Simulating Free Boundaries in 2D FEM Flow Simulation with Direct Time Integration of the Surface Velocities
We have derived a novel approach to simulate free surfaces. For two-dimensional finite-element flow simulations of the incompressible Navier-Stokes equations we integrate out the velocities on the surface obtained from the FEM-simulations with integrators for ordinary differential equations. The adv...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SAGE Publishing
2013-09-01
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| Series: | Journal of Algorithms & Computational Technology |
| Online Access: | https://doi.org/10.1260/1748-3018.7.3.287 |
| _version_ | 1818295208782069760 |
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| author | Shi Han Ng Hans-Georg Matuttis |
| author_facet | Shi Han Ng Hans-Georg Matuttis |
| author_sort | Shi Han Ng |
| collection | DOAJ |
| description | We have derived a novel approach to simulate free surfaces. For two-dimensional finite-element flow simulations of the incompressible Navier-Stokes equations we integrate out the velocities on the surface obtained from the FEM-simulations with integrators for ordinary differential equations. The advance of the fluid front does not need additional data structures or interpolated mesh points as in the front tracking for finite difference methods, the adaptive mesh of the FEM-simulation is sufficient. As we perform the time-integration of the FEM-code, the second-order Adams-Bashforth turns out to be the most suitable integrator for the surface motion. For the speed of the wavefronts, we get excellent agreement for large viscosity with the lubrication approximation by Huppert, and for small viscosity, we get very good agreement with the experimental data for water by Martin and Moyce. |
| first_indexed | 2024-12-13T03:44:00Z |
| format | Article |
| id | doaj.art-6d930ecf9970489c82a08145d0b1c9e4 |
| institution | Directory Open Access Journal |
| issn | 1748-3018 1748-3026 |
| language | English |
| last_indexed | 2024-12-13T03:44:00Z |
| publishDate | 2013-09-01 |
| publisher | SAGE Publishing |
| record_format | Article |
| series | Journal of Algorithms & Computational Technology |
| spelling | doaj.art-6d930ecf9970489c82a08145d0b1c9e42022-12-22T00:00:52ZengSAGE PublishingJournal of Algorithms & Computational Technology1748-30181748-30262013-09-01710.1260/1748-3018.7.3.287Simulating Free Boundaries in 2D FEM Flow Simulation with Direct Time Integration of the Surface VelocitiesShi Han NgHans-Georg MatuttisWe have derived a novel approach to simulate free surfaces. For two-dimensional finite-element flow simulations of the incompressible Navier-Stokes equations we integrate out the velocities on the surface obtained from the FEM-simulations with integrators for ordinary differential equations. The advance of the fluid front does not need additional data structures or interpolated mesh points as in the front tracking for finite difference methods, the adaptive mesh of the FEM-simulation is sufficient. As we perform the time-integration of the FEM-code, the second-order Adams-Bashforth turns out to be the most suitable integrator for the surface motion. For the speed of the wavefronts, we get excellent agreement for large viscosity with the lubrication approximation by Huppert, and for small viscosity, we get very good agreement with the experimental data for water by Martin and Moyce.https://doi.org/10.1260/1748-3018.7.3.287 |
| spellingShingle | Shi Han Ng Hans-Georg Matuttis Simulating Free Boundaries in 2D FEM Flow Simulation with Direct Time Integration of the Surface Velocities Journal of Algorithms & Computational Technology |
| title | Simulating Free Boundaries in 2D FEM Flow Simulation with Direct Time Integration of the Surface Velocities |
| title_full | Simulating Free Boundaries in 2D FEM Flow Simulation with Direct Time Integration of the Surface Velocities |
| title_fullStr | Simulating Free Boundaries in 2D FEM Flow Simulation with Direct Time Integration of the Surface Velocities |
| title_full_unstemmed | Simulating Free Boundaries in 2D FEM Flow Simulation with Direct Time Integration of the Surface Velocities |
| title_short | Simulating Free Boundaries in 2D FEM Flow Simulation with Direct Time Integration of the Surface Velocities |
| title_sort | simulating free boundaries in 2d fem flow simulation with direct time integration of the surface velocities |
| url | https://doi.org/10.1260/1748-3018.7.3.287 |
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