arXiv subjects

Yuta Tanabe

Publications and source records attributed to Yuta Tanabe.

5 recordsLinked to original sources

arXiv2026

4D Topology optimization of moving rigid bodies in fluid flows

This study applies $\textit{4D topology optimization}$, a framework for simultaneously optimizing the morphology and motion of a system, to a rigid body that induces fluid flow. The rigid body shape is represented on a design grid that is independent of the analysis grid, and at each time step, it undergoes rigid-body motion before being mapped onto the analysis grid. The shape is represented using a pseudo-density method, while the motion is directly parametrized by the positions at discrete time steps and smoothed using a temporal filtering technique. The fluid dynamics are evaluated through the lattice kinetic scheme, an extended version of the lattice Boltzmann method. Design sensitivities with respect to both shape and motion are derived via the adjoint variable method, and the shape and motion are intentionally updated simultaneously during the optimization process. Finally, two- and three-dimensional numerical examples are presented and discussed from a physical perspective. Furthermore, the effectiveness of the proposed method is demonstrated by comparison with cases in which only the shape or motion is optimized, as well as through several parameter studies.

physics.flu-dyn↗

arXiv2026

Topology optimization of passively moving rigid bodies in unsteady flows

This study proposes the topology optimization method for moving rigid bodies subjected to forces from fluid flow, such as sails and turbines, with an unsteady time-dependent formulation. Unlike existing topology optimization frameworks in which rigid-body motion drives the flow, which is referred to as $\textit{active}$, the present study considers rigid-body motion induced by fluid forces, i.e., $\textit{passive}$. The equations of motion governing the rigid-body dynamics are solved in a coupled manner with the continuity equation and the momentum conservation equations. The rigid body is represented on a design grid that is separated from the analysis grid on which the state and adjoint fields are defined. After updating the rigid body motion, the body is mapped onto the analysis grid. The fluid equations are solved using the lattice kinetic scheme, an extended version of the lattice Boltzmann method, owing to its suitability for unsteady flows. Design sensitivities based on the adjoint variable method are presented and applied to two- and three-dimensional problems involving translational and rotational motions. The optimized shapes for each problem are discussed from a physical perspective and compared with a reference shape or their binarized counterparts, providing insights into the effectiveness of the proposed method as well as its limitations.

physics.flu-dyn↗

arXiv2025

Topology optimization of actively moving rigid bodies in unsteady flows

This study proposes a novel topology optimization method for unsteady fluid flows induced by actively moving rigid bodies. The key idea of the proposed method is to decouple the design and analysis domains by using separate grids. The design grid undergoes rigid body motion and is then overlapped onto the analysis grid. After the overlap, key quantities such as the Brinkman coefficient are transferred between the grids. This approach provides a direct and efficient means of representing object motion and facilitates the handling of more general and complex movements in unsteady flow conditions. Since the computational cost of solving unsteady fluid problems is substantial, we employ a solver based on the lattice kinetic scheme, which is the extended version of the lattice Boltzmann method, to evaluate the design sensitivity. The fundamental equations are derived, and the accuracy of the design sensitivity calculations is validated through comparison with finite difference approximations. The effectiveness of the method is demonstrated through numerical examples in two-dimensional and three-dimensional settings.

math.OC↗

arXiv2024

Adjoint lattice kinetic scheme for topology optimization in fluid problems

This paper proposes a topology optimization method for non-thermal and thermal fluid problems using the Lattice Kinetic Scheme (LKS).LKS, which is derived from the Lattice Boltzmann Method (LBM), requires only macroscopic values, such as fluid velocity and pressure, whereas LBM requires velocity distribution functions, thereby reducing memory requirements. The proposed method computes design sensitivities based on the adjoint variable method, and the adjoint equation is solved in the same manner as LKS; thus, we refer to it as the Adjoint Lattice Kinetic Scheme (ALKS). A key contribution of this method is the proposed approximate treatment of boundary conditions for the adjoint equation, which is challenging to apply directly due to the characteristics of LKS boundary conditions. We demonstrate numerical examples for steady and unsteady problems involving non-thermal and thermal fluids, and the results are physically meaningful and consistent with previous research, exhibiting similar trends in parameter dependencies, such as the Reynolds number. Furthermore, the proposed method reduces memory usage by up to 75% compared to the conventional LBM in an unsteady thermal fluid problem.

math.NA↗

arXiv2007

Ground States of the SU(N) Heisenberg Model

The SU(N) Heisenberg model with various single-row representations is investigated by quantum Monte Carlo simulations. While the zero-temperature phase boundary agrees qualitatively with the theoretical predictions based on the 1/N expansion, some unexpected features are also observed. For N>=5 with the fundamental representation, for example, it is suggested that the ground states possess exact or approximate U(1) degeneracy. In addition, for the representation of Young tableau with more than one column, the ground state shows no valence-bond-solid order even at N greater than the threshold value.

cond-mat.stat-mech↗