Article
Engineering, Multidisciplinary
Hao Li, Tsuguo Kondoh, Pierre Jolivet, Kozo Furuta, Takayuki Yamada, Benliang Zhu, Heng Zhang, Kazuhiro Izui, Shinji Nishiwaki
Summary: This study presents an optimum design and thermal modeling for passive heat sinks cooled by natural convection using a reaction-diffusion equation-based level-set method. The research shows that the proposed methodology can capture the explicit fluid-solid boundary and solve a moderately large-scale optimization problem in parallel on a standard multi-process platform.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
Xianbao Duan, Yichen Li, Hongxia Tan, Yangyang Li
Summary: In this study, a level set based adaptive mesh method is proposed for minimizing drag in incompressible flow governed by Stokes equations. Shape sensitivity analysis of the cost functional is derived, and two levels of meshes are adopted during the optimization process. By using a coarse mesh for evolving the level set function and further refining it near the interfaces, computational cost is significantly reduced compared to using a uniform mesh over the entire domain with the same resolution. Additionally, obtaining the shape derivative value on the boundary implicitly is a challenging task in classical optimal shape design problems.
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
(2022)
Article
Computer Science, Interdisciplinary Applications
Raphael Egan, Arthur Guittet, Fernando Temprano-Coleto, Tobin Isaac, Francois J. Peaudecerf, Julien R. Landel, Paolo Luzzatto-Fegiz, Carsten Burstedde, Frederic Gibou
Summary: The study proposes a parallel approach for solving the Navier-Stokes equations on Octree grids, demonstrating strong scalability and dynamic adaptive capabilities through additional parallel algorithms and performance analyses.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Son H. Nguyen, Dongwoo Sohn, Hyun-Gyu Kim
Summary: This paper presents a new computational strategy for stress-constrained shape and topology optimization using level-set-based trimmed meshes. The proposed hr-adaptive mesh refinement scheme greatly reduces the computational cost and achieves a clear and explicit representation of desired optimal designs with stress constraints.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2022)
Article
Computer Science, Interdisciplinary Applications
Lucie Freret, Michael Williamschen, Clinton P. T. Groth
Summary: This paper presents a parallel anisotropic block-based adaptive mesh refinement (AMR) algorithm for solving physically complex flow problems with highly anisotropic features and varying spatial and temporal scales. The algorithm utilizes a binary tree data structure for anisotropic refinement and coarsening of grid blocks, and employs a non-uniform cell representation to enhance computational efficiency.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics, Applied
Hao Li, Takayuki Yamada, Pierre Jolivet, Kozo Furuta, Tsuguo Kondoh, Kazuhiro Izui, Shinji Nishiwaki
Summary: The proposed framework is a parallel distributed and open-source framework for full-scale 3D structural topology optimization, which combines parallel computing and mesh adaption techniques using a reaction-diffusion equation based level-set method. The framework can be easily extended to design complex engineering products with optimized structures represented by high-resolution and clear boundaries.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2021)
Article
Computer Science, Interdisciplinary Applications
Sheng Pan, Minghao Yu, Hao Li, Zheng Li, Mengke Ren, Junfeng Gu, Changyu Shen
Summary: This paper proposes an integrated two-step strategy for an optimal design of liquid-cooled channel layout based on the moving morphable component (MMC)-density approach. The proposed strategy combines the flexibility of the MMC approach with the topology description capacity of the density approach to obtain a reasonable layout with better thermal performance. Numerical examples demonstrate the effectiveness of the strategy.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2022)
Article
Computer Science, Interdisciplinary Applications
Yadong Zeng, Anqing Xuan, Johannes Blaschke, Lian Shen
Summary: A unified adaptive level set framework for incompressible two-phase flows is developed using a multi-level collocated grid, along with synchronization operations and a multilevel re-initialization method. The framework shows good numerical implementation and mass conservation, successfully resolving various canonical problems. Additionally, efficiency and significant speedup are demonstrated in a three-dimensional dam breaking simulation.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Engineering, Multidisciplinary
Philip Luke Karuthedath, Abhinav Gupta, Bhagath Mamindlapelly, Rajib Chowdhury
Summary: This study proposes a continuous density-field based isogeometric topology optimization method using Polynomial splines over Hierarchical T-meshes (PHT-Splines). The method achieves a very smooth topology and adaptive mesh refinement through the control points and spline basis functions. It can import complex geometry and maintain geometrical and computational accuracy. The proposed method reduces Degree's-of-Freedom (DoF) requirement and achieves a significant reduction in DoF compared to existing methods.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Computer Science, Interdisciplinary Applications
Romain Janodet, Carlos Guillamon, Vincent Moureau, Renaud Mercier, Ghislain Lartigue, Pierre Benard, Thibaut Menard, Alain Berlemont
Summary: This article presents a parallel and robust strategy for simulating turbulent incompressible two-phase flows on unstructured grids in complex geometries. The combination of a narrow-band accurate conservative level set/ghost-fluid framework with isotropic adaptive mesh refinement allows for accurate capture of interface dynamics and topology. The method has been validated through various tests and examples, demonstrating its spatial convergence, robustness, and efficiency. It also showcases the computational advantages of adaptive mesh refinement for simulating complex turbulent flows with large density ratios.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics
Victor V. Kuzenov, Sergei V. Ryzhkov, Aleksey Yu. Varaksin
Summary: This paper discusses the numerical simulation of the interaction between the cocurrent stream and the combustion products from a solid fuel rocket engine (SFRE). A single calculation methodology is used to describe gas-dynamic processes, and a hybrid computational grid is applied to calculate gas flow near complex geometric shapes. The simulation of the main phase of interaction in the Earth's atmosphere has been conducted.
Article
Engineering, Multidisciplinary
David Munoz, Jose Albelda, Juan Jose Rodenas, Enrique Nadal
Summary: The article discusses the advantages and disadvantages of the commonly used SIMP method in topology optimization, and proposes a method combining techniques to improve the performance of TO, including the use of two meshes, two h-adaptive mesh refinement strategies, and discretization error estimation based on energy norm.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2022)
Article
Mechanics
Chuong V. Tran, Xinwei Yu, David G. Dritschel
Summary: Incompressible fluid flows are characterized by high correlations between velocity and pressure, as well as between vorticity and pressure. This correlation plays a significant role in maintaining regularity in Navier-Stokes flows. The study suggests that as long as global pressure minimum (or minima) and velocity maximum (or maxima) are mutually exclusive, regularity is likely to persist.
JOURNAL OF FLUID MECHANICS
(2021)
Article
Mechanics
Wenqiang Xu, Yu Li, Hanzhang Li, Sheng Qiang, Chengpeng Zhang, Caihong Zhang
Summary: This article introduces a multi-level adaptive mesh refinement technique for solving the contradiction between calculation efficiency and accuracy of the phase-field method. The technique achieves good results in crack simulation and has potential engineering applications.
ENGINEERING FRACTURE MECHANICS
(2022)
Article
Mathematics, Applied
Thomas C. Clevenger, Timo Heister
Summary: The problems arising in Earth's mantle convection involve finding the solution to Stokes systems with large viscosity contrasts. In this study, the GMG method is proposed as a more robust option compared to the commonly used AMG method. By using a matrix-free GMG V-cycle, the study demonstrates the scalability and robustness of GMG up to 114,688 cores and 217 billion unknowns.
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
(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)