Shallow-water equations are widely used to model water flow in rivers, lakes, reservoirs,
coastal areas, and other situations in which the water depth is much smaller than the …

Shallow water models are widely used to describe and study free‐surface water flow. While
in some practical applications the bottom friction does not have much influence on the …

In this paper, we develop and present an arbitrary high order well-balanced finite volume
WENO method combined with the modified Patankar Deferred Correction (mPDeC) time …

In this paper, we construct a family of modified Patankar Runge–Kutta methods, which is
conservative and unconditionally positivity-preserving, for production–destruction equations …

We develop a family of second-order implicit-explicit (IMEX) schemes for the stiff Bhatnagar--
Gross--Krook (BGK) kinetic equation. The method is asymptotic-preserving (can capture the …

We construct a new second-order moving-water equilibria preserving central-upwind
scheme for the one-dimensional Saint-Venant system of shallow water equations. The idea …

In this paper, we extend our previous work in Huang and Shu (J Sci Comput, 2018.
https://doi. org/10.1007/s10915-018-0852-1) and develop a third-order unconditionally …

In this paper, we develop third-order conservative sign-preserving and steady-state-
preserving time integrations and seek their applications in multispecies and multireaction …

Patankar-type schemes are linearly implicit time integration methods designed to be
unconditionally positivity-preserving. However, there are only little results on their stability or …

In this paper, we develop bound-preserving modified exponential Runge–Kutta (RK)
discontinuous Galerkin (DG) schemes to solve scalar hyperbolic equations with stiff source …