Comparison between Homotopy Analysis Method (HAM) and Variational Iteration Method (VIM) in Solving the Nonlinear Wave Propagation Equations in Shallow Water
This study aims to investigate the capability of two common numerical methods, Homotopy Analysis Method (HAM) and Variational Iteration Method (VIM), and to suggest more efficient approximate solution method to the governing equations of nonlinear surface wave propagation in shallow water. To do so,...
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| Format: | Article |
| Language: | English |
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Iranian Association of Naval Architecture and Marine Engineering
2019-02-01
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| Series: | International Journal of Coastal and Offshore Engineering |
| Subjects: | |
| Online Access: | http://ijcoe.org/article-1-131-en.html |
| _version_ | 1819025423230566400 |
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| author | Mohsen Soltani Rouhollah Amirabadi |
| author_facet | Mohsen Soltani Rouhollah Amirabadi |
| author_sort | Mohsen Soltani |
| collection | DOAJ |
| description | This study aims to investigate the capability of two common numerical methods, Homotopy Analysis Method (HAM) and Variational Iteration Method (VIM), and to suggest more efficient approximate solution method to the governing equations of nonlinear surface wave propagation in shallow water. To do so, semi-flat, moderate, and sharp slope of shore which are connected to an open ocean with a uniform depth are exposed to a solitary wave with initial wave height H=2 and stationary elevation d=20. Then, the surface elevation and velocity curves for these profiles are determined and compared by HAM and VIM. To verify the numerical modeling, two slopes i.e. semi-flat and moderate slope are considered and modeled in Flow-3D. Afterwards, the results of surface elevations are compared to each other by using correlation coefficient. The correlation coefficients for the slopes represent that the results coincide well. Ultimately, although the results of both methods are quite similar, using HAM is highly recommend rather than VIM since it makes solution procedure fast-converging and more abridged. |
| first_indexed | 2024-12-21T05:10:27Z |
| format | Article |
| id | doaj.art-0488939f9f6d4f23a5df6601f97d7065 |
| institution | Directory Open Access Journal |
| issn | 2538-2667 2588-3186 |
| language | English |
| last_indexed | 2024-12-21T05:10:27Z |
| publishDate | 2019-02-01 |
| publisher | Iranian Association of Naval Architecture and Marine Engineering |
| record_format | Article |
| series | International Journal of Coastal and Offshore Engineering |
| spelling | doaj.art-0488939f9f6d4f23a5df6601f97d70652022-12-21T19:15:04ZengIranian Association of Naval Architecture and Marine EngineeringInternational Journal of Coastal and Offshore Engineering2538-26672588-31862019-02-01243746Comparison between Homotopy Analysis Method (HAM) and Variational Iteration Method (VIM) in Solving the Nonlinear Wave Propagation Equations in Shallow WaterMohsen Soltani0Rouhollah Amirabadi1 University of Qom University of Qom This study aims to investigate the capability of two common numerical methods, Homotopy Analysis Method (HAM) and Variational Iteration Method (VIM), and to suggest more efficient approximate solution method to the governing equations of nonlinear surface wave propagation in shallow water. To do so, semi-flat, moderate, and sharp slope of shore which are connected to an open ocean with a uniform depth are exposed to a solitary wave with initial wave height H=2 and stationary elevation d=20. Then, the surface elevation and velocity curves for these profiles are determined and compared by HAM and VIM. To verify the numerical modeling, two slopes i.e. semi-flat and moderate slope are considered and modeled in Flow-3D. Afterwards, the results of surface elevations are compared to each other by using correlation coefficient. The correlation coefficients for the slopes represent that the results coincide well. Ultimately, although the results of both methods are quite similar, using HAM is highly recommend rather than VIM since it makes solution procedure fast-converging and more abridged.http://ijcoe.org/article-1-131-en.htmlhomotopy analysis method (ham)variational iteration method (vim)shallow water equations |
| spellingShingle | Mohsen Soltani Rouhollah Amirabadi Comparison between Homotopy Analysis Method (HAM) and Variational Iteration Method (VIM) in Solving the Nonlinear Wave Propagation Equations in Shallow Water International Journal of Coastal and Offshore Engineering homotopy analysis method (ham) variational iteration method (vim) shallow water equations |
| title | Comparison between Homotopy Analysis Method (HAM) and Variational Iteration Method (VIM) in Solving the Nonlinear Wave Propagation Equations in Shallow Water |
| title_full | Comparison between Homotopy Analysis Method (HAM) and Variational Iteration Method (VIM) in Solving the Nonlinear Wave Propagation Equations in Shallow Water |
| title_fullStr | Comparison between Homotopy Analysis Method (HAM) and Variational Iteration Method (VIM) in Solving the Nonlinear Wave Propagation Equations in Shallow Water |
| title_full_unstemmed | Comparison between Homotopy Analysis Method (HAM) and Variational Iteration Method (VIM) in Solving the Nonlinear Wave Propagation Equations in Shallow Water |
| title_short | Comparison between Homotopy Analysis Method (HAM) and Variational Iteration Method (VIM) in Solving the Nonlinear Wave Propagation Equations in Shallow Water |
| title_sort | comparison between homotopy analysis method ham and variational iteration method vim in solving the nonlinear wave propagation equations in shallow water |
| topic | homotopy analysis method (ham) variational iteration method (vim) shallow water equations |
| url | http://ijcoe.org/article-1-131-en.html |
| work_keys_str_mv | AT mohsensoltani comparisonbetweenhomotopyanalysismethodhamandvariationaliterationmethodviminsolvingthenonlinearwavepropagationequationsinshallowwater AT rouhollahamirabadi comparisonbetweenhomotopyanalysismethodhamandvariationaliterationmethodviminsolvingthenonlinearwavepropagationequationsinshallowwater |