Dr. Marvin Müller

CAD-free adjoint shape optimisation of floating vessels

The aim of this project is to advance an efficient and robust procedure for
fluid dynamic shape optimisation of non-parameterised shapes in the context
of naval architecture. The optimisation procedure is based on the theory of
optimal control of Partial Differential Equations (PDE) and utilises the adjoint
method in PDE constraint optimisation to characterise the shape derivative
of the objective function. The goal is to determine shape deformation fields
for optimisation problems which aim to minimise the drag of a free floating
ship. The application is characterised by high Reynolds numbers and turbulent
flow. Thus, the state is described by the 3D incompressible Reynolds-Averaged
Navier-Stokes (RANS) equations with turbulence modelling and possibly a Vol-
ume of Fluid (VoF) method for free surface flows. Moreover, the geometry
must adhere to geometric constraints which have to be considered during the
shape deformation. To support the weakest possible geometry, the shape
is considered to have a Lipschitz boundary. Thus, it is necessary to determine
shape deformation field which transform Lipschitz domains again into Lipschitz
domains for which we employ a p-harmonic descent approach.

Advisor: Prof. Dr. Thomas Rung

Co-Advisor: Jun.-Prof. Dr. Martin Siebenborn

28.06.2021

EUROGEN 2021 (online): "Numerical Investigation on a p-Harmonic Descent Approach for
Shape Optimisation Under Geometrical Constraints"

25.11.2020

Lothar-Collatz-Seminar (online): "Decoupling of Control and force Objective in Adjoint-Based Fluid Dynamic Shape optimization."

1. Müller, P.M., Bletsos, G., Rung, T.: Shape transformation approaches for fluid dynamic optimization, accepted in Aerospace, 10, 519. (https://doi.org/10.3390/aerospace10060519), 2023

2. Müller, P.M., Siebenborn, M., Rung, T.: Application of p-Laplacian relaxed steepest descent to shape optimization in two-phase flows, preprint arXiv: https://arxiv.org/abs/2207.08586, 2022

3. Müller, P.M., Pinzon, J., Rung, T., Siebenborn, M.: A Scalable Algorithm for Shape Optimization with Geometric Constraints in Banach Spaces, SIAM J. Sci. Comp. 45:B231-B251 (DOI: 10.1137/22M1494609), 2023

4. Müller, P. M., Kühl, N., Siebenborn, M., Deckelnick, K., Hinze, M., Rung, T.: A Novel p-Harmonic Descent Approach Applied to Fluid Dynamic Shape Optimization. Structural and Multidisciplinary Optimization 64:3489-3503 (doi:10.1007/s00158-021-03030-x), 2021

5. Kühl, N., Müller, P.M., Rung, T.: Continuous Adjoint Complement to the Blasius Equation. Physics of Fluids 33:033608, 10.1063/5.0037779, 2021

6. Kühl, N., Müller, P.M., Rung, T.: Adjoint Complement to the Universal Momentum Law of the Wall. Flow, Turbulence and Combustion  108:329-351 (DOI 10.1007/s10494-021-00286-7), 2021

7. Kühl, N., Müller, P.M., Stück, A., Hinze, M., Rung, T.: Decoupling of Control and Force Objective in Adjoint-Based Fluid Dynamic Shape Optimization. AIAA Journal, 57(9), pp.4110-4114, 2019