Article
Engineering, Multidisciplinary
Sacha El Aouad, Aurelien Larcher, Elie Hachem
Summary: This paper proposes a novel anisotropic adaptive body-fitted mesh method for immersed solids, especially in Computational Fluid Dynamics. The method is characterized by its simplicity, generality, flexibility, and accuracy in handling complex geometries and boundary layers.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Computer Science, Software Engineering
Zhoufang Xiao, Carl Ollivier-Gooch, Jose D. Zuniga Vazquez
Summary: An enhanced mesh adaptation method is proposed to generate elements aligning with the metric, using proven local operators to modify the mesh and improve metric alignment and orthogonality. The method utilizes a metric field to define target element properties and transformations, selecting edges for splitting based on quality criteria to improve mesh alignment. The effectiveness of the method is demonstrated through numerical experiments on anisotropic meshes.
COMPUTER-AIDED DESIGN
(2022)
Article
Mathematics
Yongqiang Fan, Lihui Guo, Yanbo Hu, Shouke You
Summary: In this paper, the semi-hyperbolic patch characterized by 2D steady relativistic Euler equations is studied. The 2D steady relativistic Euler equations are transformed into a first-order hyperbolic equations using angle variables. A C1,16 -continuous sonic curve is found given a smooth streamline and the boundary data. Inside the semi-hyperbolic patch with the boundaries of the streamline associated with a characteristic curve, a C1,16 -continuous sonic-supersonic solution for 2D steady relativistic Euler equations is obtained utilizing the partial hodograph method. The corresponding regularity in the physical plane will be considered.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Computer Science, Interdisciplinary Applications
Keigan MacLean, Siva Nadarajah
Summary: This paper presents a framework for anisotropic unstructured all-quad mesh adaptation, targeting improvements in solution accuracy by modifying the discretization of the domain using a high-order Discontinuous Galerkin solver. This method extends the previous works to handle tensor product elements and incorporates both existing and experimental techniques for mesh generation.
JOURNAL OF COMPUTATIONAL PHYSICS
(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
Computer Science, Interdisciplinary Applications
R. Aubry, S. Dey, E. L. Mestreau, M. Williamschen, W. Szymczak
Summary: The new method presented in this article allows for independent modeling and evaluation of anisotropic sizing fields, ensuring the generation of correct and predictable meshes, addressing some of the issues with legacy approaches.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Computer Science, Software Engineering
Adrien Loseille, Lucien Rochery
Summary: Mesh generation and adaptation using proprietary CAD software face multiple challenges such as tolerance issues, costly and error-prone projection, and undefined surface derivatives. High-order surface meshes, particularly P3 meshes, offer a faster and more robust alternative, allowing G1 continuity enforcement while improving geometric accuracy. This paper demonstrates the capability of P3 CAD surrogates to drive anisotropic surface adaptation, using a highly anisotropic metric field on the complex HL-CRM wing model with flaps.
COMPUTER-AIDED DESIGN
(2023)
Article
Mathematics, Applied
Junjiang Lai, Zhencheng Fan
Summary: This paper analyzes the stability properties of discrete time waveform relaxation (DWR) methods based on Euler schemes and applies them to two dissipative systems. Some sufficient conditions for stability are obtained, along with two examples of instability. Furthermore, the influence of splitting functions and numerical methods on the stability of DWR methods is investigated. The obtained results demonstrate that waveform relaxation methods based on an implicit Euler scheme have better stability than those based on an explicit Euler scheme, and that methods based on classical splittings have worse stability compared to the eigenvalue splitting presented in this paper. Numerical examples are also provided to confirm the theoretical results.
Article
Mathematics, Applied
Yongqiang Fan, Lihui Guo, Yanbo Hu, Shouke You
Summary: This paper studies the existence of the sonic-supersonic solution for the 2D steady isentropic relativistic Euler equations. The equations are transformed into a first-order hyperbolic equation through characteristic decomposition. By utilizing a transformation and the method of iteration, the existence of the classical solution is proved and the sonic-supersonic solution is verified. The regularity of the solution near the sonic curve is also discussed.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2022)
Article
Mathematics, Applied
Nicola Ferro, Simona Perotto, Andrea Cangiani
Summary: A new recovery-based anisotropic error estimator and a metric-based mesh adaptation algorithm are proposed for discontinuous Galerkin finite element approximations of advection-diffusion problems. Numerical verification on various test cases demonstrates the effectiveness of the algorithm in capturing the directionalities of the solution in both steady and unsteady settings.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Materials Science, Multidisciplinary
W. S. Amer
Summary: This article examines the rotatory motion of a symmetric gyrostat around a fixed point under the influence of both a magnetic field and a Newtonian force field, simplifying the controlling system and applying Poincare's method of a small parameter to obtain asymptotic solutions. Graphical representations of the solutions for different values of charge causing the magnetic field and gyrostatic projection are provided, along with phase plane diagrams to explain the stability of the motion considered. Applications in submarines, aircraft, and satellites are also emphasized.
RESULTS IN PHYSICS
(2021)
Article
Engineering, Aerospace
Carlos Lozano, Jorge Ponsin
Summary: Numerical solutions to the adjoint Euler equations diverge near walls with mesh refinement due to a singularity at the wall, which is also found along the incoming stagnation streamline. By comparing numerical and analytic solutions, the issue is explained and extended to the fully compressible case using an analytic solution with a similar structure.
Article
Mathematics, Applied
Hossain Chizari, Vishal Singh, Farzad Ismail
Summary: An alternative cell-vertex entropy-stable finite volume method for the system of Euler equations is presented, using signals from each triangular element to control entropy. The method includes first-order and second-order versions, where the results demonstrate its accuracy and robustness compared to the current method.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Computer Science, Interdisciplinary Applications
Guglielmo Vivarelli, Ning Qin, Shahrokh Shahpar, David Radford
Summary: This paper discusses the effectiveness of an anisotropic sensor based on functional volume-mesh sensitivity quantities in improving CFD simulations. By automatically modifying grids and relocating nodes to problematic regions, the reliability of the model is enhanced.
COMPUTERS & FLUIDS
(2021)
Article
Computer Science, Interdisciplinary Applications
Hongtao Yang, Boyang Yu, Yonghai Li, Guangwei Yuan
Summary: The paper applies monotonicity correction to second-order element finite volume methods, obtaining a second-order monotone finite volume scheme. By correcting the numerical fluxes with nonlinear monotone correction, a corrected second order element finite volume scheme with a monotone matrix stiffness is obtained, leading to high order unconditional positivity-preserving finite volume schemes. Experimental results show that the corrected schemes maintain the convergence order of the original schemes while ensuring monotonicity.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Software Engineering
Frederic Alauzet, Adrien Loseille
COMPUTER-AIDED DESIGN
(2016)
Article
Computer Science, Interdisciplinary Applications
Y. Bourgault, M. Picasso, F. Alauzet, A. Loseille
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2009)
Article
Computer Science, Interdisciplinary Applications
A. Loseille, A. Dervieux, F. Alauzet
JOURNAL OF COMPUTATIONAL PHYSICS
(2010)
Article
Mathematics, Applied
Adrien Loseille, Frederic Alauzet
SIAM JOURNAL ON NUMERICAL ANALYSIS
(2011)
Article
Mathematics, Applied
Adrien Loseille, Frederic Alauzet
SIAM JOURNAL ON NUMERICAL ANALYSIS
(2011)
Article
Computer Science, Software Engineering
A. Loseille, F. Alauzet, V. Menier
COMPUTER-AIDED DESIGN
(2017)
Proceedings Paper
Engineering, Multidisciplinary
Olivier Coulaud, Adrien Loseille
25TH INTERNATIONAL MESHING ROUNDTABLE
(2016)
Proceedings Paper
Engineering, Multidisciplinary
Gautier Brethes, Adrien Loseille, Frederic Alauzet, Alain Dervieux
PROCEEDINGS OF THE 1ST PAN-AMERICAN CONGRESS ON COMPUTATIONAL MECHANICS AND XI ARGENTINE CONGRESS ON COMPUTATIONAL MECHANICS
(2015)
Proceedings Paper
Engineering, Multidisciplinary
Adrien Loseille, Victorien Menier, Frederic Alauzet
24TH INTERNATIONAL MESHING ROUNDTABLE
(2015)
Proceedings Paper
Engineering, Multidisciplinary
E. Gauci, F. Alauzet, A. Loseille, A. Dervieux
COUPLED PROBLEMS IN SCIENCE AND ENGINEERING VI
(2015)
Proceedings Paper
Engineering, Multidisciplinary
Adrien Loseille
23RD INTERNATIONAL MESHING ROUNDTABLE (IMR23)
(2014)
Proceedings Paper
Computer Science, Interdisciplinary Applications
Frederic Alauzet, Adrien Loseille
PROCEEDINGS OF THE 18TH INTERNATIONAL MESHING ROUNDTABLE
(2009)
Article
Mechanics
Frederic Alauzet, Sophie Borel-Sandou, Laurent Daumas, Alain Dervieux, Quang Dinh, Steven Kleinveld, Adrien Loseille, Youssef Mesri, Gilbert Roge
EUROPEAN JOURNAL OF COMPUTATIONAL MECHANICS
(2008)
Article
Computer Science, Interdisciplinary Applications
Tian Liang, Lin Fu
Summary: In this work, a new shock-capturing framework is proposed based on a new candidate stencil arrangement and the combination of infinitely differentiable non-polynomial RBF-based reconstruction in smooth regions with jump-like non-polynomial interpolation for genuine discontinuities. The resulting scheme achieves high order accuracy and resolves genuine discontinuities with sub-cell resolution.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Lukas Lundgren, Murtazo Nazarov
Summary: In this paper, a high-order accurate finite element method for incompressible variable density flow is introduced. The method addresses the issues of saddle point system and stability problem through Schur complement preconditioning and artificial compressibility approaches, and it is validated to have high-order accuracy for smooth problems and accurately resolve discontinuities.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Gabriele Ciaramella, Laurence Halpern, Luca Mechelli
Summary: This paper presents a novel convergence analysis of the optimized Schwarz waveform relaxation method for solving optimal control problems governed by periodic parabolic PDEs. The analysis is based on a Fourier-type technique applied to a semidiscrete-in-time form of the optimality condition, which enables a precise characterization of the convergence factor at the semidiscrete level. The behavior of the optimal transmission condition parameter is also analyzed in detail as the time discretization approaches zero.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jonas A. Actor, Xiaozhe Hu, Andy Huang, Scott A. Roberts, Nathaniel Trask
Summary: This article introduces a scientific machine learning framework that uses a partition of unity architecture to model physics through control volume analysis. The framework can extract reduced models from full field data while preserving the physics. It is applicable to manifolds in arbitrary dimension and has been demonstrated effective in specific problems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Nozomi Magome, Naoki Morita, Shigeki Kaneko, Naoto Mitsume
Summary: This paper proposes a novel strategy called B-spline based SFEM to fundamentally solve the problems of the conventional SFEM. It uses different basis functions and cubic B-spline basis functions with C-2-continuity to improve the accuracy of numerical integration and avoid matrix singularity. Numerical results show that the proposed method is superior to conventional methods in terms of accuracy and convergence.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Timothy R. Law, Philip T. Barton
Summary: This paper presents a practical cell-centred volume-of-fluid method for simulating compressible solid-fluid problems within a pure Eulerian setting. The method incorporates a mixed-cell update to maintain sharp interfaces, and can be easily extended to include other coupled physics. Various challenging test problems are used to validate the method, and its robustness and application in a multi-physics context are demonstrated.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Xing Ji, Fengxiang Zhao, Wei Shyy, Kun Xu
Summary: This paper presents the development of a third-order compact gas-kinetic scheme for compressible Euler and Navier-Stokes solutions, constructed particularly for an unstructured tetrahedral mesh. The scheme demonstrates robustness in high-speed flow computation and exhibits excellent adaptability to meshes with complex geometrical configurations.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Alsadig Ali, Abdullah Al-Mamun, Felipe Pereira, Arunasalam Rahunanthan
Summary: This paper presents a novel Bayesian statistical framework for the characterization of natural subsurface formations, and introduces the concept of multiscale sampling to localize the search in the stochastic space. The results show that the proposed framework performs well in solving inverse problems related to porous media flows.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jacob Rains, Yi Wang, Alec House, Andrew L. Kaminsky, Nathan A. Tison, Vamshi M. Korivi
Summary: This paper presents a novel method called constrained optimized DMD with Control (cOptDMDc), which extends the optimized DMD method to systems with exogenous inputs and can enforce the stability of the resulting reduced order model (ROM). The proposed method optimally places eigenvalues within the stable region, thus mitigating spurious eigenvalue issues. Comparative studies show that cOptDMDc achieves high accuracy and robustness.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Andrea La Spina, Jacob Fish
Summary: This work introduces a hybridizable discontinuous Galerkin formulation for simulating ideal plasmas. The proposed method couples the fluid and electromagnetic subproblems monolithically based on source and employs a fully implicit time integration scheme. The approach also utilizes a projection-based divergence correction method to enforce the Gauss laws in challenging scenarios. Numerical examples demonstrate the high-order accuracy, efficiency, and robustness of the proposed formulation.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Junhong Yue, Peijun Li
Summary: This paper proposes two numerical methods (IP-FEM and BP-FEM) to study the flexural wave scattering problem of an arbitrary-shaped cavity on an infinite thin plate. These methods successfully decompose the fourth-order plate wave equation into the Helmholtz and modified Helmholtz equations with coupled conditions on the cavity boundary, providing an effective solution to this challenging problem.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
William Anderson, Mohammad Farazmand
Summary: We develop fast and scalable methods, called RONS, for computing reduced-order nonlinear solutions. These methods have been proven to be highly effective in tackling challenging problems, but become computationally prohibitive as the number of parameters grows. To address this issue, three separate methods are proposed and their efficacy is demonstrated through examples. The application of RONS to neural networks is also discussed.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Marco Caliari, Fabio Cassini
Summary: In this paper, a second order exponential scheme for stiff evolutionary advection-diffusion-reaction equations is proposed. The scheme is based on a directional splitting approach and uses computation of small sized exponential-like functions and tensor-matrix products for efficient implementation. Numerical examples demonstrate the advantage of the proposed approach over state-of-the-art techniques.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Sebastiano Boscarino, Seung Yeon Cho, Giovanni Russo
Summary: This work proposes a high order conservative semi-Lagrangian method for the inhomogeneous Boltzmann equation of rarefied gas dynamics. The method combines a semi-Lagrangian scheme for the convection term, a fast spectral method for computation of the collision operator, and a high order conservative reconstruction and a weighted optimization technique to preserve conservative quantities. Numerical tests demonstrate the accuracy and efficiency of the proposed method.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jialei Li, Xiaodong Liu, Qingxiang Shi
Summary: This study shows that the number, centers, scattering strengths, inner and outer diameters of spherical shell-structured sources can be uniquely determined from the far field patterns. A numerical scheme is proposed for reconstructing the spherical shell-structured sources, which includes a migration series method for locating the centers and an iterative method for computing the inner and outer diameters without computing derivatives.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)