Eigenfunction superposition method simplifies analysis of unsteady flow in ducts with arbitrary shapes, demonstrating new results.
The eigenfunction superposition method is established for unsteady porous medium flow in long ducts of arbitrary cross section. The method utilizes the eigenfunctions of the Helmholtz equation to solve the Darcy–Brinkman equation. The method is much simpler than traditional separation of variables or Laplace transform, and the result can be expressed in simple summations. The unsteady flow in an isosceles right triangular duct, studied for the first time, is presented as an illustration.
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C. Y. Wang (2026) studied this question.
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