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This paper develops a tree-topological local mesh refinement (TLMR) method on Cartesian grids for the simulation of bio-inspired flow with multiple moving objects. The TLMR nests refinement mesh blocks of structured grids to the target regions and arrange the blocks in a tree topology. The method solves the time-dependent incompressible flow using a fractional-step method and discretizes the Navier-Stokes equation using a finite-difference formulation with an immersed boundary method to resolve the complex boundaries. When iteratively solving the discretized equations across the coarse and fine TLMR blocks, for better accuracy and faster convergence, the momentum equation is solved on all blocks simultaneously, while the Poisson equation is solved recursively from the coarsest block to the finest ones. When the refined blocks of the same block are connected, the parallel Schwarz method is used to iteratively solve both the momentum and Poisson equations. Convergence studies show that the algorithm is second-order accurate in space for both velocity and pressure, and the developed mesh refinement technique is benchmarked and demonstrated by several canonical flow problems. The TLMR enables a fast solution to an incompressible flow problem with complex boundaries or multiple moving objects. Various bio-inspired flows of multiple moving objects show that the solver can save over 80% computational time, proportional to the grid reduction when refinement is applied.
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A Robust Mesh Moving Method for Moving-Boundary Problems
This paper presents a robust mesh moving solver developed to address moving boundary problems. Crucially, the resulting deformed mesh retains the same topology as the original mesh without being overly distorted. The mesh is treated as an elastic material, and the deformation of the computational domain resulting from moving boundaries is determined by solving the equilibrium linear elasticity equations. The linear elasticity equations are discretized by the classic Galerkin finite element method and solved by the block conjugate gradient iterative method. To maintain the quality of the mesh after motion, the Young's modulus of each element is weighted by the reciprocal of the distance between the element center and the moving boundaries. The effectiveness of this approach is demonstrated through a set of 2D and 3D test cases featuring prescribed translational and/or rotational motion of the embedded object. The method is now ready for integration into our existing in-house CFD solvers.
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- Award ID(s):
- 2219542
- PAR ID:
- 10534438
- Publisher / Repository:
- American Institute of Aeronautics and Astronautics
- Date Published:
- ISBN:
- 978-1-62410-711-5
- Format(s):
- Medium: X
- Location:
- Orlando, FL
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.2514/6.2024-1163
