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<p>In the present paper, a Batchelor flow problem is reformulated as a shape optimization problem. Using the perturbation of identity approach, the material and shape derivatives of the state variables are obtained and consequently, the shape derivative of the cost functional is derived using the chain rule approach. The resultant shape derivative is utilized in a preconditioned steepest descent type algorithm to solve the shape optimization problem. Several test cases are utilized to test the proposed method. It is observed that the numerical results are in excellent agreement with the expected theoretical results.</p>

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A shape optimization approach for a Batchelor flow problem

  • 期刊论文

  • 发表日期：

    2025年10月3日

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  • Henry Kasumba

摘要

In the present paper, a Batchelor flow problem is reformulated as a shape optimization problem. Using the perturbation of identity approach, the material and shape derivatives of the state variables are obtained and consequently, the shape derivative of the cost functional is derived using the chain rule approach. The resultant shape derivative is utilized in a preconditioned steepest descent type algorithm to solve the shape optimization problem. Several test cases are utilized to test the proposed method. It is observed that the numerical results are in excellent agreement with the expected theoretical results.