Article
Computer Science, Interdisciplinary Applications
Michel Orsi, Laurent Lobry, Francois Peters
Summary: This paper presents a particle-scale simulation method for non-Brownian suspensions at low Reynolds numbers, suitable for nonlinear flows. The method, based on a Fictitious Domain Method supplemented by sub-grid corrections, successfully addresses the issue of linear flow in the underlying suspension and has been validated in various flow scenarios with different boundary conditions.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Biophysics
Chayut Teeraratkul, Zachariah Irwin, Shawn C. Shadden, Debanjan Mukherjee
Summary: Blood clots play a central role in major cardiovascular diseases, and evaluating the hemodynamics and flow-mediated transport processes near a clot is crucial. This study systematically characterizes unsteady hemodynamics and transport near an arterial thrombus, highlighting the combined influence of thrombus shape, microstructure, and extent of wall disease on flow features and transport processes.
BIOMECHANICS AND MODELING IN MECHANOBIOLOGY
(2021)
Article
Engineering, Chemical
Ramon Cabiscol, Tom Jansen, Michele Marigo, Christopher Ness
Summary: Fine grinding in wet stirred media mills is crucial for various industrial processes, with numerical simulation offering insights into the influences of grinding media, agitator speed, and slurry rheology on particle size reduction. A Discrete Element Method (DEM) simulation has been proposed to address the multiphase nature of wet milling and the computational cost associated with fluid-resolved models. The study reveals that energy dissipation in wet milling is mainly due to inter-particle forces acting tangentially, while highly energetic collisions are relatively insignificant.
Article
Engineering, Chemical
Sina Hassanzadeh Saraei, Bernhard Peters
Summary: Although CFD-DEM simulations can accurately predict long-range hydrodynamic interaction, they face challenges in capturing lubrication effects due to insufficient mesh resolution for close distance particle interactions. To address this, we used a variant of Immersed Boundary method in our CFD solver for fully resolved simulations. We also developed a second-order boundary layer reconstruction approach to improve accuracy. Additionally, we investigated the treatment of shared cells between particles and the impact of mesh resolution and time step size on force calculation accuracy, finding a specific ratio range for correct short-range hydrodynamic interaction capture.
Article
Computer Science, Interdisciplinary Applications
Tsorng-Whay Pan, Shang-Huan Chiu
Summary: In this article, a numerical method for simulating sedimentation of balls in a three-dimensional channel filled with an Oldroyd-B fluid is presented. The method combines a distributed Lagrange multiplier/fictitious domain method with a factorization approach. The validity of the method is confirmed by comparing the obtained results with those reported in literature. Additionally, the influence of fluid elasticity on the formation of ball chain in Oldroyd-B fluids is studied, showing the capability of the method.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics, Applied
Michel Duprez, Vanessa Lleras, Alexei Lozinski
Summary: In this study, a new finite element method (phi-FEM) is proposed for numerically solving elliptic partial differential equations with natural boundary conditions. The method uses simple computational grids and incorporates boundary data using a level-set function. Unlike existing methods, phi-FEM does not require nonstandard numerical integration on cut mesh elements or the actual boundary, while ensuring convergence and well-conditioned discrete problems.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Chemistry, Multidisciplinary
Zhaosheng Yu, Yutian Yang, Jianzhong Lin
Summary: This paper develops an efficient three-dimensional fictitious domain method for the direct numerical simulation of the motion of a non-colloidal spherical particle in a DLD device. The results indicate that the lubrication force saturation is important to the particle critical separation size.
APPLIED SCIENCES-BASEL
(2022)
Article
Mathematics, Applied
Yiqi Gu, Jie Shen
Summary: The method utilizes the fictitious domain concept and circular embedding to transform elliptic boundary value problems in domains of complex geometry into a sequence of one-dimensional problems efficiently solvable by a spectral Petrov-Galerkin formulation. It is demonstrated to be well-posed in at least the special case, with error estimates showing spectral convergence. Numerical results showcase the effectiveness of the approach for both smooth and singular solution problems.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2021)
Article
Materials Science, Multidisciplinary
Kui Liu, Ang Zhao, Zhendong Hu
Summary: The fat boundary method (FBM), a fictitious domain method proposed for Poisson problems with small perforations, can achieve higher accuracy around holes. Despite strict restrictions on the original FBM, this article attempts to break these limitations and apply the method to elasticity by introducing Neumann boundary conditions and proposing a dual fat boundary method. The conditional convergence of the algorithm is mathematically proven and compared with the Lagrange multiplier method to show that FBM is a weak imposition method.
MATHEMATICS AND MECHANICS OF SOLIDS
(2021)
Article
Mechanics
Yun Chen, Rui Luo, Li Wang, Sungyon Lee
Summary: The combination of shear-induced migration, advancing fluid-fluid interface, and Taylor dispersion results in the self-similar and gradual accumulation of particles. The self-similarity in the concentration profile of the accumulating particles is a striking feature observed in experiments, with theoretical explanations based on the suspension balance model and particle transport equation. The solutions to the particle transport equation show self-similarity with slight deviations and are in excellent agreement with experimental observations.
JOURNAL OF FLUID MECHANICS
(2021)
Article
Mechanics
Chenlin Zhu, Lijuan Qian, Zhaowu Lin, Zhaosheng Yu
Summary: This study investigates the turbulent channel flow of a binary mixture of finite-size neutrally buoyant ellipsoidal particles using a parallel direct-forcing fictitious domain method. The results reveal that the variation of particle volume concentration has an impact on the flow properties under different friction Reynolds numbers and particle aspect ratios.
Article
Engineering, Multidisciplinary
Hector Navarro-Garcia, Ruben Sevilla, Enrique Nadal, Juan Jose Rodenas
Summary: The Cartesian grid discontinuous Galerkin finite element method combines the accuracy and efficiency of high-order discontinuous Galerkin discretization with the simplicity of a Cartesian mesh. Special treatment is required for elements intersecting the physical domain boundary to minimize their impact on the algorithm's performance. By implementing a stabilization procedure, unstable degrees of freedom are eliminated and supporting regions of their shape functions are reassigned to neighboring elements, improving the method's stability and accuracy.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2021)
Article
Engineering, Multidisciplinary
Michael Poluektov, Lukasz Figiel
Summary: Cut finite-element methods (CutFEMs) are a class of methods that allow boundaries/interfaces to cut through elements, avoiding meshing/remeshing problems, especially for non-stationary interfaces. The method has been extended to complex physics of interfaces such as fracture and contact problems, showing promising computational results in practical applications.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Physics, Multidisciplinary
Chong Shi, Wenhao Zhang, Xiao Chen, Lerong Wang
Summary: The study establishes a pipe domain seepage analysis model for fractured rock mass by improving the seepage model. The model is verified and found to be reliable for investigating the deformation and failure of underground caverns. The results have important theoretical and practical implications.
FRONTIERS IN PHYSICS
(2022)
Article
Mathematics, Applied
Erik Burman, Cuiyu He, Mats G. Larson
Summary: In this work, we introduce, analyze, and implement a residual-based a posteriori error estimation method for the CutFEM fictitious domain method in solving an elliptic model problem. The method takes into account both the geometry approximation error on the smooth boundary and the numerical approximation error. Theoretical analysis proves that the error estimation is reliable and efficient. Furthermore, the method is robust as the reliability and efficiency constants are independent of the arbitrary boundary-mesh intersection.
IMA JOURNAL OF NUMERICAL ANALYSIS
(2022)
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)