Article
Computer Science, Interdisciplinary Applications
Marin Lauber, Gabriel D. Weymouth, Georges Limbert
Summary: Immersed boundary methods are widely used for simulating interactions between dynamic solid objects and fluids due to their computational efficiency and modeling flexibility. However, thin geometries often violate the boundary conditions in existing immersed boundary projection algorithms. This study proposes a minimal thickness modification for the Boundary Data Immersion Method (BDIM-sigma) to address this issue and improve the accuracy of high-speed immersed surface simulations.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Jeff D. Eldredge
Summary: The study introduces a discrete Heaviside function to mask fields on the grid and develop operators and identities for any surface geometry. The derived equations include familiar IBM forcing terms as well as additional terms to regularize field jumps onto the grid and specify constraints on field behavior on each side of the interface, referred to as immersed layers. The method is demonstrated on various incompressible flow problems, showcasing its effectiveness in simulation.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mechanics
Raghav Singhal, Jiten C. Kalita
Summary: In this study, a novel hybrid explicit jump immersed interface approach in conjunction with a higher-order compact scheme was proposed for simulating transient complex flows governed by the streamfunction-vorticity (psi-zeta) formulation of the Navier-Stokes (N-S) equations for incompressible viscous flows. The approach demonstrated superior performance by reducing errors and decaying faster compared to existing methods. It efficiently handled various fluid flow problems, including those involving multiple and moving bodies. The accuracy and robustness of the approach were exemplified by the close agreement between computed solutions and existing numerical and experimental results.
Article
Computer Science, Interdisciplinary Applications
Quanxiang Wang, Zhiyue Zhang, Liqun Wang
Summary: A new immersed finite volume element method is proposed in this paper to solve elliptic problems on Cartesian mesh with discontinuous diffusion coefficient and sharp-edged interfaces. Extensive numerical experiments show that the method achieves approximately second-order convergence for piecewise smooth solutions, and more than 1.65th order accuracy for solutions with singularity.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Engineering, Mechanical
Jonathan Boustani, Michael F. Barad, Cetin C. Kiris, Christoph Brehm
Summary: This study extends the capability of a computational fluid-structure interaction method to simulate supersonic spacecraft parachutes, utilizing an immersed boundary method and a nonlinear structural dynamics solver. The representation and motion tracking of thin shell structures in a static Eulerian background mesh are detailed, along with reliable near-wall finite difference operators and logical functions for thin geometries.
JOURNAL OF FLUIDS AND STRUCTURES
(2022)
Article
Mathematics, Applied
Quanxiang Wang, Jianqiang Xie, Zhiyue Zhang, Liqun Wang
Summary: This paper presents a new bilinear immersed finite volume element method based on rectangular mesh to solve elliptic interface problems with non-homogeneous jump conditions and sharp-edged interfaces. Numerical experiments show that the method achieves nearly second-order accuracy for the solution and first-order accuracy for the solution gradient in the L-infinity norm.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Computer Science, Interdisciplinary Applications
Damien P. Huet, Anthony Wachs
Summary: This paper presents an open-source adaptive front-tracking solver for biological capsules in viscous flows. The solver demonstrates accuracy and robustness in solving membrane elastic and bending forces, fluid flow, and communication between Lagrangian and Eulerian grids. It also showcases its capability to simulate inertial capsule-laden flows in complex geometries, making it suitable for bioengineering applications. The source code and test cases are freely available.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Masaya Funada, Taro Imamura
Summary: We propose a novel high-order immersed boundary method for simulating inviscid flows using the flux reconstruction method on hierarchical Cartesian grids. The method achieves the same accuracy near the wall as in the interior domain by utilizing a high-order distribution of physical quantities derived from the flux reconstruction method to interpolate flow variables. The curvature effect of the wall is also investigated in depth, and the accuracy is validated through 2D and 3D simulations of inviscid flows.
COMPUTERS & FLUIDS
(2023)
Article
Computer Science, Interdisciplinary Applications
Xinxin Wang, Ralf Deiterding, Jianhan Liang, Xiaodong Cai, Wandong Zhao
Summary: This study presents an improved ghost-cell immersed boundary method for geometrically complex boundaries in compressible flow simulations. The proposed hybrid GCM, combining the baseline GCM and improved GCM, shows higher accuracy and convergence compared to other GCMs in various test cases. A comprehensive comparison of accuracy and computation time measurements demonstrates the significant advantages of the hybrid GCM in compressible flow simulations.
COMPUTERS & FLUIDS
(2022)
Article
Computer Science, Interdisciplinary Applications
Slimane Adjerid, Tao Lin, Haroun Meghaichi
Summary: We propose an immersed discontinuous Galerkin method for simulating interface problems in acoustic-elastic media. The method utilizes an interface independent mesh, allowing the cutting of elements by the material interface resulting in elements consisting of both acoustic and elastic medium. The proposed method utilizes piecewise polynomials according to interface jump conditions to treat different wave propagation models in each interface element. Computational examples and results are presented to demonstrate the stability, efficacy, and accuracy of the method.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Jaeyong Jeong, Sanghyun Ha, Donghyun You
Summary: A new numerical method is proposed for solving three-dimensional wave equations in media with arbitrarily-shaped interfaces on a Cartesian grid. The method aims to achieve two objectives: handling wave interaction at interfaces with high ratios of acoustic material properties, and treating complex geometries involving smooth and non-smooth interfaces. This method extends the solution smoothly across the interface in the normal direction and approximates the interface geometry using an unstructured surface mesh.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Bryce K. Campbell
Summary: This work presents a newly developed high-order Cartesian-grid method for reconstructing material interfaces from volume fraction fields. The method utilizes finite differences to calculate gradients and estimate surface normals to accurately reconstruct the interfaces. By fitting cumulative integrals with b-splines, high-order convergence rates of the interface shapes can be achieved, allowing for efficient and accurate representation of the geometry of the interfaces.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Emilia Bazhlekova, Ivan Bazhlekov
Summary: The study focuses on a class of linear viscoelastic models of Zener type, which are generalizations of the fractional Zener model, using the Bernstein functions technique. It has been proven that the corresponding relaxation moduli are completely monotone functions under suitable thermodynamic restrictions on the parameters. Based on this property, the propagation function of the Zener-type wave equation is investigated, and the subordination principle is established, providing an integral representation of the solution using the propagation function and the solution of a related classical wave equation. Numerical examples validate the analytical findings.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Applied
Quanxiang Wang, Liqun Wang, Jianqiang Xie
Summary: In this paper, an immersed finite volume element method is proposed for solving semi-linear elliptic interface problems with non-homogeneous jump conditions. Two-grid techniques are used to improve computational efficiency. Numerical results show that the proposed method can efficiently solve the semi-linear elliptic interface problems and obtain approximate second-order accuracy for the solution in the L' norm.
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS
(2022)
Article
Mathematics, Applied
Yanping Chen, Huaming Yi, Yang Wang, Yunqing Huang
Summary: In this paper, we propose and analyze the two-grid immersed finite element methods for semi-linear parabolic interface problems with discontinuous diffusion coefficients. The methods use immersed finite element methods for spatial discretization and allow meshes that are not aligned with the interface. Optimal error estimates are derived for both spatially semi-discrete schemes and fully discrete schemes. The two-grid algorithms based on the Newton methods are used to handle the nonlinear term. Theoretical and numerical results demonstrate that the two-grid immersed finite element methods can achieve optimal convergence order when the coarse mesh satisfies certain conditions.
APPLIED NUMERICAL MATHEMATICS
(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)