Article
Computer Science, Interdisciplinary Applications
Chen Liu, Xiangxiong Zhang
Summary: In this paper, a scheme for solving compressible Navier-Stokes equations with desired properties is constructed. The scheme achieves high order spatial accuracy, conservation, and positivity-preserving of density and internal energy. Numerical tests show that higher order polynomial basis produces better numerical solutions.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Yimin Lin, Jesse Chan, Ignacio Tomas
Summary: In this work, high-order entropy-stable discontinuous Galerkin methods for the compressible Euler and Navier-Stokes equations are studied. A positivity limiting strategy is introduced to ensure the well-posedness of the methods, by blending high-order solutions with a low-order positivity-preserving discretization. The proposed strategy is shown to be accurate and robust through numerical experiments.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Vit Dolejsi, Magnus Svard
Summary: The aim of this study is to evaluate a recently proposed model for viscous and heat conducting compressible fluids and compare it with the Navier-Stokes model. By accurately simulating a suite of test cases and comparing various measures, it was found that both models exhibit remarkable similarity when alpha equals 1, with differences typically around 1%.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
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
Mathematics, Applied
Qiaolin He, Xiaoding Shi
Summary: This paper introduces a fully discrete method combining LDG finite element method and SAV approach for the compressible Navier-Stokes-Allen-Cahn system, allowing separate solution of velocity, density, and mass concentration of fluid mixture, and using SDC method to improve temporal accuracy. Numerical experiments demonstrate the high accuracy in both time and space, discretized energy stability, and efficiency of the proposed method.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2021)
Article
Computer Science, Interdisciplinary Applications
Chuan Fan, Xiangxiong Zhang, Jianxian Qiu
Summary: This paper introduces a positivity-preserving hybrid HWENO scheme for compressible Navier-Stokes equations, which is more efficient and robust than the conventional HWENO method, especially suitable for solving gas dynamics equations in low density and low pressure conditions.
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
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
Mathematics, Applied
Jian Cheng, Fan Zhang
Summary: We have developed a high-order path-conservative discontinuous Galerkin method for simulating compressible two-medium flows. The method satisfies the equilibrium condition and improves robustness for complex flows with large density and pressure ratios.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2022)
Article
Computer Science, Interdisciplinary Applications
Fernando Manrique de Lara, Esteban Ferrer
Summary: We propose using neural networks to accelerate a high order discontinuous Galerkin solver and enhance its accuracy by including a corrective forcing obtained from training a deep fully connected neural network. We have applied this methodology to the 1D Burgers' equation and the 3D Navier-Stokes equations, testing it with different Reynolds numbers. The results show that the corrective forcing is effective in improving the accuracy and speeding up the simulations.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Mustafa E. Danis, Jue Yan
Summary: This study proposes a new formula for the nonlinear viscous numerical flux and extends it to the compressible Navier-Stokes equations using the direct discontinuous Galerkin method with interface correction (DDGIC). The new method simplifies the implementation and enables accurate calculation of physical quantities.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics, Applied
Nail K. Yamaleev, Johnathon Upperman
Summary: This paper extends the high-order positivity-preserving, entropy stable spectral collocation schemes developed for the one-dimensional compressible Navier-Stokes equations to three spatial dimensions. The proposed schemes combine a positivity-violating entropy stable method with a novel first-order positivity-preserving entropy stable finite volume-type scheme. The schemes achieve positivity-preserving and excellent discontinuity-capturing properties by adding artificial dissipation in the form of low- and high-order Brenner-Navier-Stokes diffusion operators. The new schemes are also entropy conservative and freestream preserving.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Computer Science, Interdisciplinary Applications
Walter Boscheri, Giacomo Dimarco, Lorenzo Pareschi
Summary: We propose a novel Structure-Preserving Discontinuous Galerkin (SPDG) operator that recovers the algebraic property related to the div-curl problem at the discrete level. A staggered Cartesian grid is adopted in 3D, and a high order DG divergence operator is built upon integration by parts. The novel SPDG schemes are capable of obtaining a zero div-curl identity with high accuracy and can be applied to solving the incompressible Navier-Stokes equations.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Nail K. Yamaleev, Johnathon Upperman
Summary: This paper presents a new positivity-preserving, entropy stable spectral collocation scheme for the 1-D compressible Navier-Stokes equations. The method guarantees the pointwise positivity of thermodynamic variables and captures discontinuities effectively.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Giuseppe Orlando, Paolo Francesco Barbante, Luca Bonaventura
Summary: This paper proposes an efficient, accurate, and robust IMEX solver for the compressible Navier-Stokes equations, which describe non-ideal gases with a general cubic equation of state and Stiffened-Gas EOS. The method utilizes an h-adaptive Discontinuous Galerkin spatial discretization and an Additive Runge Kutta IMEX method for time discretization. It is specifically designed for low Mach number applications and allows for simulation at a reduced computational cost.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Sashank Srinivasan, Jonathan Poggie, Xiangxiong Zhang
JOURNAL OF COMPUTATIONAL PHYSICS
(2018)
Article
Mathematics, Applied
Jingwei Hu, Ruiwen Shu, Xiangxiong Zhang
SIAM JOURNAL ON NUMERICAL ANALYSIS
(2018)
Article
Mathematics, Applied
Hao Li, Xiangxiong Zhang
JOURNAL OF SCIENTIFIC COMPUTING
(2019)
Article
Mathematics, Applied
Hao Li, Xiangxiong Zhang
JOURNAL OF SCIENTIFIC COMPUTING
(2020)
Article
Mathematics, Applied
Hao Li, Xiangxiong Zhang
NUMERISCHE MATHEMATIK
(2020)
Article
Computer Science, Interdisciplinary Applications
Maojun Li, Yongping Cheng, Jie Shen, Xiangxiong Zhang
Summary: In this study, numerical schemes for the incompressible Navier-Stokes equations with variable density are investigated, focusing on preserving density bounds. It is found that a combination of continuous finite element method for momentum evolution and bound-preserving DG method for density evolution can achieve high accuracy and boundedness. Numerical tests demonstrate the effectiveness of the proposed scheme in various representative examples.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Chuan Fan, Xiangxiong Zhang, Jianxian Qiu
Summary: This paper introduces a positivity-preserving hybrid HWENO scheme for compressible Navier-Stokes equations, which is more efficient and robust than the conventional HWENO method, especially suitable for solving gas dynamics equations in low density and low pressure conditions.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Mathematics, Applied
Hao Li, Daniel Appelo, Xiangxiong Zhang
Summary: This article introduces a spectral element method based on the Qk continuous finite element method and Gauss-Lobatto quadrature, for solving wave equations. The method achieves (k + 2)-order accuracy in the discrete 2-norm for smooth solutions and can be extended to solve linear parabolic and Schroding equations.
SIAM JOURNAL ON NUMERICAL ANALYSIS
(2022)
Article
Mathematics, Applied
Jingwei Hu, Xiangxiong Zhang
Summary: In this work, semi-implicit or implicit finite difference schemes for the continuity equation with a gradient flow structure are introduced. The proposed schemes are first-order accurate in time and second-order and fourth-order accurate in space. These schemes preserve positivity and dissipate energy, making them suitable for long time simulation and accurate steady state solutions.
IMA JOURNAL OF NUMERICAL ANALYSIS
(2023)
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
Mathematics, Applied
Hao Li, Xiangxiong Zhang
Summary: In this paper, we solve the two-dimensional incompressible flow in the vorticity form using the fourth-order compact finite difference scheme and explicit strong stability preserving temporal discretizations. We demonstrate that the bound-preserving limiter proposed by Li et al. (2018) can enforce strict bounds on the vorticity, given that the velocity field satisfies a discrete divergence-free constraint. To reduce oscillations, we introduce a modified TVB limiter based on Cockburn and Shu (1994) that does not affect the bound-preserving property. This bound-preserving finite difference method can be applied to any passive convection equation with a divergence-free velocity field.
COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Computer Science, Interdisciplinary Applications
Chen Liu, Xiangxiong Zhang
Summary: In this paper, a scheme for solving compressible Navier-Stokes equations with desired properties is constructed. The scheme achieves high order spatial accuracy, conservation, and positivity-preserving of density and internal energy. Numerical tests show that higher order polynomial basis produces better numerical solutions.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics, Applied
J. I. E. Shen, Xiangxiong Zhang
Summary: This study investigates the solution of a generalized Allen-Cahn equation coupled with a passive convection problem for a given incompressible velocity field. A numerical scheme is proposed and it is proven that the discrete maximum principle holds. The same result applies to the construcion of a bound-preserving scheme for any passive convection with an incompressible velocity field.
COMMUNICATIONS IN MATHEMATICAL SCIENCES
(2022)
Article
Mathematics, Applied
Hao Li, Shusen Xie, Xiangxiong Zhang
SIAM JOURNAL ON NUMERICAL ANALYSIS
(2018)
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)
