Article
Computer Science, Interdisciplinary Applications
Wenbin Wu, Na Liu, Chao Huang, Pan Zhang, Moubin Liu
Summary: A new cell-centered Lagrangian discontinuous Galerkin (DG) scheme is proposed for simulating gas-water compressible flows. The scheme combines the Lagrangian DG scheme with an exact gas-water Riemann solver to address the stiff features of gas-water compressible flows. Positivity-preserving limiter and strong stability preserving temporal integral are also incorporated for numerical stability. Numerical examples demonstrate the accuracy, robustness, and positivity-preserving property of the proposed scheme, especially in challenging cases involving large density ratio and strong shock.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2023)
Article
Mathematics, Applied
Siavash Hedayati Nasab, Carlos A. Pereira, Brian C. Vermeire
Summary: This paper presents optimized Runge-Kutta stability polynomials for multidimensional discontinuous Galerkin methods using the flux reconstruction approach. The stability polynomials significantly increase time-step sizes for various elements, with up to a speedup factor of 1.97 compared to classical methods. The optimization also yields modest performance benefits for certain elements and maintains the designed accuracy levels.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Computer Science, Interdisciplinary Applications
Xiaofeng Cai, Sebastiano Boscarino, Jing-Mei Qiu
Summary: The paper introduces a semi-Lagrangian discontinuous Galerkin method coupled with Runge-Kutta exponential integrators for solving nonlinear Vlasov dynamics, achieving high spatial and temporal accuracy. Inherit advantages from the SLDG method, the proposed method performs well in resolving complex solution structures, conserves mass and positivity, and can evolve with adaptive time stepping.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Yun-Long Liu, Chi-Wang Shu, A-Man Zhang
Summary: A new interface treatment method is proposed for simulating compressible two-medium problems using the RKDG method. The method ensures a smooth transition of the interface while minimizing overshoots or undershoots with the adoption of entropy-fix technique. It demonstrates high accuracy and compactness in handling interfaces with large entropy ratios.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Mathematics, Applied
Lingling Zhou, Yinhua Xia
Summary: In this paper, an arbitrary Lagrangian-Eulerian local discontinuous Galerkin (ALE-LDG) method for one-dimensional linear convection-diffusion problems is presented and analyzed. The semi-discrete ALE-LDG method is shown to preserve L-2-stability and sub-optimal (k + 1/2) convergence rate, while the fully discrete ALE-LDG schemes are proved to be stable and have optimal convergence rate under a time step restriction. Numerical examples are provided to illustrate the theoretical results.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Physics, Applied
Abhilash Chand, S. Saha Ray
Summary: This paper uses the local discontinuous Galerkin method to analyze the numerical solutions of nonlinear Allen-Cahn equations with nonperiodic boundary conditions. The spatial variables are discretized to generate a semi-discrete method of lines scheme, and the resulting ordinary differential equation system in the temporal variable is solved using the higher-order total variation diminishing Runge-Kutta method. A comparison of the numerical results with exact results for different test problems confirms the effectiveness and accuracy of the proposed method.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2023)
Article
Mathematics, Applied
Xiuhui Guo, Lulu Tian, Yang Yang, Hui Guo
Summary: In this paper, the local discontinuous Galerkin (LDG) methods are applied to solve the pattern formation dynamical model in polymerizing actin flocks. Two main difficulties are addressed in designing effective numerical solvers: dealing with the non-negative density function and solving the model with stiff source. The proposed method combines the positivity-preserving LDG methods with the semi-implicit Runge-Kutta methods, demonstrating accurate numerical approximations with relatively large time steps.
JOURNAL OF COMPUTATIONAL MATHEMATICS
(2023)
Article
Engineering, Aerospace
Georg May, Koen Devesse, Ajay Rangarajan, Thierry Magin
Summary: This paper presents a high-order consistent compressible flow solver based on a hybridized discontinuous Galerkin discretization, suitable for applications ranging from subsonic to hypersonic flow. The discussion includes the challenges of high-order discretization and solutions, as well as the physical modeling requirements for high-Enthalpy flow.
Article
Computer Science, Interdisciplinary Applications
Nuo Lei, Juan Cheng, Chi -Wang Shu
Summary: In this paper, a high-order positivity-preserving polynomial projection remapping method is developed for the discontinuous Galerkin scheme based on the L2 projection. An indirect arbitrary Lagrangian-Eulerian discontinuous Galerkin method is presented by combining the Lagrangian type DG scheme and the rezoning strategies. The remapping method, which accurately clips the intersections between the old distorted mesh and the new rezoned mesh, is highly accurate and suitable for large deformable problems. A positivity-preserving limiter is added for the physical variables in computational fluid dynamics without compromising the original high-order accuracy and conservation. A multi-resolution weighted essentially non-oscillatory limiter is used to overcome numerical oscillations and maintain high-order accuracy in smooth regions.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics, Applied
R. Al Jahdali, L. Dalcin, R. Boukharfane, I. R. Nolasco, D. E. Keyes, M. Parsani
Summary: This study proposes new optimized explicit Runge-Kutta schemes for the integration of systems of ordinary differential equations arising from high-order entropy stable collocated discontinuous Galerkin methods. By optimizing the stability region of the time integration schemes, the efficiency and robustness of computational fluid dynamics simulations can be improved, leading to significant time and resource savings.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Computer Science, Interdisciplinary Applications
Pei Fu, Yinhua Xia
Summary: This paper presents an almost arbitrary Lagrangian-Eulerian discontinuous Galerkin (ALE-DG) method to solve the compressible Euler equations in one and two space dimensions, and considers their positivity preserving property of states density and pressure. The proposed ALE-DG method, coupled with a modified strong stability-preserving Runge-Kutta method and the positivity preserving limiter, ensures the geometric conservation law and the positivity property of the scheme.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics, Applied
Jiming Yang, Jing Zhou, Cunyun Nie
Summary: This paper discusses the application of discontinuous Galerkin approximations to the compressible miscible displacement problem. A two-grid algorithm is proposed, consisting of one coarse grid space and one fine grid space. Error estimates for concentration and velocity are presented, showing that the two-grid method achieves optimal approximations under certain conditions. Numerical results confirm the effectiveness of the algorithm.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Physics, Fluids & Plasmas
L. M. Yang, C. Shu, Z. Chen, Y. Y. Liu, J. Wu, X. Shen
Summary: A high-order gas kinetic flux solver (GKFS) is developed for 2D compressible flows, which evaluates numerical fluxes based on the local asymptotic solution to the Boltzmann equation. It achieves high-order accuracy through a simplified local asymptotic solution and outperforms the second-order counterpart in numerical examples, demonstrating its accuracy and capability.
Article
Computer Science, Interdisciplinary Applications
Jordi Vila-Perez, Matteo Giacomini, Ruben Sevilla, Antonio Huerta
Summary: This work introduces a face-centred finite volume (FCFV) method for simulating compressible flows. It provides first-order accurate approximations of conservative quantities without the need for gradient reconstruction, demonstrating strong adaptability in various flow scenarios.
COMPUTERS & FLUIDS
(2022)
Article
Mathematics, Applied
Caixia Nan, Huailing Song
Summary: This paper presents a numerical method for two-phase miscible flow in porous media, utilizing the local discontinuous Galerkin method and IMEX-RK method. The method achieves second-order time discretization and optimal convergence analysis for pressure and concentration in L2-norm, demonstrated through numerical examples.
APPLIED NUMERICAL MATHEMATICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Duan Maochang, Yu Xijun, Chen Dawei, Qing Fang, Zou Shijun
DISCRETE DYNAMICS IN NATURE AND SOCIETY
(2019)
Article
Computer Science, Interdisciplinary Applications
Shijun Zou, Xijun Yu, Zihuan Dai
JOURNAL OF COMPUTATIONAL PHYSICS
(2019)
Article
Computer Science, Interdisciplinary Applications
Xufeng Xiao, Zihuan Dai, Xinlong Feng
COMPUTER PHYSICS COMMUNICATIONS
(2020)
Article
Mathematics
Chaobao Huang, Na An, Xijun Yu, Huili Zhang
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS
(2020)
Article
Computer Science, Interdisciplinary Applications
Xiaolong Zhao, Xijun Yu, Maochang Duan, Fang Qing, Shijun Zou
JOURNAL OF COMPUTATIONAL PHYSICS
(2019)
Article
Mathematics, Applied
Maosheng Jiang, Jiansong Zhang, Jiang Zhu, Xijun Yu, Luiz Bevilacqua
APPLIED MATHEMATICS LETTERS
(2019)
Article
Engineering, Multidisciplinary
Maosheng Jiang, Jiansong Zhang, Jiang Zhu, Xijun Yu, Luiz Bevilacqua
Summary: The study introduces a mass-preserving numerical approximation method for simulating the dynamic process of active colloids, and conducts theoretical analysis and numerical experiments to validate its performance.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Mathematics, Applied
Na An, Xijun Yu, Chaobao Huang
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2017)
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)
