A simple and robust boundary treatment for the forced Korteweg-de Vries equation

Hyun Geun Lee, Junseok Kim

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In this paper, we propose a simple and robust numerical method for the forced Korteweg-de Vries (fKdV) equation which models free surface waves of an incompressible and inviscid fluid flow over a bump. The fKdV equation is defined in an infinite domain. However, to solve the equation numerically we must truncate the infinite domain to a bounded domain by introducing an artificial boundary and imposing boundary conditions there. Due to unsuitable artificial boundary conditions, most wave propagation problems have numerical difficulties (e.g., the truncated computational domain must be large enough or the numerical simulation must be terminated before the wave approaches the artificial boundary for the quality of the numerical solution). To solve this boundary problem, we develop an absorbing non-reflecting boundary treatment which uses outward wave velocity. The basic idea of the proposing algorithm is that we first calculate an outward wave velocity from the solutions at the previous and present time steps and then we obtain a solution at the next time step on the artificial boundary by moving the solution at the present time step with the velocity. And then we update solutions at the next time step inside the domain using the calculated solution on the artificial boundary. Numerical experiments with various initial conditions for the KdV and fKdV equations are presented to illustrate the accuracy and efficiency of our method.

Original languageEnglish
Pages (from-to)2262-2271
Number of pages10
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume19
Issue number7
DOIs
Publication statusPublished - 2014 Jul 1

Fingerprint

Korteweg-de Vries equation
Artificial Boundary
Korteweg-de Vries Equation
Infinite Domain
Artificial Boundary Conditions
Truncate
Inviscid Flow
Boundary conditions
Robust Methods
Surface Waves
Boundary Problem
Absorbing
Free Surface
Wave Propagation
Fluid Flow
Bounded Domain
Initial conditions
Update
Surface waves
Wave propagation

Keywords

  • Absorbing non-reflecting boundary treatment
  • Forced Korteweg-de Vries equation
  • Free surface waves
  • Semi-implicit finite difference method

ASJC Scopus subject areas

  • Modelling and Simulation
  • Numerical Analysis
  • Applied Mathematics

Cite this

A simple and robust boundary treatment for the forced Korteweg-de Vries equation. / Lee, Hyun Geun; Kim, Junseok.

In: Communications in Nonlinear Science and Numerical Simulation, Vol. 19, No. 7, 01.07.2014, p. 2262-2271.

Research output: Contribution to journalArticle

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