Two methods of surface tension treatment in free surface flow simulations
Nikitin K. D., Terekhov K. M., Vasilevskij Yu. V.
Applied Mathematics Letters
Vol.86, P. 236-242
Опубликовано: 2018
Тип ресурса: Статья
DOI:10.1016/j.aml.2018.07.005
Аннотация:
We describe our approach to treatment of surface tension in free surface flow simulations on adaptive octree-type grids. The approach is based on the semi-Lagrangian method for the transport and momentum equations and the pressure projection method to enforce the incompressibility constrain. The surface tension contributes to the Dirichlet boundary condition for the pressure equation at the projection step. The treatment of surface tension is based either on accurate finite difference calculation of the mean curvature or on a curvature estimation by the implicit solution of conservative mean curvature flow problem. The first method provides almost the second order accuracy in space for surface tension forces. The second method is characterized by greater stability and essentially larger time steps. Numerical experiments illustrate the main features of the methods. © 2018 Elsevier Ltd
Ключевые слова:
Free surface; Incompressible Navier–Stokes equations; Level-set method; Semi-Lagrangian method; Surface tension
Boundary conditions; Flow simulation; Lagrange multipliers; Navier Stokes equations; Surface tension; Surface treatment; Dirichlet boundary condition; Finite difference calculations; Free surfaces; Level Set method; Numerical experiments; Second-order accuracy; Semi-Lagrangian methods; Stokes equations; Numerical methods
Язык текста: Английский
ISSN: 0893-9659
Nikitin K. D.
Terekhov K. M.
Vasilevskij Yu. V. Yurij Viktorovich 1967-
Никитин К. Д.
Терехов К. М.
Василевский Ю. В. Юрий Викторович 1967-
Two methods of surface tension treatment in free surface flow simulations
Текст визуальный непосредственный
Applied Mathematics Letters
Elsevier Science Publisher B.V.
Vol.86 P. 236-242
2018
Статья
Free surface Incompressible Navier–Stokes equations Level-set method Semi-Lagrangian method Surface tension
Boundary conditions Flow simulation Lagrange multipliers Navier Stokes equations Surface tension Surface treatment Dirichlet boundary condition Finite difference calculations Free surfaces Level Set method Numerical experiments Second-order accuracy Semi-Lagrangian methods Stokes equations Numerical methods
We describe our approach to treatment of surface tension in free surface flow simulations on adaptive octree-type grids. The approach is based on the semi-Lagrangian method for the transport and momentum equations and the pressure projection method to enforce the incompressibility constrain. The surface tension contributes to the Dirichlet boundary condition for the pressure equation at the projection step. The treatment of surface tension is based either on accurate finite difference calculation of the mean curvature or on a curvature estimation by the implicit solution of conservative mean curvature flow problem. The first method provides almost the second order accuracy in space for surface tension forces. The second method is characterized by greater stability and essentially larger time steps. Numerical experiments illustrate the main features of the methods. © 2018 Elsevier Ltd