Control and Optimization of Interfacial Flows Using Adjoint-Based Techniques
Abstract
1. Introduction
2. Continuous Governing Equations
2.1. Objective Functional
2.2. Primal (Forward) Problem
2.3. Dual (Adjoint) Problem
3. Discrete Governing Equations
3.1. Objective Functional
3.2. The Thinc Scheme
- is the non-dimensional slope steepness, defining the sharpness of the interface. Larger values imply sharper interfaces. Note that is often expressed in terms of two other parameters as follows
- is the interface direction
- is the non-dimensional intercept or jump location, which defines the level set of , and is imposed by the volume conservation constraint
3.3. Primal (Forward) Problem
3.4. Dual (Adjoint) Problem
4. Optimisation Algorithm
Algorithm 1: Optimization algorithm for Equation (1) |
5. Results
5.1. Validation: One-Dimensional Droplets
5.2. Two-Dimensional Tests
6. Conclusions and Future Work
Author Contributions
Funding
Conflicts of Interest
References
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Fikl, A.; Le Chenadec, V.; Sayadi, T. Control and Optimization of Interfacial Flows Using Adjoint-Based Techniques. Fluids 2020, 5, 156. https://doi.org/10.3390/fluids5030156
Fikl A, Le Chenadec V, Sayadi T. Control and Optimization of Interfacial Flows Using Adjoint-Based Techniques. Fluids. 2020; 5(3):156. https://doi.org/10.3390/fluids5030156
Chicago/Turabian StyleFikl, Alexandru, Vincent Le Chenadec, and Taraneh Sayadi. 2020. "Control and Optimization of Interfacial Flows Using Adjoint-Based Techniques" Fluids 5, no. 3: 156. https://doi.org/10.3390/fluids5030156
APA StyleFikl, A., Le Chenadec, V., & Sayadi, T. (2020). Control and Optimization of Interfacial Flows Using Adjoint-Based Techniques. Fluids, 5(3), 156. https://doi.org/10.3390/fluids5030156