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 …
[HTML][HTML] A unified theory for bubble dynamics
In this work, we established a novel theory for the dynamics of oscillating bubbles such as
cavitation bubbles, underwater explosion bubbles, and air bubbles. For the first time, we …
cavitation bubbles, underwater explosion bubbles, and air bubbles. For the first time, we …
A comprehensive and fair comparison of two neural operators (with practical extensions) based on fair data
Neural operators can learn nonlinear mappings between function spaces and offer a new
simulation paradigm for real-time prediction of complex dynamics for realistic diverse …
simulation paradigm for real-time prediction of complex dynamics for realistic diverse …
DeepM&Mnet for hypersonics: Predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators
In high-speed flow past a normal shock, the fluid temperature rises rapidly triggering
downstream chemical dissociation reactions. The chemical changes lead to appreciable …
downstream chemical dissociation reactions. The chemical changes lead to appreciable …
Positivity-preserving high order finite difference WENO schemes for compressible Euler equations
In Zhang and Shu (2010)[20], Zhang and Shu (2011)[21] and Zhang et al.(in press)[23], we
constructed uniformly high order accurate discontinuous Galerkin (DG) and finite volume …
constructed uniformly high order accurate discontinuous Galerkin (DG) and finite volume …
On positivity-preserving high order discontinuous Galerkin schemes for compressible Navier–Stokes equations
X Zhang - Journal of Computational Physics, 2017 - Elsevier
We construct a local Lax–Friedrichs type positivity-preserving flux for compressible Navier–
Stokes equations, which can be easily extended to multiple dimensions for generic forms of …
Stokes equations, which can be easily extended to multiple dimensions for generic forms of …
High-order fully general-relativistic hydrodynamics: new approaches and tests
We present a new approach for achieving high-order convergence in fully general-
relativistic hydrodynamic simulations. The approach is implemented in WhiskyTHC, a new …
relativistic hydrodynamic simulations. The approach is implemented in WhiskyTHC, a new …
Positivity-preserving entropy-based adaptive filtering for discontinuous spectral element methods
T Dzanic, FD Witherden - Journal of Computational Physics, 2022 - Elsevier
In this work, we present a positivity-preserving entropy-based adaptive filtering method for
shock capturing in discontinuous spectral element methods. By adapting the filter strength to …
shock capturing in discontinuous spectral element methods. By adapting the filter strength to …
Robust high order discontinuous Galerkin schemes for two-dimensional gaseous detonations
One of the main challenges in computational simulations of gas detonation propagation is
that negative density or negative pressure may emerge during the time evolution, which will …
that negative density or negative pressure may emerge during the time evolution, which will …