Article
Computer Science, Software Engineering
Guillermo Aparicio-Estrems, Abel Gargallo-Peiro, Xevi Roca
Summary: In this paper, we provide detailed instructions on how to use Newton's method for distortion-based curved r-adaption with a discrete high-order metric field. We combine a distortion term that measures the deviation from the target metric and a penalty term that measures the deviation from the target boundary. To achieve this, we introduce a log-Euclidean high-order metric interpolation on a curved mesh and an implicit representation for the domain boundaries. These techniques allow us to minimize the objective function and simultaneously match the curved features of the target metric and boundary, which is a novel capability in curved r-adaption.
COMPUTER-AIDED DESIGN
(2023)
Article
Engineering, Multidisciplinary
Zhe Ji, Lin Fu, Xiangyu Hu, Nikolaus Adams
Summary: In this paper, a feature-aware SPH method is proposed for concurrent and automated isotropic unstructured mesh generation. Compared to the original SPH-based mesh generator, this method addresses issues of incomplete kernel support at boundaries and feature size adaptation, achieving high-quality meshes with a faster convergence speed.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Computer Science, Interdisciplinary Applications
Luca Cirrottola, Mario Ricchiuto, Algiane Froehly, Barbara Re, Alberto Guardone, Giuseppe Quaranta
Summary: This paper presents an adaptive moving mesh method for unstructured meshes, which is an extension of previous works in three dimensions. The method uses an iterative solution of a variable diffusion Laplacian model on the reference domain to adapt the mesh to moving sharp solution fronts and impose slip conditions for displacements on curved boundary surfaces. The effectiveness of the adapted mesh is ensured over non-convex curved boundaries with singularities through node projection and a-posteriori limiters.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Computer Science, Hardware & Architecture
Kangjin Huang, Yonggang Che, Chuanfu Xu, Zhe Dai, Jian Zhang
Summary: This paper reports the optimization of the CUDA code for a high-order CFD application based on OP2. The novel methods used in the optimization significantly improve the performance of the generated CUDA code, while maintaining the application's portability.
JOURNAL OF SUPERCOMPUTING
(2023)
Article
Physics, Mathematical
Weijie Zhang, Yulong Xing, Yinhua Xia, Yan Xu
Summary: This paper proposes a high-order accurate DG method for the compressible Euler equations on unstructured meshes under gravitational fields, which preserves a general hydrostatic equilibrium state and guarantees the positivity of density and pressure. Through a special way to recover the equilibrium state and the design of novel interface variables, the scheme achieves well-balanced and positivity-preserving properties.
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Hao Li, Tsuguo Kondoh, Pierre Jolivet, Nari Nakayama, Kozo Furuta, Heng Zhang, Benliang Zhu, Kazuhiro Izui, Shinji Nishiwaki
Summary: This note introduces the application of distributed unstructured mesh adaptation in fluid-related topology optimization. It incorporates three different remeshing techniques into the reaction-diffusion equation-based fluid topology optimization method. The note also conducts a comparative study of two different flow modeling strategies and presents numerical examples to validate the computational efficiency of the framework.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2022)
Article
Computer Science, Interdisciplinary Applications
Mohammad Zandsalimy, Carl Ollivier-Gooch
Summary: The stability of different computational fluid dynamics problems is evaluated, and a mesh modification-based stabilization approach is presented. The selection and perturbation of vertices are optimized to ensure the fastest optimization process. In addition, a new method is proposed to address opposing eigenmodes in larger problems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Bin Zhang, Chunlei Liang
Summary: In this work, two concepts of polynomial mortar and transfinite mortar are introduced and applied to curved nonconforming sliding meshes. It is found that transfinite mortar is superior to polynomial mortar on curved meshes in terms of geometric errors, accuracies, and numerical disturbances. The proposed sliding-mesh method utilizing transfinite mortar is the most accurate and thoroughly studied method, with applications to various flow problems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Nianhua Wang, Laiping Zhang, Xiaogang Deng
Summary: In numerical simulations, mesh quality plays a direct and significant role in determining simulation accuracy. This paper proposes a new smoothing method that combines the advantages of heuristic smoothing methods and optimization-based methods using deep reinforcement learning. The method is trained and validated on 2D triangular meshes and 3D surface meshes, demonstrating its efficiency and mesh quality.
COMPUTATIONAL MECHANICS
(2023)
Article
Engineering, Multidisciplinary
Teseo Schneider, Daniele Panozzo, Xianlian Zhou
Summary: The paper introduces a new posteriori method to generate high order curved meshes using a poly-spline isogeometric method, ensuring continuity and smoothness between elements. Fitting algorithms adjust control points for final mesh interpolation or approximation, outperforming an elastic analogy based approach in terms of computational performance and overall mesh quality. The method can be extended for higher order IGA basis construction and smooth refinement important for high order physics simulations.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Computer Science, Software Engineering
Jorge-Luis Barrera, Tzanio Kolev, Ketan Mittal, Vladimir Tomov
Summary: We propose a method for morphing high-order meshes to align with implicitly defined geometries. The method formulates the mesh optimization problem using a variational minimization approach and a penalty term. It utilizes a source mesh to represent the level set function accurately and incorporates adaptive strategies for setting the penalization weight and selecting the faces of the mesh to fit the target isocontour. The proposed method is demonstrated to be robust for generating boundary-and interface-fitted meshes for curvilinear domains.
COMPUTER-AIDED DESIGN
(2023)
Article
Mathematics, Applied
Mirco Ciallella, Elena Gaburro, Marco Lorini, Mario Ricchiuto
Summary: In this paper, a simple yet effective high order polynomial correction method is proposed to enhance the consistency of various boundary conditions for the Euler equations in 2D and 3D simulations. The method is a simplified reformulation of the Shifted Boundary Method (SBM) and utilizes a correction based on the extrapolated value of the in cell polynomial to the true geometry. It does not require the explicit evaluation of high order Taylor series and can be easily implemented into existing finite element and finite volume codes. Several validation tests demonstrate the convergence properties and effective extension to flows with shocks.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Computer Science, Interdisciplinary Applications
Patrick Knupp
Summary: This paper discusses methods for improving and optimizing mesh quality through node movement. The goal is to improve the worst quality in the mesh when it is unacceptable. Three fundamental methods for addressing worst case quality are presented, but each method has its limitations. By using a composition of functions and a two-stage optimization procedure, it is possible to simultaneously increase the minimum value and decrease the maximum value of the optimization metric, resulting in effective improvement of mesh quality.
ENGINEERING WITH COMPUTERS
(2022)
Article
Computer Science, Interdisciplinary Applications
Patrick Knupp
Summary: This paper introduces a general method for target construction in the target matrix optimization paradigm (TMOP). The method is based on independent geometric parameters and establishes correspondences between primary and secondary data, as well as a numerical testing process. The systematic approach to target construction is illustrated with examples, demonstrating its applicability to various mesh optimization problems.
ENGINEERING WITH COMPUTERS
(2022)
Article
Computer Science, Software Engineering
Nathan Scheirer, Stephen D. Holland, Adarsh Krishnamurthy
Summary: This study introduces a new two-step process for defining optimal composite fiber paths for use in automated fiber placement machines and finite element analysis models. By predicting minimum strain energy paths via fast approximate geodesic paths, the process is shown to be fast, accurate, and suitable for commercial applications. It effectively finds optimal fiber paths on complex, non-developable surfaces, improving finite element analysis models and enabling the creation of components with complex geometry.
COMPUTER-AIDED DESIGN
(2021)
Article
Computer Science, Software Engineering
Eloi Ruiz-Girones, Abel Gargallo-Peiro, Josep Sarrate, Xevi Roca
COMPUTER-AIDED DESIGN
(2019)
Article
Mechanics
A. Costa-Sole, E. Ruiz-Girones, J. Sarrate
INTERNATIONAL JOURNAL OF COMPUTATIONAL FLUID DYNAMICS
(2019)
Article
Meteorology & Atmospheric Sciences
C. Pavan, P. Fontanes, M. Urbani, N. C. Nguyen, M. Martinez-Sanchez, J. Peraire, J. Montanya, C. Guerra-Garcia
JOURNAL OF GEOPHYSICAL RESEARCH-ATMOSPHERES
(2020)
Editorial Material
Computer Science, Software Engineering
Xevi Roca, Adrien Loseille, Scott Mitchell
COMPUTER-AIDED DESIGN
(2020)
Article
Engineering, Multidisciplinary
Manuel A. Sanchez, Bernardo Cockburn, Ngoc-Cuong Nguyen, Jaime Peraire
Summary: This paper presents a class of high-order finite element methods that conserve linear and angular momenta as well as energy for equations of linear elastodynamics by exploiting and preserving the Hamiltonian structure. Experimental results confirm optimal convergence and conservation properties of these methods.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Engineering, Multidisciplinary
N. Pares, N. C. Nguyen, P. Diez, J. Peraire
Summary: The study introduces a general framework to compute upper and lower bounds for linear-functional outputs of the exact solutions of the Poisson equation based on reconstructions of the field variable and flux for both the primal and adjoint problems. The method is developed from a generalization of the complementary energy principle and duality theory, reducing the computation of bounds to finding independent potential and equilibrated flux reconstructions.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Computer Science, Interdisciplinary Applications
Eloi Ruiz-Girones, Josep Sarrate, Xevi Roca
Summary: A new disparity functional is proposed to measure and improve the geometric accuracy of a curved high-order mesh. Minimizing the disparity can assess and enhance the geometric accuracy of a given mesh.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Engineering, Multidisciplinary
Manuel A. Sanchez, Shukai Du, Bernardo Cockburn, Ngoc-Cuong Nguyen, Jaime Peraire
Summary: In this paper, several high-order accurate finite element methods for the Maxwell's equations are presented, which provide time-invariant, non-drifting approximations to the total electric and magnetic charges, and to the total energy. These methods are devised by taking advantage of the Hamiltonian structures of the Maxwell's equations and using spatial and temporal discretization techniques to ensure the conservation properties and convergence of the methods.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Computer Science, Software Engineering
Abel Gargallo-Peiro, Matias Avila, Arnau Folch
Summary: This paper presents a new topography-adapted mesh generation framework for simulating Atmospheric Boundary Layer (ABL) flows on complex terrains. The framework is fully automatic and includes smooth topography modeling, adaptive meshing procedure, and ABL mesher. The convergence of the meshing approach and the efficiency of the solver are analyzed, showing significant improvement compared to standard methods. The generated meshes and simulation results for a complex topographic scenario are also presented.
COMPUTER-AIDED DESIGN
(2022)
Article
Computer Science, Software Engineering
Albert Jimenez-Ramos, Abel Gargallo-Peiro, Xevi Roca
Summary: This paper presents a nodal interpolation method for approximating a subdivision model, which is capable of modeling and representing curved geometry without gaps. It maintains sharp features and smooths indicated ones, and can handle unstructured configurations of simulation points, curves, and surfaces.
COMPUTER-AIDED DESIGN
(2022)
Article
Computer Science, Software Engineering
Eloi Ruiz-Girones, Xevi Roca
Summary: In this paper, a distributed parallel mesh curving method for virtual geometry is presented. The method is mainly used to generate large-scale curved meshes suitable for analysis with unstructured high-order methods on complex geometry. The technique focuses on generating geometrically accurate meshes composed of high-quality elements. To reduce memory footprint, waiting time, and energy consumption, the method combines a matrix-free GMRES solver, an adaptive penalty technique, and an indicator of the required linear solver tolerance. The method is able to curve large meshes on thousands of cores, featuring highly stretched elements while matching a virtual topology.
COMPUTER-AIDED DESIGN
(2022)
Article
Computer Science, Software Engineering
Guillem Belda-Ferrin, Eloi Ruiz-Girones, Abel Gargallo-Peiro, Xevi Roca
Summary: This study presents an n-dimensional marked bisection method for unstructured conformal meshes, which is suitable for local refinement in adaptive n-dimensional applications. The method utilizes mesh marking pre-processing and three marked bisection stages to achieve mesh refinement. The results demonstrate the effectiveness of the proposed bisection method for local refinement of unstructured conformal meshes.
COMPUTER-AIDED DESIGN
(2023)
Article
Computer Science, Software Engineering
Guillermo Aparicio-Estrems, Abel Gargallo-Peiro, Xevi Roca
Summary: In this paper, we provide detailed instructions on how to use Newton's method for distortion-based curved r-adaption with a discrete high-order metric field. We combine a distortion term that measures the deviation from the target metric and a penalty term that measures the deviation from the target boundary. To achieve this, we introduce a log-Euclidean high-order metric interpolation on a curved mesh and an implicit representation for the domain boundaries. These techniques allow us to minimize the objective function and simultaneously match the curved features of the target metric and boundary, which is a novel capability in curved r-adaption.
COMPUTER-AIDED DESIGN
(2023)
Article
Energy & Fuels
Abel Gargallo-Peiro, Gonzalo Revilla, Matias Avila, Guillaume Houzeaux
Summary: A novel approach for wind farm simulation is presented, featuring realignment and mesh adaptation. The method utilizes actuator discs to model turbines and combines a level-set-based simulation framework with an adaptation cycle. The results demonstrate the accuracy and efficiency of the proposed approach in simulating complex wind farm configurations.