Article
Multidisciplinary Sciences
M. T. Gallagher, D. J. Smith
Summary: The use of Richardson extrapolation with coarse values of the regularization parameter proves to be an effective method in reducing computational costs without sacrificing accuracy in the regularized stokeslets method for microscale biological fluid dynamics. Numerical experiments show significant improvement in accuracy and efficiency in solving resistance and mobility problems in Stokes flow.
ROYAL SOCIETY OPEN SCIENCE
(2021)
Article
Thermodynamics
Sandipan Kumar Das
Summary: This study proposes a new method within the BIM framework to handle symmetry, zero normal-velocity gradient and specified pressure boundary conditions. The method is successfully applied to simple Stokes flow problems and shows good agreement with analytical solutions and literature data.
INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW
(2023)
Article
Mechanics
Henrique Nunes Lengler
Summary: This study investigates the applicability of the Method of Regularized Stokeslets (MRS) in simulating micro-swimmers at low Reynolds number, showing excellent agreement with the lattice Boltzmann method and analytical solution. MRS is well suited for this type of simulation, offering advantages such as ease of implementation and representation of complex geometries, making it a suitable candidate for more complex simulations.
Article
Mathematics, Applied
Nicholas J. Moore, Jake Cherry, Shang-Huan Chiu, Bryan D. Quaife
Summary: Using a Cauchy integral formulation, we simulated the erosion of a porous medium consisting of solid bodies in a two-dimensional Stokes flow. Microscopic changes in grain morphology resulted in larger-scale features and anisotropy in the medium. Our results suggest that erosion from groundwater flows may contribute to anisotropy in natural porous media.
PHYSICA D-NONLINEAR PHENOMENA
(2023)
Article
Physics, Fluids & Plasmas
Anirudh Jonnalagadda, Atul Sharma, Amit Agrawal
Summary: The regularized class of lattice Boltzmann methods improves stability and accuracy by filtering out spurious nonhydrodynamic moments, with a proposed alternative approach based on kinetic theory showing significant improvement in simulations compared to existing methods.
Article
Mathematics, Applied
Tsegaye G. Ayele, Mulugeta A. Dagnaw
Summary: This paper considers the boundary-domain integral equations for a compressible Stokes system in 2D with variable coefficients. An appropriate parametrix is used to simplify the problem, and conditions are set to ensure unique solvability. Properties of potential operators and equivalence to the mixed boundary value problem are investigated and proved in appropriate Sobolev spaces.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Applied
Tsegaye G. Ayele, Mulugeta A. Dagnaw
Summary: This paper considers the Dirichlet and Neumann boundary value problems for the steady-state Stokes system of partial differential equations for a compressible viscous fluid with variable viscosity coefficient in a two-dimensional bounded domain. It shows the equivalence of the BDIE systems to the Dirichlet and Neumann BVPs and the invertibility of the corresponding boundary-domain integral operators in appropriate Sobolev spaces. The special properties of BDIEs in the two-dimensional case, compared to the three dimension, are due to the logarithmic term in the parametrix for the associated partial differential equations.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Computer Science, Interdisciplinary Applications
Jun Wang, Ehssan Nazockdast, Alex Barnett
Summary: The study introduces a fast solver for simulating the rheological behavior of an infinite lattice containing rigid particles, achieving 10-digit accuracy through a combination of boundary integral equations, Nystrom method, and fast multipole method. Numerical simulations reveal equilibration at long times, formation of force chains, and two types of jamming phenomena.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Joar Bagge, Anna -Karin Tornberg
Summary: A fast and spectrally accurate Ewald summation method is proposed in this paper for the evaluation of stokeslet, stresslet and rotlet potentials of three-dimensional Stokes flow. The method is extended to periodic boundary conditions in any number of spatial directions, and it shows computational efficiency and accuracy in simulating three-dimensional Stokes flow with arbitrary periodicity.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Geochemistry & Geophysics
Yanqing Chu, Kuiwen Xu, Fazhong Shen, Gaofeng Wang
Summary: The MR-IUBM method proposes a solution for electromagnetic inverse scattering problems involving inhomogeneous and homogeneous background media using difference integral equations. By consistently updating the inhomogeneous background media from the unknown scatterers via Green's function with homogeneous medium, it aims to improve the ability to solve highly nonlinear problems. The method introduces MR into the cost function to greatly enhance stability and capability in handling highly nonlinear ISPs.
IEEE GEOSCIENCE AND REMOTE SENSING LETTERS
(2021)
Article
Computer Science, Interdisciplinary Applications
Svetlana Tlupova
Summary: A robust and highly accurate numerical solution framework is developed for the coupled Stokes-Darcy system in three dimensions. The method employs domain decomposition and iterative solving of separate Stokes and Darcy problems. Boundary integral equations are formulated and utilize smoothing of the kernels and direct quadrature for high accuracy on the boundary.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Alexander Z. Zinchenko, Robert H. Davis
Summary: A multipole-accelerated 3D boundary-integral algorithm is developed to model pressure-driven flow of highly-concentrated emulsions of deformable drops through periodic channels with tight constrictions. The algorithm shows significant improvement in computational efficiency and allows for simulations of long-time dynamics and drop rearrangements in extreme cases. The study also investigates the squeezing interactions of drops in the constriction, which can lead to extreme drop elongations but are not sufficient to promote breakup under the considered conditions.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Physics, Fluids & Plasmas
Nicholas G. G. Chisholm, Sarah D. D. Olson
Summary: Error in the method of regularized Stokeslets is highly dependent on the choice of the blob or regularization function. This study develops a general framework to choose regularizations using smoothing factors in the vector potential. Error analysis is performed for both far-field flow and the location of the forces, and the newly derived smoothing factors are related to commonly used blob functions and moment conditions. The framework is extended to non-radial regularizations for forces on surfaces, and its utility is demonstrated in solving the forward and inverse problems of a translating sphere using radial and surface-oriented regularizations.
Article
Mathematics, Applied
Thomas G. Anderson, Marc Bonnet, Shravan Veerapaneni
Summary: This study focuses on the mixing of passive tracers by an incompressible viscous fluid. A physically inspired surrogate norm, the negative index Sobolev norm, is used to quantify mixing in the complex fluid mixing domain. The computation of the norm requires the computation of an eigenbasis for L-2(Omega). Instead, a representative of the scalar concentration field in an appropriate Sobolev space is computed to obtain an equivalent definition of the norm. Fast and accurate potential theoretic methods are used to efficiently solve the elliptic problems related to the concentration field, and numerical results demonstrate the convergence of the approach.
NUMERICAL ALGORITHMS
(2023)
Article
Computer Science, Interdisciplinary Applications
William H. Mitchell, Henry G. Bell, Yoichiro Mori, Laurel Ohm, Daniel Spirn
Summary: Fluid flows containing dilute or dense suspensions of thin fibers are common in biological and industrial processes. To describe the motion of these fibers and the forces acting on them, one-dimensional fiber centerlines and force densities are used. Slender body theories provide a method to model and simulate the motion of immersed fibers using one-dimensional data. However, standard formulations may fail when the fiber surface approaches self-intersections or intersections with other fibers. This paper introduces a numerical method for a three-dimensional slender body boundary value problem, which can be stated in terms of a one-dimensional distribution of forces on the fiber centerline. The method is based on a new formulation of fluid velocity and demonstrates good conditioning and improved performance in the presence of near-intersections.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Biophysics
Julie Simons, Lisa Fauci, Ricardo Cortez
JOURNAL OF BIOMECHANICS
(2015)
Article
Computer Science, Interdisciplinary Applications
Jacek K. Wrobel, Ricardo Cortez, Douglas Varela, Lisa Fauci
JOURNAL OF COMPUTATIONAL PHYSICS
(2016)
Article
Mechanics
Jacek K. Wrobel, Sabrina Lynch, Aaron Barrett, Lisa Fauci, Ricardo Cortez
JOURNAL OF FLUID MECHANICS
(2016)
Article
Mechanics
Alexander P. Hoover, Ricardo Cortez, Eric D. Tytell, Lisa J. Fauci
JOURNAL OF FLUID MECHANICS
(2018)
Article
Computer Science, Interdisciplinary Applications
Ricardo Cortez
JOURNAL OF COMPUTATIONAL PHYSICS
(2018)
Article
Physics, Fluids & Plasmas
John LaGrone, Ricardo Cortez, Lisa Fauci
PHYSICAL REVIEW FLUIDS
(2019)
Article
Mechanics
John LaGrone, Ricardo Cortez, Wen Yan, Lisa Fauci
JOURNAL OF NON-NEWTONIAN FLUID MECHANICS
(2019)
Article
Physics, Multidisciplinary
Brato Chakrabarti, Yanan Liu, John LaGrone, Ricardo Cortez, Lisa Fauci, Olivia du Roure, David Saintillan, Anke Lindner
Correction
Physics, Multidisciplinary
Brato Chakrabarti, Yanan Liu, John LaGrone, Ricardo Cortez, Lisa Fauci, Olivia du Roure, David Saintillan, Anke Lindner
Article
Physics, Fluids & Plasmas
Ricardo Cortez, Marian Hernandez-Viera, Owen Richfield
Summary: The proposed computational model simulates viscous incompressible flows bounded by porous membranes using regularized Stokeslets and source doublets. The model allows calibration of parameters and is applicable in various scenarios, including volume loss in closed domains, flow in channels of fixed geometry, and biological flow in capillaries.
Article
Education & Educational Research
Cynthia Oropesa Anhalt, Ricardo Cortez, Amy Been Bennett
MATHEMATICAL THINKING AND LEARNING
(2018)
Article
Physics, Mathematical
Franz Hoffmann, Ricardo Cortez
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
(2017)
Article
Physics, Mathematical
Jingxuan Zhuo, Ricardo Cortez, Robert Dillon
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
(2017)
Article
Mechanics
E. Ahmadi, R. Cortez, H. Fujioka
JOURNAL OF FLUID MECHANICS
(2017)
Article
Education & Educational Research
Cynthia Oropesa Anhalt, Ricardo Cortez
JOURNAL OF MATHEMATICS TEACHER EDUCATION
(2016)
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)