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Continuous and Discrete Adjoint Approach Based on Lattice Boltzmann Method in Aerodynamic Optimization Part I: Mathematical Derivation of Adjoint Lattice Boltzmann Equations

Published online by Cambridge University Press:  03 June 2015

Mohamad Hamed Hekmat  and
Masoud Mirzaei
Mohamad Hamed Hekmat*
Affiliation:
Center of Excellence for Design & Simulation of Space Systems, K. N. Toosi University of Technology, Tehran, 891567, Iran
Masoud Mirzaei*
Affiliation:
Center of Excellence for Design & Simulation of Space Systems, K. N. Toosi University of Technology, Tehran, 891567, Iran
*
Corresponding author. Email: mhekmat@dena.kntu.ac.ir
Email: mirzaei@kntu.ac.ir
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Abstract

The significance of flow optimization utilizing the lattice Boltzmann (LB) method becomes obvious regarding its advantages as a novel flow field solution method compared to the other conventional computational fluid dynamics techniques. These unique characteristics of the LB method form the main idea of its application to optimization problems. In this research, for the first time, both continuous and discrete adjoint equations were extracted based on the LB method using a general procedure with low implementation cost. The proposed approach could be performed similarly for any optimization problem with the corresponding cost function and design variables vector. Moreover, this approach was not limited to flow fields and could be employed for steady as well as unsteady flows. Initially, the continuous and discrete adjoint LB equations and the cost function gradient vector were derived mathematically in detail using the continuous and discrete LB equations in space and time, respectively. Meanwhile, new adjoint concepts in lattice space were introduced. Finally, the analytical evaluation of the adjoint distribution functions and the cost function gradients was carried out.

Keywords

76D5549Q9993B40Aerodynamic optimizationcontinuous and discrete adjoint approachlattice Boltzmann method
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 6 , Issue 5 , October 2014 , pp. 570 - 589
Copyright
Copyright © Global-Science Press 2014

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