Article
Mathematics, Applied
Corrado Lattanzio, Delyan Zhelyazov
Summary: This paper investigates the spectral stability of traveling wave solutions to 1D quantum hydrodynamics system with nonlinear viscosity in the (rho,u) variables. A sufficient condition for the stability of the essential spectrum is derived, and the maximum modulus of eigenvalues with non-negative real part is estimated. Numerical computations of the Evans function are also presented to provide numerical evidence of point spectrum stability in a sufficiently large domain of the unstable half-plane.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2021)
Article
Mathematics
Raffaele Folino, Ramon G. Plaza, Delyan Zhelyazov
Summary: This paper studies the stability of weak dispersive shock profiles for a quantum hydrodynamics system in one space dimension with nonlinear viscosity and dispersive (quantum) effects due to a Bohm potential. It is shown that, if the shock amplitude is sufficiently small, then the profiles are spectrally stable. This analytical result is consistent with numerical estimations of the location of the spectrum [43]. The proof is based on energy estimates at the spectral level, on the choice of an appropriate weighted energy function for the perturbations involving both the dispersive potential and the nonlinear viscosity, and on the montonicity of the dispersive profiles in the small-amplitude regime.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
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
Engineering, Multidisciplinary
Zhe Ji, Lin Fu, Xiangyu Hu, Nikolaus Adams
Summary: In this paper, a feature-aware SPH method is proposed for concurrent and automated isotropic unstructured mesh generation. Compared to the original SPH-based mesh generator, this method addresses issues of incomplete kernel support at boundaries and feature size adaptation, achieving high-quality meshes with a faster convergence speed.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Computer Science, Interdisciplinary Applications
E. M. J. Komen, J. A. Hopman, E. M. A. Frederix, F. X. Trias, R. W. C. P. Verstappen
Summary: A new conservative symmetry-preserving second-order time-accurate PISO-based method for solving the incompressible Navier-Stokes equations on unstructured collocated grids is presented and compared with an explicit method. The new method shows advantages in energy conservation and numerical stability, making it potentially valuable for high-fidelity simulations in complex geometries. Implemented in the widely used OpenFOAM, these methods are expected to benefit the CFD community by paving the way for truly energy-conservative high-fidelity simulations.
COMPUTERS & FLUIDS
(2021)
Article
Mathematics, Applied
Sathyanarayanan Chandramouli, Nicholas Ossi, Ziad H. Musslimani, Konstantinos G. Makris
Summary: This paper explores dispersive hydrodynamics associated with the non-Hermitian non-linear Schrödinger equation and obtains a set of dispersive hydrodynamic equations with additional source terms that alter the density and momentum equations. The study focuses on a class of Wadati-type complex potentials and identifies non-Hermitian potentials that lead to modulationally stable constant intensity states. An initial value problem related to a Riemann problem is constructed and studied, which allows the interpretation of the underlying non-Hermitian Riemann problem in terms of an 'optical flow' over an obstacle. The resulting long-time dynamics exhibit a dependence on the location of the step relative to the potential, leading to the formation of diverse nonlinear wave patterns.
Article
Mathematics, Applied
Bingzhen Zhou, Bo Wang, Li-Lian Wang, Ziqing Xie
Summary: In this paper, a hybridizable discontinuous triangular spectral element method (HDTSEM) using tensorial nodal basis functions on unstructured meshes is proposed and analyzed. The method allows for mismatch in nodal points across elements, reduces global degrees of freedom, and maintains the high accuracy and mesh adaptivity of a typical spectral element method.
NUMERICAL ALGORITHMS
(2022)
Article
Materials Science, Multidisciplinary
Salam Md Abdus, Akbar M. Ali, Ali M. Zulfikar
Summary: This study investigates the effects of higher-order nonlinear and dispersive terms on the basic features of dust-ion-acoustic solitary waves in a magnetized dusty plasma, and examines how external magnetic field, adiabaticity and obliquity influence the wave structures.
RESULTS IN PHYSICS
(2022)
Article
Engineering, Mechanical
Hai-Ping Zhu, Hai-Yan Chen
Summary: A generalized nonlinear Schrodinger equation is presented to describe pulse propagation in negative index materials, with higher-order dispersive and nonlinear effects included. Solutions in the form of Jacobian elliptic functions and corresponding soliton solutions are found using the mapping method. The study also explores parameter modulation of higher-order dispersive effects and nonlinearities for periodic waves and solitons.
NONLINEAR DYNAMICS
(2021)
Article
Mathematics, Interdisciplinary Applications
A. Gansen, M. El Hachemi, S. Belouettar, O. Hassan, K. Morgan
Summary: The standard Yee FDTD algorithm is extended to 3D unstructured co-volume meshes using Delaunay primal mesh and high quality Voronoi dual to avoid accuracy losses. This approach has been successfully applied to modeling problems involving various material types and extended to challenging chiral material modeling.
COMPUTATIONAL MECHANICS
(2021)
Article
Engineering, Multidisciplinary
Ola El-shamy, Reda El-barkoki, Hamdy M. Ahmed, W. Abbas, Islam Samir
Summary: In this article, the improved modified extended tanh function method is proposed and applied to derive fresh travelling wave alternative solutions in different forms of nonlinear Schro-dinger equation with higher-order dispersive and nonlinear effects. The solutions include solitons (bright, dark and singular), exponential, singular periodic and Jacobi elliptic solutions. Graphical representations of selected solutions are provided to demonstrate their physical properties.
ALEXANDRIA ENGINEERING JOURNAL
(2023)
Article
Engineering, Ocean
Fazlolah Mohaghegh, Jayathi Murthy, Mohammad-Reza Alam
Summary: The authors have successfully overcome the challenges in predicting ocean waves by utilizing advanced machine learning techniques and a new concept of convolution. Their methodology can predict ocean surface gravity waves more than two orders of magnitude faster than traditional numerical methods, with high accuracy.
APPLIED OCEAN RESEARCH
(2021)
Article
Mathematics, Applied
Corrado Lattanzio, Delyan Zhelyazov
Summary: This paper investigates the existence of traveling waves in a 1-D compressible Euler system with dispersion and nonlinear viscosity, showing the importance of dispersion in certain regimes. The interplay of dispersion and viscosity plays a crucial role in proving the existence of oscillatory profiles. Numerical experiments analyze the sensitivity of these profiles with respect to viscosity/dispersion terms and nearness to vacuum.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mechanics
Wooyoung Choi
Summary: This paper investigates high-order strongly nonlinear long wave models and finds that the system for the bottom velocity is stable to all disturbances at any order of approximation. However, systems for other velocities can be unstable or even ill-posed. A new third-order solitary wave solution of the Euler equations is obtained using the high-order strongly nonlinear system and is expanded in an amplitude parameter. The paper shows the importance of using a more accurate spatial discretization scheme for numerical computations and successfully solves the strongly nonlinear systems for the propagation of solitary waves and their collision.
JOURNAL OF FLUID MECHANICS
(2022)
Article
Astronomy & Astrophysics
Miha Cernetic, Volker Springel, Thomas Guillet, Ruediger Pakmor
Summary: This article investigates the application of numerical methods in astrophysical studies, focusing on the Discontinuous Galerkin (DG) methods for high-order convergence and computational efficiency. The authors address the challenge of treating physical discontinuities, such as shocks, by introducing an artificial viscosity field and incorporating physical viscosity and thermal conductivity. They demonstrate the effectiveness and scalability of their approach through experiments and simulations.
MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY
(2023)
Article
Acoustics
Finnur Pind, Cheol-Ho Jeong, Jan S. Hesthaven, Allan P. Engsig-Karup, Jakob Stromann-Andersen
Summary: The paper presents a phenomenological method for modeling angle dependent surface impedance properties in time-domain wave-based simulations, which improves accuracy with little computational cost.
Article
Energy & Fuels
Morten Bech Kramer, Jacob Andersen, Sarah Thomas, Flemming Buus Bendixen, Harry Bingham, Robert Read, Nikolaj Holk, Edward Ransley, Scott Brown, Yi-Hsiang Yu, Thanh Toan Tran, Josh Davidson, Csaba Horvath, Carl-Erik Janson, Kim Nielsen, Claes Eskilsson
Summary: Highly accurate and precise heave decay tests were conducted on a 300 mm diameter sphere in a meticulously designed test setup at Aalborg University, Denmark, aiming to provide a rigorous benchmark dataset for numerical model validation. The results showed a high correlation between physical and numerical test results, making the physical test results very suitable for numerical model validation.
Article
Engineering, Ocean
Jacob B. H. Hicks, Harry B. Bingham, Robert W. Read, Allan P. Engsig-Karup
Summary: This paper investigates the optimization of second-order control signals for producing stable non-linear deep-water waves using a wedge-shaped wave generator. Both numerical and experimental methods are utilized, with the results demonstrating the applicability of the optimization procedure and the suitability of the heaving wedge for generating stable nonlinear deep-water waves.
APPLIED OCEAN RESEARCH
(2021)
Article
Engineering, Civil
V Sriram, Shagun Agarwal, Shiqiang Yan, Zhihua Xie, Shaswat Saincher, Torsten Schlurmann, Qingwei Ma, Thorsten Stoesser, Yuan Zhuang, Bo Han, Weiwen Zhao, Xiaotong Yang, Z. Li, Decheng Wan, Yi Zhang, Bin Teng, Dezhi Ning, Ningbo Zhang, Xing Zheng, Guochun Xu, Jiaye Gong, Yunbo Li, Kangping Liao, Wenyan Duan, Ronggui Hann, Windiman Asnim, Zana Sulaiman, Zhongbing Zhou, Jianmin Qin, Yucheng Li, Zhiwei Song, Xiaofan Lou, Lin Lu, Changfu Yuan, Yuxiang Ma, Congfang Ai, Guohai Dong, Hanbing Sun, Qiang Wang, Zhi-Tao Zhai, Yan-Lin Shao, Zaibin Lin, Ling Qian, Wei Bai, Zhihua Ma, Pablo Higuera, Eugeny Buldakov, Dimitris Stagonas, Santiago Martelo Lopez, Aristos Christou, Pengzhi Lin, Yanyan Li, Jinshu Lu, Sa Young Hong, Yoon-Jin Ha, Kyong-Hwan Kim, Seok-Kyu Cho, Dong-Min Park, Wojciech Laskowski, Claes Eskilsson, Mario Ricchiuto, Allan P. Engsig-Karup, Lin Cheng, Jinhai Zheng, Hanbin Gu, Guangnian Li
Summary: This paper presents a comparative study on the interaction between focused waves and a fixed cylinder, using 20 numerical solvers developed by various universities. The qualitative and quantitative comparisons based on wave probe and pressure probe time histories and spectral components show differences among different solvers. The relative error analysis indicates variations in performance among the solvers, providing insights for industrial applications.
INTERNATIONAL JOURNAL OF OFFSHORE AND POLAR ENGINEERING
(2021)
Article
Computer Science, Interdisciplinary Applications
Allan P. Engsig-Karup, Wojciech L. Laskowski
Summary: In this study, a fully nonlinear potential flow model discretized using a Galerkin spectral element method is developed for efficiently simulating unsteady water waves and their interaction with bodies in marine offshore engineering. An O(n)-scalable computational procedure based on geometric p-multigrid is proposed for solving the Laplace problem, showing improved efficiency in numerical simulations. Results demonstrate that using iterative geometric p-multigrid methods can significantly enhance the runtime efficiency of FNPF simulators.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2021)
Article
Acoustics
Hermes Sampedro Llopis, Allan P. Engsig-Karup, Cheol-Ho Jeong, Finnur Pind, Jan S. Hesthaven
Summary: This paper presents a computational efficient and accurate method for room acoustic simulations using a reduced basis method. By solving the problem in a low-dimensional subspace for parametrized boundary conditions, the computational burden is significantly reduced. The use of the Laplace domain ensures the stability of the model. Experimental results show that this method achieves significant speedups compared to traditional methods.
JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA
(2022)
Article
Engineering, Environmental
Rocco Palmitessa, Morten Grum, Allan Peter Engsig-Karup, Roland Lowe
Summary: This study proposes a physics-guided machine learning approach for fast and accurate surrogate modelling of urban drainage system hydraulics. It significantly reduces simulation times compared to traditional HiFi models while preserving a high level of model detail.
Article
Computer Science, Interdisciplinary Applications
Jens Visbech, Allan P. Engsig-Karup, Harry B. Bingham
Summary: This study presents a scalable two-dimensional Galerkin spectral element method for solving the radiation problem in linearized potential flow induced by waves on a floating offshore structure. The method shows excellent agreement with known benchmark results and demonstrates high accuracy and efficiency.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2023)
Article
Energy & Fuels
Claes Eskilsson, Johannes Palm
Summary: This study presents two recent developments in high-fidelity wave-body-mooring (WBM) modeling, including a new fluid-mooring coupling method and support for inter-moored multibody simulations. Experimental tests verify the accuracy of the fluid-mooring coupling, and the model performs well in predicting the actual response of a floating offshore wind turbine.
JOURNAL OF OCEAN ENGINEERING AND MARINE ENERGY
(2022)
Article
Engineering, Marine
Eirini Katsidoniotaki, Zahra Shahroozi, Claes Eskilsson, Johannes Palm, Jens Engstrom, Malin Goteman
Summary: The study develops a high-fidelity CFD model for wave energy converters and validates it using experimental data. The model is able to accurately simulate the system under extreme wave conditions. A new methodology for handling mesh deformation in CFD codes is also successfully applied and validated.
Article
Acoustics
Hermes Sampedro Llopis, Cheol-Ho Jeong, Allan P. Engsig-Karup
Summary: Quick simulations using the reduced basis method (RBM) are essential for finding optimal acoustic conditions in building design. RBM enables quick evaluations of changing absorption materials for different surfaces in room acoustic simulations with inhomogeneous properties. This study investigates the application of RBM in various geometries and inhomogeneous surface absorption with significant speedup compared to high fidelity numerical solver.
JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA
(2023)
Proceedings Paper
Automation & Control Systems
Morten Ryberg Wahlgreen, Kristian Meyer, Tobias K. S. Ritschel, Allan Peter Engsig-Karup, Krist Gernaey, John Bagterp Jorgensen
Summary: In this study, a numerical case study is presented to model and simulate the upstream and downstream processes of monoclonal antibody (mAb) production. A systematic and intuitive modeling methodology is applied to the existing upstream and downstream processes. The resulting models are based on differential mass balances and kinetic expressions for reactions and adsorption. The simulation model, coupling the upstream and downstream processes, serves as a benchmark for numerical estimation, control, and optimization studies.
Article
Mathematical & Computational Biology
Bjorn C. S. Jensen, Allan P. Engsig-Karup, Kim Knudsen
Summary: The use of epidemic modelling and predictions is crucial for understanding disease dynamics and making informed decisions. This study proposes the use of the generalized Polynomial Chaos framework for efficient uncertainty quantification in compartmental epidemic models. The results of two case studies based on Danish Covid-19 data demonstrate the applicability and efficiency of this technique for uncertainty quantification in epidemic modelling.
MATHEMATICAL MODELLING OF NATURAL PHENOMENA
(2022)
Article
Acoustics
Nikolas Borrel-Jensen, Allan P. Engsig-Karup, Cheol-Ho Jeong
Summary: This paper presents a one-dimensional physics-informed neural network (PINN) method, which learns a compact and efficient surrogate model for handling dynamic scenes with moving sources and impedance boundaries. The model shows low mean errors and proposes some ideas for implementing realistic three-dimensional scenes.
JASA EXPRESS LETTERS
(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)