Adjoint Complement to the Volume-of-Fluid Method for Immiscible Flows

Publikationstyp
Preprint
Publikationsdatum
2020-09-06
Sprache
English
Author
Kühl, Niklas orcid-logo
Kröger, Jörn 
Siebenborn, Martin
Hinze, Michael 
Rung, Thomas orcid-logo
Institut
Fluiddynamik und Schiffstheorie M-8 
TORE-URI
http://hdl.handle.net/11420/7451
Citation
arXiv:2009.03957 (2020-09-06)
ArXiv ID
2009.03957v1
Is Previous Version of
10.1016/j.jcp.2021.110411
The paper is concerned with an adjoint complement to the Volume-of-Fluid (VoF) method for immiscible two-phase flows, e.g. air and water, which is widely used in marine engineering due to its computational efficiency. The particular challenge of the primal and the corresponding adjoint VoF-approach refers to the sharp interface treatment featuring discontinuous physical properties. Both the continuous adjoint two-phase system (integration-by-parts) and the corresponding dual compressive convection schemes (summation-by-parts) are derived for two prominent compressive convection schemes, namely the High Resolution Interface Capturing Scheme (HRIC) and Compressive Interface Capturing Scheme for Arbitrary Meshes (CICSAM). The dual scheme rigorously mirrors the primal Normalized-Variable-Diagram (NVD) stencils. Attention is restricted to steady state applications. Thus both the primal and the dual procedures are performed in pseudo time and the backward integration of the dual approach is performed around the (pseudo-temporal) converged primal field. The paper analyses the primal and adjoint equations for an engineering model problem. An analytical solution to the model problem is initially presented, which displays that the adjoint part does not offer a unique, non-trivial solution. As a remedy, an additional diffusive concentration term is introduced to the adjoint concentration equation. Numerical results obtained from the modified approach are benchmarked against the analytical solution for the model problem. Supplementary, the influence of the modification on the sensitivities obtained from simulations for the two-dimensional flow around a submerged hydrofoil are discussed. The final application refers to a shape-optimization of a generic 3D underwater vehicle and underlines a negligible influence of the free mobility parameter.
Schlagworte
Physics - Fluid Dynamics
Physics - Fluid Dynamics
Mathematics - Optimization and Control

Version History

Now showing1 - 2 of 2
VersionDateSummary
2
2021-10-08 16:17:30
Artikel erschienen
1 *
 2020-10-01 16:11:40
* Selected version