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 …

For solving time-dependent convection-dominated partial differential equations (PDEs),
which arise frequently in computational physics, high order numerical methods, including …

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 …

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 …

In high-speed flow past a normal shock, the fluid temperature rises rapidly triggering
downstream chemical dissociation reactions. The chemical changes lead to appreciable …

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 …

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 …

We present a new approach for achieving high-order convergence in fully general-
relativistic hydrodynamic simulations. The approach is implemented in WhiskyTHC, a new …

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 …

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 …