Abstract

This contribution describes the implementation of a data-driven shape optimization pipeline in a naval architecture application. We adopt reduced order models in order to improve the efficiency of the overall optimization, keeping a modular and equation-free nature to target the industrial demand. We applied the above mentioned pipeline to a realistic cruise ship in order to reduce the total drag. We begin by defining the design space, generated by deforming an initial shape in a parametric way using free form deformation. The evaluation of the performance of each new hull is determined by simulating the flux via finite volume discretization of a two-phase (water and air) fluid. Since the fluid dynamics model can result very expensive—especially dealing with complex industrial geometries—we propose also a dynamic mode decomposition enhancement to reduce the computational cost of a single numerical simulation. The real-time computation is finally achieved by means of proper orthogonal decomposition with Gaussian process regression technique. Thanks to the quick approximation, a genetic optimization algorithm becomes feasible to converge towards the optimal shape.

Highlights

  • Introduction and motivationsA shape optimization problem consists of finding the geometric configuration of an object that maximizes the performance of such object

  • We extend the computational pipeline already presented in [5], using two different reduced order modeling (ROM) approaches to address the high computational demand of optimization problems based on partial differential equations (PDEs) in parametric domains

  • Thanks to this validation and enrichment step, we are able to limit the error induced by the ROM techniques: due to equation-free nature of the pipeline, we are not able to bound the error without any information regarding the full-order model, but we can estimate it by validating the parametric configuration with the high-fidelity solutions

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Summary

Introduction and motivations

A shape optimization problem consists of finding the geometric configuration of an object that maximizes the performance of such object. We extend the computational pipeline already presented in [5], using two different reduced order modeling (ROM) approaches to address the high computational demand of optimization problems based on partial differential equations (PDEs) in parametric domains. We propose in this work an application on the shape optimization of a cruise ship, but the pipeline can be modified to plug different algorithms or software All these features make the framework especially suited for industry, thanks to the huge speedup in optimization—and design—contexts and the natural capacity to be even coupled with commercial software. 3 we present the numerical setting of the resistance minimization problem for a parametric cruise ship and the results obtained by applying the described framework on it, before proposing a conclusive comment and some future perspectives in Sect.

The complete computational pipeline
Free-form deformation for shape parametrization
Finite volume for high-fidelity database
Dynamic mode decomposition for regime state prediction
Reduced order model exploiting proper orthogonal decomposition
Genetic algorithm for global optimization
Numerical results: a cruise ship shape optimization
Conclusion and future perspectives
Findings
28. OpenCFD
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