The novel and simple nonlinear affine-invariant weights (Ai-weights) are devised for the Ai-
WENO operator to handle the case when the function being reconstructed undergoes an …

This article develops a new discontinuous Galerkin (DG) method on structured meshes for
solving shallow water equations. The method here applies the one-stage ADER (Arbitrary …

The shallow water equations (SWEs) admit still water steady-state solutions in which the flux
gradients are exactly balanced by the source term. Furthermore, the no-water dry areas …

In this paper, a new fifth-order finite difference well-balanced multi-resolution weighted
essentially non-oscillatory (WENO) scheme is designed to solve for one-dimensional and …

This paper develops the structure-preserving finite volume weighted essentially non-
oscillatory (WENO) hybrid schemes for the shallow water equations under the arbitrary …

In this paper, we present high order finite difference weighted essentially non-oscillatory
(WENO) schemes for the shallow water flows along open channels with irregular geometry …

This article presents well-balanced finite volume weighted essentially nonoscillatory
(WENO) schemes to solve the shallow water equations (SWEs). Wellbalanced schemes are …

Shallow water equations have important applications in civil engineering. For these balance
models, a numerical scheme with a well-balanced property is useful for reducing numerical …

Sediment transport model in shallow water admits steady-state solutions in which the non-
zero flux gradient is exactly balanced by the source term. In this paper, we develop high …

A numerical wave tank equipped with a piston type wave-maker is presented for long-
duration simulations of long waves in shallow water. Both wave maker and tank are …