Article
Computer Science, Interdisciplinary Applications
Alexander Cicchino, David C. Del Rey Fernandez, Siva Nadarajah, Jesse Chan, Mark H. Carpenter
Summary: Provably stable flux reconstruction (FR) schemes for partial differential equations in curvilinear coordinates are derived. The analysis shows that the split form is essential for developing stable DG schemes and motivates the construction of metric dependent ESFR correction functions. The proposed FR schemes differ from previous schemes by incorporating the correction functions on the full split form of equations. Numerical verification demonstrates stability and optimal orders of convergence of the proposed FR schemes.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics, Applied
Jesse Chan, Mario J. Bencomo, David C. Del Rey Fernandez
Summary: The study extends entropy-stable Gauss collocation schemes to non-conforming meshes, introducing a friction-based treatment of non-conforming interfaces with a face-local correction term for high-order accuracy. Numerical experiments for the compressible Euler equations confirm the stability and accuracy of this approach in two and three dimensions.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Computer Science, Interdisciplinary Applications
Andres M. Rueda-Ramirez, Sebastian Hennemann, Florian J. Hindenlang, Andrew R. Winters, Gregor J. Gassner
Summary: This paper presents two robust entropy stable shock-capturing methods for discontinuous Galerkin spectral element discretizations of compressible magneto-hydrodynamics (MHD) equations. The methods are extended to systems with non-conservative terms, using a hybrid FV/DGSEM scheme for discretization and proving semi-discrete entropy stability on three-dimensional unstructured curvilinear meshes. The second method involves a subcell reconstruction procedure that enhances resolution and ensures entropy stability, with numerical verification on curvilinear meshes and benchmark cases showing robustness and accuracy.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Hendrik Ranocha
Summary: Nishikawa (2007) proposed a reformulation of the classical Poisson equation as a steady state problem for a linear hyperbolic system, which provides optimal error estimates for the solution of the elliptic equation and its gradient. However, it hinders the use of well-known solvers for elliptic problems. We establish connections to a discontinuous Galerkin (DG) method studied by Cockburn, Guzman, and Wang (2009) that is generally difficult to implement. Additionally, we demonstrate the efficient implementation of this method using summation by parts (SBP) operators, particularly in the context of SBP DG methods like the DG spectral element method (DGSEM). The resulting scheme combines desirable properties from both the hyperbolic and the elliptic perspective, offering a higher order of convergence for the gradients than what is typically expected from DG methods for elliptic problems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics, Applied
Mi-Young Kim
Summary: An arbitrary order discontinuous Galerkin method is proposed to approximate the solution to hyperbolic systems of multi-dimensional conservation laws in space and time. The weak formulation is derived through weak divergence definition and stability of the approximate solution is proven in broken L-2(L-2) and l∞(L-2) norms. Error estimates of O(h^r + k(n)^q) are derived in broken L-2(L-2) norm with specific element and time step conditions.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Astronomy & Astrophysics
Kuangxu Chen, Chunlei Liang
Summary: This paper presents a method that combines high-order spectral difference method with divergence cleaning for accurate simulations on curved unstructured grids. The method can achieve arbitrarily high accuracy in spatial discretization and is able to capture details of shock interfaces and small-scale vortex structures.
ASTROPHYSICAL JOURNAL
(2022)
Article
Mathematics, Applied
Yong Liu, Jianfang Lu, Chi-Wang Shu
Summary: In this paper, an essentially oscillation-free discontinuous Galerkin method is developed for systems of hyperbolic conservation laws. The method introduces numerical damping terms to control spurious oscillations. Both classical Runge-Kutta method and modified exponential Runge-Kutta method are used in time discretization. Extensive numerical experiments demonstrate the robustness and effectiveness of the algorithm.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2022)
Article
Engineering, Multidisciplinary
Andrea La Spina, Jacob Fish
Summary: The work proposes a hybridizable discontinuous Galerkin (HDG) method for weakly compressible magnetohydrodynamic (MHD) problems, demonstrating its superior properties and superconvergence characteristics. Different MHD formulations are discussed, and the convergence properties of the proposed methods under various conditions are extensively examined through numerical examples.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Computer Science, Interdisciplinary Applications
Krishna Dutt, Lilia Krivodonova
Summary: The proposed method introduces a moment limiter of arbitrary high order for unstructured triangular meshes, which hierarchically limits solution coefficients to maintain stability and convergence of the numerical solution.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Lingquan Li, Jialin Lou, Hiroaki Nishikawa, Hong Luo
Summary: In this study, a new hyperbolic Navier-Stokes system is proposed, introducing gradients as auxiliary variables and developing efficient reconstructed Galerkin methods. By recycling gradient variables, higher order polynomial solutions for primary variables can be obtained without increasing degrees of freedom. Numerical experiments demonstrate that the developed methods can achieve the designed accuracy and provide an attractive alternative for solving the compressible Navier-Stokes equations.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Mathematics, Applied
Valentin Carlier, Florent Renac
Summary: We investigate the stability properties of general fully discrete time explicit high-order spectral discontinuous schemes for the approximation of nonlinear hyperbolic systems of conservation laws. The scheme guarantees that the cell-averaged approximate solution is a convex combination of states that are contained in all the invariant domains of the conservation laws. The scheme also includes the use of local bounds and linear scaling limiters for stability enhancement.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2023)
Article
Physics, Mathematical
Paul J. Dellar
Summary: Magnetohydrodynamics involves coupling of the Navier-Stokes and Maxwell's equations to describe the flow of electrically conducting fluids in magnetic fields. The numerical algorithms used to solve these equations often result in a non-zero divergence of the magnetic field, which can lead to artifacts and the failure of structural properties of the equations. Hyperbolic divergence cleaning in magnetohydrodynamics allows for a non-zero divergence that is damped and propagated away from sources, without significantly increasing computational cost. By adjusting relaxation rates and using change of variables, hyperbolic divergence cleaning can be achieved in lattice Boltzmann algorithms for magnetohydrodynamics.
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
(2023)
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
Mathematics, Applied
Andrew Giuliani
Summary: We propose a state redistribution method for high order discontinuous Galerkin methods on curvilinear embedded boundary grids. The method relaxes the CFL condition and allows for larger time steps, while still maintaining stability. Numerical experiments show that our scheme can converge with high accuracy for problems with both smooth solutions and shocks.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
Erica R. Johnson, James A. Rossmanith, Christine Vaughan
Summary: The HyQMOM variant of QMOM is proven to have moment-invertibility over a convex region in solution space. A high-order discontinuous Galerkin (DG) scheme is developed to solve the resulting fluid system, with novel limiters introduced to guarantee the system's hyperbolicity. The scheme is also extended to include a BGK collision operator, which is shown to be asymptotic-preserving in the high-collision limit.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Astronomy & Astrophysics
Joachim Saur, Clarissa Willmes, Christian Fischer, Alexandre Wennmacher, Lorenz Roth, Allison Youngblood, Darrell F. Strobel, Ansgar Reiners
Summary: This study investigates the potential of brown dwarfs to produce UV auroral emissions outside the Solar System. Results indicate that, due to their strong magnetic fields and rapid rotation, brown dwarfs have the capability to generate high levels of UV auroral powers. While possible emissions were observed in the UV wavelength bands from 2MASS J1237+6526, it was difficult to conclusively attribute them to the brown dwarf due to low signal-to-noise ratios.
ASTRONOMY & ASTROPHYSICS
(2021)
Article
Astronomy & Astrophysics
Daniel Verscharen, Robert T. Wicks, Olga Alexandrova, Roberto Bruno, David Burgess, Christopher H. K. Chen, Raffaella D'Amicis, Johan De Keyser, Thierry Dudok de Wit, Luca Franci, Jiansen He, Pierre Henri, Satoshi Kasahara, Yuri Khotyaintsev, Kristopher G. Klein, Benoit Lavraud, Bennett A. Maruca, Milan Maksimovic, Ferdinand Plaschke, Stefaan Poedts, Christopher S. Reynolds, Owen Roberts, Fouad Sahraoui, Shinji Saito, Chadi S. Salem, Joachim Saur, Sergio Servidio, Julia E. Stawarz, Stepan Stverak, Daniel Told
Summary: The focus of space and astrophysical plasma research is shifting towards the smallest characteristic scales where electron dynamics determines plasma behavior, which is the core of electron-astrophysics research theme. The electron scales are crucial for plasma turbulence dissipation and spatial thermal energy transfer, yet these processes remain poorly understood. Addressing these fundamental electron processes and answering outstanding questions in space physics, astrophysics, and laboratory plasma physics are the goals of electron-astrophysics research.
EXPERIMENTAL ASTRONOMY
(2022)
Article
Astronomy & Astrophysics
F. Allegrini, W. S. Kurth, S. S. Elliott, J. Saur, G. Livadiotis, G. Nicolaou, F. Bagenal, S. Bolton, G. Clark, J. E. P. Connerney, R. W. Ebert, G. R. Gladstone, P. Louarn, B. H. Mauk, D. J. McComas, A. H. Sulaiman, J. R. Szalay, P. W. Valek, R. J. Wilson
Summary: This study investigates the electron partial densities and temperatures in Jupiter's main auroral emission region using data from the Jovian Auroral Distributions Experiment (JADE) on Juno. The results show that electron partial densities and temperatures exhibit consistent trends across different longitudes and hemispheres, with no significant correlation with radial distance.
JOURNAL OF GEOPHYSICAL RESEARCH-SPACE PHYSICS
(2021)
Article
Astronomy & Astrophysics
Ali H. Sulaiman, Nicholas Achilleos, Cesar Bertucci, Andrew Coates, Michele Dougherty, Lina Hadid, Mika Holmberg, Hsiang-Wen Hsu, Tomoki Kimura, William Kurth, Alice Le Gall, James McKevitt, Michiko Morooka, Go Murakami, Leonardo Regoli, Elias Roussos, Joachim Saur, Oleg Shebanits, Anezina Solomonidou, Jan-Erik Wahlund, J. Hunter Waite
Summary: The recent Cassini-Huygens mission has significantly enhanced our understanding of Saturn's moons Titan and Enceladus. Advocating for further exploration of these moons, the mission's success has highlighted the importance of including Titan and Enceladus science in ESA's long-term roadmap. By addressing important science questions and themes related to these moons, significant advancements can be made in our knowledge of the Solar System and the potential for habitable environments beyond Earth.
EXPERIMENTAL ASTRONOMY
(2022)
Article
Astronomy & Astrophysics
Gael Choblet, Gabriel Tobie, Arnaud Buch, Ondrej Cadek, Laura M. Barge, Marie Behounkova, Eloi Camprubi, Caroline Freissinet, Matt Hedman, Geraint Jones, Valery Lainey, Alice Le Gall, Alice Lucchetti, Shannon MacKenzie, Giuseppe Mitri, Marc Neveu, Francis Nimmo, Karen Olsson-Francis, Mark Panning, Frank Postberg, Joachim Saur, Juergen Schmidt, Yasuhito Sekine, Takazo Shibuya, Christophe Sotin, Ondrej Soucek, Cyril Szopa, Tomohiro Usui, Steven Vance, Tim Van Hoolst
Summary: Enceladus has the potential to support life, with direct sampling revealing the possibility of habitability. Future missions involving advanced instruments and sample return are needed to further investigate the potential emergence of life on this intriguing moon.
EXPERIMENTAL ASTRONOMY
(2022)
Article
Mathematics, Applied
Gregor J. Gassner, Magnus Svard, Florian J. Hindenlang
Summary: The focus of this research is to analyze the local energy stability of high-order summation-by-parts methods, including split-form methods, with two-point entropy-conserving fluxes. The main finding is that local energy stability is not guaranteed even when the scheme is non-linearly stable, which can have adverse implications for simulation results. It is demonstrated that two-point fluxes are inherently locally energy unstable, leading to exponential growth of errors in the simulation.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Astronomy & Astrophysics
Masatoshi Yamauchi, Johan De Keyser, George Parks, Shin-ichiro Oyama, Peter Wurz, Takumi Abe, Arnaud Beth, Ioannis A. Daglis, Iannis Dandouras, Malcolm Dunlop, Pierre Henri, Nickolay Ivchenko, Esa Kallio, Harald Kucharek, Yong C-M Liu, Ingrid Mann, Octav Marghitu, Georgios Nicolaou, Zhaojin Rong, Takeshi Sakanoi, Joachim Saur, Manabu Shimoyama, Satoshi Taguchi, Feng Tian, Takuo Tsuda, Bruce Tsurutani, Drew Turner, Thomas Ulich, Andrew Yau, Ichiro Yoshikawa
Summary: The White Paper highlights the importance of plasma-neutral gas interactions and emphasizes that addressing fundamental questions in this area is crucial for understanding atmospheric escape and the origin of biomolecules. It also suggests using a minimum core instrument package for investigations in various conditions, which should be included in all deep-space missions.
EXPERIMENTAL ASTRONOMY
(2022)
Article
Geochemistry & Geophysics
A. Marzok, S. Schlegel, J. Saur, L. Roth, D. Grodent, D. F. Strobel, K. D. Retherford
Summary: We analyzed Hubble Space Telescope observations of Ganymede and generated a brightness map of its oxygen emission. We found that the brightness of Ganymede's auroral ovals varies significantly with longitude and is asymmetric with respect to the 270 degrees meridian. The southern auroral oval is brighter than the northern oval.
JOURNAL OF GEOPHYSICAL RESEARCH-PLANETS
(2022)
Article
Astronomy & Astrophysics
Stephan Schlegel, Joachim Saur
Summary: This study investigates the substructure of the Io Footprint (IFP) and its tail in Jupiter's magnetosphere, and identifies the Hall effect as the key mechanism breaking the symmetry.
JOURNAL OF GEOPHYSICAL RESEARCH-SPACE PHYSICS
(2022)
Article
Astronomy & Astrophysics
A. Salveter, J. Saur, G. Clark, B. H. Mauk
Summary: The recent observations by the Juno spacecraft have revealed that the electrons contributing to Jupiter's main auroral emission exhibit both broadband and mono-energetic distributions. Statistical analysis of these electron distributions has shown that field-aligned accelerated electrons dominate at high magnetic latitudes, while pancake distributions are more prominent at lower latitudes. There is a correlation between electron distribution types and acceleration mechanisms, with stochastic acceleration being the primary driver of Jupiter's auroral processes.
JOURNAL OF GEOPHYSICAL RESEARCH-SPACE PHYSICS
(2022)
Article
Astronomy & Astrophysics
A. H. Sulaiman, B. H. Mauk, J. R. Szalay, F. Allegrini, G. Clark, G. R. Gladstone, S. Kotsiaros, W. S. Kurth, F. Bagenal, B. Bonfond, J. E. P. Connerney, R. W. Ebert, S. S. Elliott, D. J. Gershman, G. B. Hospodarsky, V Hue, R. L. Lysak, A. Masters, O. Santolik, J. Saur, S. J. Bolton
Summary: The Juno spacecraft's polar orbits have allowed scientists to directly sample Jupiter's low-altitude auroral field lines. By combining various data sets, researchers have identified unique features in Jupiter's main aurora and categorized them into distinct zones. They observed well-defined boundaries in Zone-I, which carries upward field-aligned currents, and sporadic signatures in Zone-II, which carries downward field-aligned currents. The researchers also discovered features such as solitary waves and significant electron density depletions in these zones.
JOURNAL OF GEOPHYSICAL RESEARCH-SPACE PHYSICS
(2022)
Article
Astronomy & Astrophysics
S. Cervantes, J. Saur
Summary: By combining observations from the Hubble Space Telescope and the Galileo spacecraft, we have constrained the density and location of oxygen and water in Europa's atmosphere. Our results provide additional evidence for the existence of a stable water atmosphere on Europa, but there is still uncertainty in the density measurements.
JOURNAL OF GEOPHYSICAL RESEARCH-SPACE PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Jan Michael Breuer, Samuel Leweke, Johannes Schmoelder, Gregor Gassner, Eric von Lieres
Summary: We have developed spatial arbitrary order DG methods for three commonly used liquid chromatography models, and implemented them in the open source software CADET, providing efficient implementations publicly for the first time. Validation and benchmarking against the original finite volume CADET code show great performance advantages for DG, depending on the problem size. For a four-component steric mass action GRM model, we achieve a speed-up of an order of magnitude within the typical range of engineering applications. We have also explored the performance of a collocation Legendre-Gauss-Lobatto quadrature DG method in comparison to an exact integration DG method, finding a slight advantage for the collocation DG method in performance benchmarks.
COMPUTERS & CHEMICAL ENGINEERING
(2023)
Article
Mathematics, Applied
Hendrik Ranocha, Gregor J. Gassner
Summary: The study investigates the local linear stability issues of entropy-conserving/dissipative high-order split-form discontinuous Galerkin methods for the compressible Euler equations and examines the impact of pressure equilibrium preservation on these issues.
COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Astronomy & Astrophysics
Joachim Saur
Summary: Moon-magnetosphere interaction refers to the interaction between a moon orbiting within a host planet's magnetosphere with the planet's magnetospheric plasma. This interaction helps in understanding the basic physics of plasma flows in the universe and provides geophysical information about the moons' interiors. The interaction is influenced by various factors both locally near the moon and further away in the magnetospheric plasma.
MAGNETOSPHERES IN THE SOLAR SYSTEM
(2021)
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)