Article
Computer Science, Interdisciplinary Applications
P. Y. Vrionis, K. D. Samouchos, K. C. Giannakoglou
Summary: A continuous adjoint formulation for shape optimization in steady-state, cavitating flows is developed, utilizing a Transport Equation-based mixture model and the Kunz cavitation model. Emphasis is placed on the accurate computation of geometric sensitivities at the cut-cells. The proposed adjoint formulation is assessed through three shape optimizations, demonstrating its effectiveness in handling different objectives.
COMPUTERS & FLUIDS
(2021)
Article
Thermodynamics
Yi Ye, Xueying Li, Jing Ren, Bengt Sunden
Summary: With the advancement of additive manufacturing, there has been an increased freedom in developing complex cooling structures. This research presents an algorithm of topology optimization with heat transfer and provides a detailed explanation of the optimization procedure and basic assumptions.
NUMERICAL HEAT TRANSFER PART A-APPLICATIONS
(2023)
Article
Mathematics, Applied
Suqiong Xie, Kentaro Yaji, Toru Takahashi, Hiroshi Isakari, Masato Yoshino, Toshiro Matsumoto
Summary: This paper introduces a topology optimization method for flow channel design using the lattice kinetic scheme (LKS), which requires less storage space compared to the lattice Boltzmann method and can impose macroscopic boundary conditions directly. The optimization is based on the gradient of the objective functional with respect to the design variables and the design sensitivity is computed using the adjoint variable method.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Engineering, Multidisciplinary
Zhihua Xie
Summary: A versatile conservative three-dimensional Cartesian cut-cell method is proposed for simulation of incompressible viscous flows over complex geometries. The method is based on the finite volume method on a non-uniform staggered grid with consistent mass and momentum flux computation. Strict conservation of mass and momentum is enforced through the pressure-velocity coupling algorithm.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Mathematics
Reda El Bechari, Frederic Guyomarch, Stephane Brisset
Summary: This paper provides a detailed explanation of the adjoint variable method in the context of electromagnetic modeling and presents a comprehensive methodology for optimizing engineering problems involving magnetostatics. The methodology supports both linear and nonlinear problems and has been successfully applied to optimize parameters in superconducting energy storage devices, magnet presses, and electromagnet topology.
Article
Multidisciplinary Sciences
Gregor Wautischer, Claas Abert, Florian Bruckner, Florian Slanovc, Dieter Suess
Summary: This paper presents a method for optimizing the topology of hard and soft magnetic structures using the density approach for topology optimization. The stray field is calculated using a hybrid finite element-boundary element method, and the necessary gradients for optimization are efficiently calculated using the adjoint approach. The method's capabilities are showcased by optimizing the topology of hard and soft magnetic thin film structures and the results are verified by comparison with an analytical solution.
SCIENTIFIC REPORTS
(2022)
Article
Engineering, Multidisciplinary
Luis Fernando Garcia-Rodriguez, Cesar Yukishigue Kiyono, Renato Picelli, Emilio Carlos Nelli Silva
Summary: This paper investigates the influence of an integer continuous variable-based optimizer on turbulent fluid flow and analyzes its impact on the near wall distance calculation. The method avoids grey regions during the optimization process. The turbulence phenomenon is treated using the Spalart-Allmaras model and the near wall distance calculation is approached by the Hamilton-Jacobi formulation. A permeability independence proposal is also introduced to avoid miscalculations in the fluid cells.
APPLIED MATHEMATICAL MODELLING
(2023)
Article
Mathematics, Applied
Carlos M. Okubo Jr, Cesar Y. Kiyono, Luis F. N. Sa, Emilio C. N. Silva
Summary: Flow behavior inside rotors is complex and three-dimensional, making the design of these components challenging due to a large number of free geometrical parameters. This study proposes a new approach to design rotors using topology optimization, with an objective function measured at boundaries and derived from energy dissipation. The Globally Convergent Method of Moving Asymptotes (GCMMA) is applied for optimization, with numerical examples comparing an optimized design with a traditional one.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Engineering, Multidisciplinary
Carlos M. Okubo, Luis F. N. Sa, Cesar Y. Kiyono, Emilio C. N. Silva
Summary: Topology optimization methods have been widely used for fluid problems, with this study focusing on using the discrete adjoint approach in combination with a finite differences scheme to calculate sensitivity. The proposed methodology is particularly useful for complex physical problems and utilizes adaptive mesh refinement to enhance the solid-fluid interface definition while keeping computational costs competitive. The implementation is done using the OpenFOAM platform, with evaluations conducted on traditional 2D incompressible flow cases and explorations on compressible flow cases with different cell types and 3D models.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Mechanics
Silong Yong, Weifeng Zhao
Summary: This paper introduces a low-storage adjoint lattice Boltzmann method, which adopts a velocity-independent approximate equilibrium for the adjoint variable, eliminating the need to store the space-time history of the flow field and overcoming drawbacks of existing adjoint methods. The method produces ideal results in controlling unsteady incompressible flows.
Article
Computer Science, Interdisciplinary Applications
Luis F. N. Sa, Carlos M. Okubo, Andre N. Sa, Emilio C. N. Silva
Summary: This work presents a continuous boundary propagation model that can be used as an auxiliary model to propagate boundary conditions in topology optimization problems. The model can handle multiple behaviors of the solid domain resulting from different boundary conditions and is applicable to 3D problems.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2022)
Article
Computer Science, Interdisciplinary Applications
Diego Hayashi Alonso, Luis Fernando Garcia Rodriguez, Emilio Carlos Nelli Silva
Summary: In order to tackle the challenges of complex fluid flow dynamics and topology optimization, this work proposes combining OpenFOAM (R) and FEniCS/dolfin-adjoint software. While OpenFOAM (R) offers efficient implementations for various fluid flow models, FEniCS combined with dolfin-adjoint library provides a high-level discrete adjoint model, simplifying the implementation of adjoint models in more complex fluid flows.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2021)
Article
Engineering, Multidisciplinary
Sandilya Kambampati, Hayoung Chung, H. Alicia Kim
Summary: This paper proposes a new methodology for computing boundary sensitivities in level set topology optimization using the discrete adjoint method. By combining local perturbations with derivatives of the objective function, boundary sensitivities can be calculated. This method avoids the smoothing or interpolation methods typically used in sensitivity calculations, improving accuracy and convergence characteristics.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Computer Science, Interdisciplinary Applications
Kaiwen Guan, Kei Matsushima, Yuki Noguchi, Takayuki Yamada
Summary: This paper presents a topology optimization method based on direct simulation Monte Carlo (DSMC) for rarefied gas flows. The distribution of fluid and solid is characterized by a pseudo density in the design domain. The traditional DSMC algorithm is extended to include the pseudo density, and design sensitivity is obtained using the Lagrangian multiplier method and adjoint state method. The extended DSMC algorithm is verified through numerical examples and applied to optimize the design of a bent pipe.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Engineering, Multidisciplinary
Lixue Fang, Xuan Wang, Huanlin Zhou
Summary: Thermoelastic problems involve elastic responses affected by temperature variation, while the Moving Morphable Void approach describes void material using a closed B-spline curve in design domain. This study uses the MMV method to topologically optimize thermoelastic structures, combining heat conduction and elasticity weak formulations, constructing an optimization mathematical model with material distribution updated by the method of moving asymptote algorithm.
APPLIED MATHEMATICAL MODELLING
(2022)
Article
Computer Science, Interdisciplinary Applications
P. Y. Vrionis, K. D. Samouchos, K. C. Giannakoglou
Summary: A continuous adjoint formulation for shape optimization in steady-state, cavitating flows is developed, utilizing a Transport Equation-based mixture model and the Kunz cavitation model. Emphasis is placed on the accurate computation of geometric sensitivities at the cut-cells. The proposed adjoint formulation is assessed through three shape optimizations, demonstrating its effectiveness in handling different objectives.
COMPUTERS & FLUIDS
(2021)
Article
Mathematics, Applied
Junfeng Cao, Ke Chen, Huan Han
Summary: This paper proposes a two-stage image segmentation model based on structure tensor and fractional-order regularization. In the first stage, fractional-order regularization is used to approximate the Hausdorff measure of the MS model. The solution is found using the ADI scheme. In the second stage, thresholding is used for target segmentation. The proposed model demonstrates superior performance compared to state-of-the-art methods.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Dylan J. Oliver, Ian W. Turner, Elliot J. Carr
Summary: This paper discusses a projection-based framework for numerical computation of advection-diffusion-reaction (ADR) equations in heterogeneous media with multiple layers or complex geometric structures. By obtaining approximate solutions on a coarse grid and reconstructing solutions on a fine grid, the computational cost is significantly reduced while accurately approximating complex solutions.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Nathan V. Roberts, Sean T. Miller, Stephen D. Bond, Eric C. Cyr
Summary: In this study, the time-marching discontinuous Petrov-Galerkin (DPG) method is applied to the Vlasov equation for the first time, using backward Euler for a Vlasov-Poisson discretization. Adaptive mesh refinement is demonstrated on two problems: the two-stream instability problem and a cold diode problem.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Yizhi Sun, Zhilin Sun
Summary: This work investigates the convexity of a specific class of positive definite probability measures and demonstrates the preservation of convexity under multiplication and intertwining product. The study reveals that any integrable function on an interval with a polynomial expansion of fast absolute convergence can be decomposed into a pair of positive convex interval probabilities, simplifying the study of interval distributions and discontinuous probabilistic Galerkin schemes.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Bhagwan Singh, Komal Jangid, Santwana Mukhopadhyay
Summary: This paper examines the prediction of bending characteristics of nanoscale materials using the Moore-Gibson-Thompson thermoelasticity theory in conjunction with the nonlocal strain gradient theory. The study finds that the stiffness of the materials can be affected by nonlocal and length-scale parameters, and the aspect ratios of the beam structure play a significant role in bending simulations.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Guoliang Wang, Bo Zheng, Yueqiang Shang
Summary: This paper presents and analyzes a parallel finite element post-processing algorithm for the simulation of Stokes equations with a nonlinear damping term, which integrates the algorithmic advantages of the two-level approach, the partition of unity method, and the post-processing technique. The algorithm generates a global continuous approximate solution using the partition of unity method and improves the smoothness of the solution by adding an extra coarse grid correction step. It has good parallel performance and is validated through theoretical error estimates and numerical test examples.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Hao Xu, Zeng-Qi Wang
Summary: Fluid flow control problems are crucial in industrial applications, and solving the optimal control of Navier-Stokes equations is challenging. By using Oseen's approximation and matrix splitting preconditioners, we can efficiently solve the linear systems and improve convergence.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Zhengya Yang, Xuejuan Chen, Yanping Chen, Jing Wang
Summary: This paper focuses on the high-order stable numerical solutions of the time-space fractional diffusion equation. The Fourier spectral method is used for spatial discretization and the Spectral Deferred Correction (SDC) method is used for numerical solutions in time. As a result, a high-precision numerical discretization scheme for solving the fractional diffusion equation is obtained, and the convergence and stability of the scheme are proved. Several numerical examples are presented to demonstrate the effectiveness and feasibility of the proposed numerical scheme.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)