Publisher DOI: 10.1016/j.jcp.2021.110411
arXiv ID: 2009.03957v1
Title: Adjoint Complement to the Volume-of-Fluid Method for Immiscible Flows
Language: English
Authors: Kühl, Niklas  
Kröger, Jörn 
Siebenborn, Martin 
Hinze, Michael 
Rung, Thomas  
Keywords: Physics - Fluid Dynamics;Physics - Fluid Dynamics;Mathematics - Optimization and Control
Issue Date: 1-Sep-2021
Source: Journal of computational physics 444: 110411 (2021-09-01)
Journal: Journal of computational physics 
Abstract (english): 
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.
URI: http://hdl.handle.net/11420/7451.2
ISSN: 0021-9991
Institute: Fluiddynamik und Schiffstheorie M-8 
Document Type: Article
Project: Hydrodynamische Widerstandsoptimierung von Schiffsrümpfen 
Weiterentwicklung von praxistauglichen simulationsbasierten Methoden zur Verbesserung der Leistungsfähigkeit von Schiffen mittels Formoptimierung 
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2 doi:10.15480/882.3817.2 2021-10-08 16:17:30.809 Artikel erschienen
1 hdl:11420/7451 2020-10-01 16:11:40.0

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