Article
Computer Science, Interdisciplinary Applications
Yuichi Kuya, Soshi Kawai
Summary: This study examines the spectral characteristics of split convective forms for compressible flows in finite difference methods. Theoretical analysis reveals that the split forms do not reduce aliasing errors but rather increase them compared to the divergence form. Numerical tests confirm the findings of the theoretical analysis, indicating that the split forms do not reduce aliasing errors in finite difference methods.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Nao Shima, Yuichi Kuya, Yoshiharu Tamaki, Soshi Kawai
Summary: This paper discusses issues in split convective form discretization and proposes a discretization method for the internal energy convective term that strictly maintains pressure equilibrium, achieving physically-consistent, stable, and shock-free compressible flow simulations. The proposed method is shown to have superior numerical stability in tests while maintaining excellent kinetic energy and entropy preservation.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Yoshiharu Tamaki, Yuichi Kuya, Soshi Kawai
Summary: Theoretical analysis was conducted on entropy conservation properties to explain the behavior of non-dissipative finite-difference spatial discretization schemes. It was found that terms relating to velocity difference between grid points significantly contribute to entropy conservation error. The redefined KEEP schemes show improved entropy conservation properties through adjustable strictness.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics, Applied
Walter Boscheri, Maurizio Tavelli
Summary: In this article, a high order cell-centered numerical scheme is presented for the solution of the compressible Navier-Stokes equations. The scheme utilizes a semi-implicit time discretization to deal with multiscale phenomena and improve efficiency. High order accuracy is achieved through implicit finite difference and explicit CWENO reconstruction operators. The scheme is proven to be accurate and robust in the challenging stiff limit characterized by low Mach numbers.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Mathematics, Applied
Yue Li, Lin Fu, Nikolaus A. Adams
Summary: This paper proposes a new class of high-order fast multi-resolution essentially non-oscillatory (FMRENO) schemes that emphasize both performance and computational efficiency. A new candidate stencil arrangement is developed for multi-resolution representation, and a multi-resolution stencil selection strategy is proposed. The new FMRENO schemes feature low numerical dissipation and enhanced computational efficiency compared to standard schemes.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Computer Science, Interdisciplinary Applications
Zhiwei He, Yucang Ruan, Yaqun Yu, Baolin Tian, Feng Xiao
Summary: This paper proposes a novel framework of self-adjusting steepness-based schemes to overcome the problem of sharp resolution for various discontinuities in conventional schemes. By designing a slope limiter and using an adaptive algorithm, the proposed schemes achieve second-order accuracy in smooth regions while preserving discontinuous flow structures, especially contact discontinuities, even after long computation times.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Stephane Del Pino, Isabelle Marmajou
Summary: In this paper, an adaptive mesh refinement method for 2D multi-material compressible non-viscous flows in semi-Lagrangian coordinates is proposed. The method utilizes a local mesh adaptation procedure and a discrete metric field evaluation. The remapping method used is second-order accurate and its stability is proven. A multi-material treatment is proposed using a combination of local remeshing and interface reconstruction methods to minimize the creation of mixed cells and the diffusion of material interfaces. Numerical tests are provided to verify the validity and robustness of the method.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Gregory S. Shallcross, Jesse Capecelatro
Summary: The characteristic-based volume penalization combined with a high-order energy-stable finite difference framework is a computationally efficient method for compressible flows. It improves stability by avoiding increased stiffness associated with boundary treatment and does not require modifications to the computational stencil.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics, Applied
Naga Raju Gande, Ashlesha A. Bhise
Summary: The weighted essentially non-oscillatory scheme has been enhanced in this study by adding extra weight to less smooth substencils, improving the resolution of solutions at discontinuities or sharp gradients. The numerical solutions obtained by the proposed third-order scheme are comparable to those obtained using some native fifth-order WENO schemes.
NUMERICAL ALGORITHMS
(2021)
Article
Computer Science, Interdisciplinary Applications
Feng Zheng, Chi-Wang Shu, Jianxian Qiu
Summary: The proposed high order finite difference conservative scheme demonstrates advantages in conservation, high accuracy, and non-oscillatory solution for solving two medium flows. By utilizing nodal values and the WENO interpolation method, the algorithm shows efficient performance in maintaining equilibrium and capturing main features.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Xi Deng, Zhen-hua Jiang, Peter Vincent, Feng Xiao, Chao Yan
Summary: This study proposes a new dissipation-adjustable shock-capturing scheme for resolving multi-scale flow structures in high speed compressible flow. The scheme has the advantages of capturing large-scale discontinuous structures, adjustable numerical dissipation property, and suitability for solving small-scale structures.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Zhenming Wang, Jun Zhu, Chunwu Wang, Ning Zhao
Summary: In this paper, a hybrid finite difference fifth-order multi-resolution weighted compact nonlinear scheme (WCNS) is proposed for simulating inviscid and viscous compressible flows. The scheme combines the idea of the multi-resolution WENO scheme and implements higher-order approximate interpolation at midpoints. A hybridization strategy is also introduced to enhance the computational efficiency of the WCNS scheme. Several benchmark examples are used to validate the performance of the proposed scheme.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Lidong Cheng, Xi Deng, Bin Xie, Yi Jiang, Feng Xiao
Summary: This paper presents two novel hybrid schemes to resolve vortical and discontinuous solutions on unstructured grids with reduced numerical dissipation. The proposed schemes employ a polynomial and a sigmoid function as candidate reconstruction functions, showing superior performance in capturing discontinuous and vortical flow structures compared to existing schemes. The schemes are capable of capturing sharp discontinuous profiles without numerical oscillations and resolving vortical structures with significantly improved solution quality.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Mathematics, Applied
Shujiang Tang
Summary: This paper investigates the impact of the structure of local smoothness indicators on the computational performance of the WENO-Z scheme. A new class of two-parameter local smoothness indicators is proposed, which combines the classical WENO-JS and WENO-UD5 schemes and appends the coefficients of higher-order terms. A new WENO scheme, WENO-NSLI, is constructed using the global smoothness indicators of WENO-UD5. Numerical experiments show that the new scheme achieves optimal accuracy and has higher resolution compared to WENO-JS, WENO-Z, and WENO-UD5.
APPLIED NUMERICAL MATHEMATICS
(2024)
Article
Polymer Science
Li-Bo Chen, Yan-Hao Huang, Chuan-Yun Dai, Li-Qing Zhu, Xin Zhao, Kai Zhang, Xiao-Rong Fu, Wei Yang, Ming-Bo Yang
Summary: This study investigates the effect of different interpolation schemes on the melt penetration in multi-phase polymer melt processing. Five different schemes were compared, and it was found that the compressive interface capturing scheme for arbitrary meshes (CICSAM) is the most accurate method. The results provide insights into the variation patterns of interfacial morphologies during multi-phase polymer melt processing.
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)
