Generating optimal topologies in structural design using a homogenization method
Computer Methods in Applied Mechanics and Engineering
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
On the Topological Derivative in Shape Optimization
SIAM Journal on Control and Optimization
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Incorporating topological derivatives into level set methods
Journal of Computational Physics
Structural optimization using sensitivity analysis and a level-set method
Journal of Computational Physics
Shape-topology optimization for Navier-Stokes problem using variational level set method
Journal of Computational and Applied Mathematics
A variational level set method for the topology optimization of steady-state Navier-Stokes flow
Journal of Computational Physics
Topological optimization method for a geometric control problem in Stokes flow
Applied Numerical Mathematics
Optimal design for non-Newtonian flows using a topology optimization approach
Computers & Mathematics with Applications
Topology optimization of fluid channels with flow rate equality constraints
Structural and Multidisciplinary Optimization
Topology optimization of unsteady incompressible Navier-Stokes flows
Journal of Computational Physics
Combination of topology optimization and optimal control method
Journal of Computational Physics
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This paper presents the topology optimization method for the steady and unsteady incompressible Navier---Stokes flows driven by body forces, which typically include the constant force (e.g. the gravity) and the centrifugal and Coriolis forces. In the topology optimization problem, the artificial friction force with design variable interpolated porosity is added into the Navier---Stokes equations as the conventional method, and the physical body forces in the Navier---Stokes equations are penalized using the power-law approach. The topology optimization problem is analyzed by the continuous adjoint method, and solved by the finite element method in conjunction with the gradient based approach. In the numerical examples, the topology optimization of the fluidic channel, mass distribution of the flow and local velocity control are presented for the flows driven by body forces. The numerical results demonstrate that the presented method achieves the topology optimization of the flows driven by body forces robustly.