A Numerical Solution Method for Nonlinear Shallow Water Waves (First Report)

Nonlinear edge waves and shallow-water theory

A Numerical Study for the Solution of Time Fractional Nonlinear Shallow Water Equation in Oceans

In this paper, an analytical solution for the coupled one-dimensional time fractional nonlinear shallow water system is obtained by using the homotopy perturbation method (HPM). The shallow water equations are a system of partial differential equations governing fluid flow in the oceans (sometimes), coastal regions (usually), estuaries (almost always), rivers and channels (almost always). The g...

Numerical solution of nonlinear SPDEs using a multi-scale method

‎In this paper we establish a new numerical method for solving a class of stochastic partial differential equations (SPDEs) based on B-splines wavelets‎. ‎The method combines implicit collocation with the multi-scale method‎. Using the multi-scale method‎, ‎SPDEs can be solved on a given subdomain with more accuracy and lower computational cost than the rest of the domain‎. ‎The stability and c...

Numerical study of nonlinear shallow water waves produced by a submerged moving disturbance in viscous flow

Two-dimensional solitary waves generated by a submerged body moving near the critical speed in a shallow water channel are studied numerically. The incompressible Navier–Stokes equations in a curvilinear free-surface-fitted coordinate system are solved by the finite difference method. The present numerical results are compared with the existing experimental data, and with the numerical solution...

A Stable Numerical Method for the Double-gyre Nonlinear Shallow-water Model

We present a numerical method for the reduced-gravity shallow-water equations on a beta plane, subjected to a constant wind forcing that leads to the formation of double-gyre circulation in a closed ocean basin. The novelty of the method is that we reformulate the governing equations into a nonlinear hyperbolic conservation law plus source terms. A second-order fractional-step algorithm is used...