(2 intermediate revisions by 2 users not shown)
Line 3: Line 3:
 
== Abstract ==
 
== Abstract ==
  
An adaptive Finite Point Method (FPM) for solving shallow water problems is presented. The numerical methodology we propose, which is based on weighted‐least squares approximations on clouds of points, adopts an upwind‐biased discretization for dealing with the convective terms in the governing equations. The viscous and source terms are discretized in a pointwise manner and the semi‐discrete equations are integrated explicitly in time by means of a multi‐stage scheme. Moreover, with the aim of exploiting meshless capabilities, an adaptive h‐refinement technique is coupled to the described flow solver. The success of this approach in solving typical shallow water flows is illustrated by means of several numerical examples and special emphasis is placed on the adaptive technique performance. This has been assessed by carrying out a numerical simulation of the 26th December 2004 Indian Ocean tsunami with highly encouraging results. Overall, the adaptive FPM is presented as an accurate enough, cost‐effective tool for solving practical shallow water problems. Copyright © 2011 John Wiley & Sons, Ltd.
+
An adaptive Finite Point Method (FPM) for solving shallow water problems is presented. The numerical methodology we propose, which is based on weighted‐least squares approximations on clouds of points, adopts an upwind‐biased discretization for dealing with the convective terms in the governing equations. The viscous and source terms are discretized in a pointwise manner and the semi‐discrete equations are integrated explicitly in time by means of a multi‐stage scheme. Moreover, with the aim of exploiting meshless capabilities, an adaptive h‐refinement technique is coupled to the described flow solver. The success of this approach in solving typical shallow water flows is illustrated by means of several numerical examples and special emphasis is placed on the adaptive technique performance. This has been assessed by carrying out a numerical simulation of the 26th December 2004 Indian Ocean tsunami with highly encouraging results. Overall, the adaptive FPM is presented as an accurate enough, cost‐effective tool for solving practical shallow water problems.
  
 
<pdf>Media:Draft_Samper_402574503_2944_nme.3171.pdf</pdf>
 
<pdf>Media:Draft_Samper_402574503_2944_nme.3171.pdf</pdf>

Latest revision as of 11:10, 12 February 2019

Published in Int. Journal for Numerical Methods in Engineering Vol. 88 (2), pp. 180-204, 2011
doi: 10.1002/nme.3171

Abstract

An adaptive Finite Point Method (FPM) for solving shallow water problems is presented. The numerical methodology we propose, which is based on weighted‐least squares approximations on clouds of points, adopts an upwind‐biased discretization for dealing with the convective terms in the governing equations. The viscous and source terms are discretized in a pointwise manner and the semi‐discrete equations are integrated explicitly in time by means of a multi‐stage scheme. Moreover, with the aim of exploiting meshless capabilities, an adaptive h‐refinement technique is coupled to the described flow solver. The success of this approach in solving typical shallow water flows is illustrated by means of several numerical examples and special emphasis is placed on the adaptive technique performance. This has been assessed by carrying out a numerical simulation of the 26th December 2004 Indian Ocean tsunami with highly encouraging results. Overall, the adaptive FPM is presented as an accurate enough, cost‐effective tool for solving practical shallow water problems.

The PDF file did not load properly or your web browser does not support viewing PDF files. Download directly to your device: Download PDF document
Back to Top

Document information

Published on 01/01/2011

DOI: 10.1002/nme.3171
Licence: CC BY-NC-SA license

Document Score

0

Times cited: 5
Views 9
Recommendations 0

Share this document

claim authorship

Are you one of the authors of this document?