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Computer Science, Interdisciplinary Applications
R. Touma, M. A. Saleh
Summary: A new one-dimensional hybrid second-order accurate well-balanced unstaggered central scheme/particle method is proposed for computing pollutant transport in water flows. The scheme avoids solving Riemann problems at boundaries and achieves balance and non-dissipativity while being second-order accurate in space and time.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
Article
Computer Science, Interdisciplinary Applications
A. Mignone, L. Del Zanna
Summary: The research focuses on comparing and extending existing upwind constrained transport methods for maintaining robustness and accuracy in MHD simulations, while proposing a new flux formula applicable to the induction equation.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Pavan K. Inguva, Richard D. Braatz
Summary: Multidimensional population balance models (PBMs) are used to describe chemical and biological processes with distribution over multiple intrinsic properties. We propose a low-cost finite difference scheme based on operator splitting that achieves a discretization error of zero for certain classes of PBMs. The scheme exploits the commutative property of the differential operators and can be computationally efficient.
COMPUTERS & CHEMICAL ENGINEERING
(2023)
Article
Mathematics, Applied
Li Chai, Yang Liu, Hong Li
Summary: In this article, fourth-order compact difference schemes based on the linearized generalized BDF2-theta were developed to solve two-dimensional nonlinear fractional M/I transport equations. Theoretical results, including unconditional stability and error estimates, were derived, and extensive numerical examples were provided to demonstrate the effectiveness and accuracy of the schemes. A corrected compact difference scheme was also developed to achieve convergence results with nonsmooth solutions.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Physics, Mathematical
Dan Ling, Huazhong Tang
Summary: This paper develops a genuinely multidimensional HLL Riemann solver for the two-dimensional special relativistic hydrodynamic equations on Cartesian meshes and studies its physical-constraint-preserving property. Based on this solver, first- and high-order accurate physical-constraint-preserving finite volume schemes are proposed. Numerical results demonstrate the accuracy, performance and resolution of our physical-constraint-preserving finite volume schemes in shock wave and genuinely multi-dimensional wave structure simulations.
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics, Applied
Alexander Kurganov, Ruixiao Xin
Summary: In this paper, new second-order low-dissipation central-upwind (LDCU) schemes are developed for hyperbolic systems of conservation laws. The proposed schemes involve reconstruction, evolution, and projection, with a major novelty being in the projection step. The schemes are designed to approximate contact waves accurately and achieve higher resolution compared to existing schemes, as demonstrated by numerical examples.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Mathematics
Alexander Sukhinov, Valentina Sidoryakina
Summary: The paper considers the initial boundary value problem for the 3D convection-diffusion equation corresponding to the mathematical model of suspended matter transport in coastal marine systems. A two-dimensional-one-dimensional splitting scheme has been proposed for operational suspension spread prediction in coastal systems. The accuracy and efficiency of the approach have been investigated, demonstrating its suitability for solving grid convection-diffusion equations in a parallel manner.
Article
Computer Science, Interdisciplinary Applications
Amareshwara Sainadh Chamarthi, Sean Bokor, Steven H. Frankel
Summary: This paper discusses the significance of high-frequency damping in high-order conservative finite-difference schemes for viscous terms in the Navier-Stokes equations. Through investigating the nonlinear instability in a high-resolution viscous shock-tube simulation, it is found that modifying the viscous scheme can resolve spurious oscillations around shocks.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics
Luis Barreira, Claudia Valls
Summary: This paper presents a method to characterize the hyperbolicity of nonautonomous dynamics using a lifted autonomous delay-difference equation, which can be described in terms of the evolution map, the invertibility of a linear operator, and the perturbations of the equation.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Astronomy & Astrophysics
L. Adhikari, G. P. Zank, L-L Zhao, D. Telloni
Summary: In this study, we investigated the anisotropic magnetohydrodynamic (MHD) turbulence in the slow solar wind observed by Parker Solar Probe (PSP) and Solar Orbiter (SolO). We analyzed the variance anisotropy and correlation anisotropy using two different methods and compared the theoretical results with the observations, finding good agreement.
ASTROPHYSICAL JOURNAL
(2022)
Article
Computer Science, Interdisciplinary Applications
Junming Duan, Huazhong Tang
Summary: This paper develops high-order accurate entropy stable finite difference schemes for the shallow water magnetohydrodynamic equations, based on numerical approximation and construction of well-balanced semi-discrete entropy conservative schemes and the addition of dissipation term to suppress numerical oscillations. Extensive numerical tests validate the accuracy, well-balanced property, entropy stable property, positivity-preserving property, and ability to capture discontinuities of the proposed schemes.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Nadia Loy, Mattia Zanella
Summary: In this work, an extension of a structure-preserving numerical scheme for nonlinear Fokker-Planck-type equations to handle nonconstant full diffusion matrices in a two-dimensional setting is considered. The proposed schemes are shown to preserve fundamental structural properties such as non-negativity of the solution and entropy dissipation, with at least second order accuracy in transient regimes and potentially high order accuracy for large times under certain conditions. Suitable numerical tests are presented to confirm the theoretical results.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
Article
Physics, Mathematical
Farah Kanbar, Rony Touma, Christian Klingenberg
Summary: A well-balanced second order finite volume central scheme for the MHD equations with gravitational source term is developed in this paper. The scheme avoids solving Riemann problems at the cell interfaces by evolving the numerical solution on a single grid. By using a subtraction technique on the conservative variables with the support of a known steady state, the well-balanced property of the scheme is manifested. The robustness of the proposed scheme is verified on a list of numerical test cases from the literature.
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
(2022)
Article
Automation & Control Systems
Shaoying Wang, Zidong Wang, Hongli Dong, Bo Shen, Yun Chen
Summary: This paper addresses the problem of recursive quadratic filtering for a class of linear discrete-time systems subject to non-Gaussian noises. A binary encoding scheme is used for data transmission to enhance robustness against channel noises. The paper proposes a recursive quadratic filter to minimize the upper bound on the filtering error covariance for the underlying non-Gaussian systems. An augmented system is constructed and certain Riccati-like difference equations are solved to obtain the upper bound on the filtering error covariance, which is then minimized by selecting the filter parameter appropriately. Sufficient conditions are also established to ensure the boundedness of the filtering error covariance. A numerical example is provided to demonstrate the effectiveness of the proposed quadratic filtering algorithm.
Article
Computer Science, Interdisciplinary Applications
Chuan Fan, Xiangxiong Zhang, Jianxian Qiu
Summary: In this paper, a high order weighted essentially non-oscillatory (WENO) finite difference discretization method is constructed for solving the compressible Navier-Stokes (NS) equations. The method achieves positivity preservation of density and internal energy through a positivity-preserving flux splitting and a scaling positivity-preserving limiter. The core advantages of the proposed method are robustness and efficiency, making it particularly suitable for solving challenging problems involving low density and low pressure flow regime.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Theory & Methods
Ulrik S. Fjordholm, Roger Kaeppeli, Siddhartha Mishra, Eitan Tadmor
FOUNDATIONS OF COMPUTATIONAL MATHEMATICS
(2017)
Article
Computer Science, Interdisciplinary Applications
Alina Chertock, Shumo Cui, Alexander Kurganov, Seyma Nur Ozcan, Eitan Tadmor
JOURNAL OF COMPUTATIONAL PHYSICS
(2018)
Article
Mathematics, Applied
Siming He, Eitan Tadmor
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
(2019)
Article
Physics, Mathematical
Javier Morales, Jan Peszek, Eitan Tadmor
JOURNAL OF STATISTICAL PHYSICS
(2019)
Article
Mathematics, Applied
Ayoub Gouasmi, Karthik Duraisamy, Scott M. Murman, Eitan Tadmor
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
(2020)
Article
Mathematics, Applied
Ruiwen Shu, Eitan Tadmor
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
(2020)
Article
Mathematics, Applied
Benjamin Gess, Jonas Sauer, Eitan Tadmor
Article
Mathematics, Applied
Ruiwen Shu, Eitan Tadmor
Summary: This study investigates the large-time behavior of systems driven by radial potentials, showing that anticipation-driven systems tend to exhibit velocity alignment and spatial concentration. The research concludes that anticipation plays a crucial role in driving systems with attractive potentials into velocity alignment and spatial concentration.
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
(2021)
Article
Mathematics
Simon Foucart, Eitan Tadmor, Ming Zhong
Summary: This paper presents a detailed analysis of the unconstrained l(1)-weighted LASSO method for recovering sparse data. The analysis proves that if the data is k-sparse, the size of the support of the LASSO minimizer maintains a comparable sparsity. The paper also derives new l(2)/l(1) error bounds that highlight the dependence on k and the LASSO parameter lambda.
CONSTRUCTIVE APPROXIMATION
(2023)
Article
Mathematics, Applied
Jingcheng Lu, Eitan Tadmor
Summary: This study investigates the long-time hydrodynamic behavior of multi-species systems, specifically examining the effects of inter-species and intra-species interactions on the flocking behavior. The research shows that, under certain conditions, different species tend to flock towards the mean velocity.
QUARTERLY OF APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Douglas Hardin, Edward B. Saff, Ruiwen Shu, Eitan Tadmor
Summary: The study shows that regardless of their initial positions, N particles restricted to a curve will have their normalized Riesz s-energy close to the minimal possible energy for all N and large time t. Additionally, the distribution of such particles will be close to uniform with respect to arclength measure along the curve.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
(2021)
Article
Mathematics, Applied
Roman Shvydkoy, Eitan Tadmor
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
(2020)
Article
Mathematics
Omishwary Bhatoo, Arshad Ahmud Iqbal Peer, Eitan Tadmor, Desire Yannick Tangman, Aslam Aly El Faidal Saib
VIETNAM JOURNAL OF MATHEMATICS
(2019)
Article
Business, Finance
Omishwary Bhatoo, Arshad Ahmud Iqbal Peer, Eitan Tadmor, Desire Yannick Tangman, Aslam Aly El Faidal Saib
JOURNAL OF COMPUTATIONAL FINANCE
(2019)
Article
Mathematics
Siming He, Eitan Tadmor
COMPTES RENDUS MATHEMATIQUE
(2017)
