In 1917, the British scientist LF Richardson made the first reported attempt to predict the
weather by solving partial differential equations numerically, by hand! It is generally …

High order accurate weighted essentially nonoscillatory (WENO) schemes are relatively new
but have gained rapid popularity in numerical solutions of hyperbolic partial differential …

We introduce new Godunov-type semidiscrete central schemes for hyperbolic systems of
conservation laws and Hamilton--Jacobi equations. The schemes are based on the use of …

We describe the implementation of a computational fluid dynamics solver for the simulation
of high‐speed flows. It comprises a finite volume (FV) discretization using semi‐discrete, non …

Solution of twoâ•’dimensional Riemann problems for gas dynamics without Riemann problem
solvers Page 1 Solution of Two-Dimensional Riemann Problems for Gas Dynamics without …

We present one-and two-dimensional central-upwind schemes for approximating solutions
of the Saint-Venant system with source terms due to bottom topography. The Saint-Venant …

In this paper, we review and construct fifth-and ninth-order central weighted essentially
nonoscillatory (WENO) schemes based on a finite volume formulation, staggered mesh, and …

We study central-upwind schemes for systems of hyperbolic conservation laws, recently
introduced in [13]. Similarly to staggered non-oscillatory central schemes, these schemes …

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 …

We present the first fourth-order central scheme for two-dimensional hyperbolic systems of
conservation laws. Our new method is based on a central weighted nonoscillatory approach …