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 …

In this paper, we develop new second-order low-dissipation central-upwind (LDCU)
schemes for hyperbolic systems of conservation laws. Like all of the Godunov-type schemes …

We develop fifth-order A-WENO finite-difference schemes based on the path-conservative
central-upwind method for nonconservative one-and two-dimensional hyperbolic systems of …

We develop a new second-order flux globalization based path-conservative central-upwind
(PCCU) scheme for rotating shallow water magnetohydrodynamic equations. The new …

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 …

We develop path-conservative central-upwind schemes for nonconservative one-
dimensional hyperbolic systems of nonlinear partial differential equations. Such systems …

We propose novel less diffusive schemes for conservative one-and two-dimensional
hyperbolic systems of nonlinear partial differential equations (PDEs). The main challenges …

In this paper, we construct an improved well-balanced positivity preserving central-upwind
scheme for the two-dimensional Saint-Venant system of shallow water equations. As in …

We propose a numerical dissipation switch, which helps to control the amount of numerical
dissipation present in central-upwind schemes. Our main goal is to reduce the numerical …

We construct new fifth-order alternative WENO (A-WENO) schemes for the Euler equations
of gas dynamics. The new scheme is based on a new adaptive diffusion central-upwind …