A variational-difference method for numerical simulation of equilibrium capillary surfaces
Objectives. A variational-difference method for numerical simulation of equilibrium capillary surfaces based on the minimization of the energy functional is proposed. As a test task a well-known axisymmetric hydrostatic problem on equilibrium shapes of a drop adjacent to a horizontal rotating plane...
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| Main Authors: | , |
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| Format: | Article |
| Language: | Russian |
| Published: |
National Academy of Sciences of Belarus, the United Institute of Informatics Problems
2023-12-01
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| Series: | Informatika |
| Subjects: | |
| Online Access: | https://inf.grid.by/jour/article/view/1264 |
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| Summary: | Objectives. A variational-difference method for numerical simulation of equilibrium capillary surfaces based on the minimization of the energy functional is proposed. As a test task a well-known axisymmetric hydrostatic problem on equilibrium shapes of a drop adjacent to a horizontal rotating plane under gravity is considered. The mathematical model of the problem is built on the basis of the variational principle: the shape of the drop satisfies the minimum total energy for a given volume. The problem of the functional minimization is reduced to a system of nonlinear equations using the finite element method. To solve the system a Newton's iterative method is applied.Methods. The variational-difference approach (the finite element method) is used. The finite linear functions are chosen as basic functions.Results. Equilibrium shapes of a drop on a rotating plane are constructed by the finite element method in a wide range of defining parameters: Bond number, rotational Weber number and wetting angle. The influence of these parameters on the shape of a drop is investigated. The numerical results are matched with the results obtained using the iterative-difference approach over the entire range of physical stability with respect to axisymmetric perturbations.Conclusion. The finite element method responds to the loss of stability of a drop with respect to axisymmetric perturbations. Therefore it can be used to study the stability of the equilibrium of axisymmetric capillary surfaces. |
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| ISSN: | 1816-0301 |