On uniformly accurate high-order Boussinesq difference equations for water waves

✍ Scribed by Yaron Toledo; Yehuda Agnon

• Publisher: John Wiley and Sons
• Year: 2006
• Tongue: English
• Weight: 753 KB
• Volume: 50
• Category: Article
• ISSN: 0271-2091
• DOI: 10.1002/fld.1088

✦ Synopsis

A new accurate ÿnite-di erence (AFD) numerical method is developed speciÿcally for solving highorder Boussinesq (HOB) equations. The method solves the water-wave ow with much higher accuracy compared to the standard ÿnite-di erence (SFD) method for the same computer resources. It is ÿrst developed for linear water waves and then for the nonlinear problem. It is presented for a horizontal bottom, but can be used for variable depth as well. The method can be developed for other equations as long as they use Padà e approximation, for example extensions of the parabolic equation for acoustic wave problems. Finally, the results of the new method and the SFD method are compared with the accurate solution for nonlinear progressive waves over a horizontal bottom that is found using the stream function theory. The agreement of the AFD to the accurate solution is found to be excellent compared to the SFD solution.