin (DG) methods
satisfying a strict maximum principle for Fokker--Planck equations. A procedure is …
satisfying a strict maximum principle for Fokker--Planck equations. A procedure is …