Article
Mathematics, Applied
Elena Gaburro, Philipp oeffner, Mario Ricchiuto, Davide Torlo
Summary: In this paper, a fully discrete entropy preserving ADER-DG method is developed by introducing entropy correction terms and applying the relaxation approach to maintain entropy precision. The theoretical results are verified through numerical simulations.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Computer Science, Interdisciplinary Applications
Yoshiaki Abe, Ziyao Sun, Feng Xiao
Summary: A novel approach for selecting appropriate reconstructions is implemented to address the failure of high-order polynomial approximation in capturing strong discontinuities. The boundary variation diminishing reconstruction algorithm can achieve oscillation suppression and numerical dissipation in one-dimensional linear advection and nonlinear system equations.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2021)
Article
Computer Science, Interdisciplinary Applications
Gabor Toth
Summary: We propose a new principle for numerical schemes of conservation laws in one and multiple dimensions. The new formulation is based on the concept of Total of Time Variation (TOTV), which is defined as the volume integral of the magnitude of the time derivative. We show that TOTV is a conserved quantity for both one-dimensional and multi-dimensional scalar conservation laws. We introduce the Total of Time Variation Diminishing (TOTVD) method, which ensures that the discrete form of TOTV does not increase with time, making the scheme stable against catastrophic instabilities.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics, Applied
Ulrik Skre Fjordholm, Kjetil Olsen Lye
Summary: We prove the convergence rates of monotone schemes for conservation laws with initial data that have unbounded total variation but Holder continuous, given that the Holder exponent of the initial data is greater than 1/2. Additionally, for strictly Lip(+) stable monotone schemes, we demonstrate convergence for any positive Holder exponent. Numerical experiments are conducted to validate the theory.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Computer Science, Interdisciplinary Applications
Jiayin Li, Chi-Wang Shu, Jianxian Qiu
Summary: This paper presents a new type of high-order finite volume and finite difference multi-resolution Hermite weighted essentially non-oscillatory (HWENO) schemes for solving hyperbolic conservation laws. The schemes utilize information defined on central spatial stencils without introducing equivalent multi-resolution representation, demonstrating robustness and good performance in numerical experiments. The spatial reconstruction is derived from the original HWENO schemes, using large stencils similar to classical HWENO schemes but narrower than classical WENO schemes.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Mathematics, Applied
Biswarup Biswas, Harish Kumar, Deepak Bhoriya
Summary: This article presents entropy stable discontinuous Galerkin numerical schemes for special relativistic hydrodynamics equations with the ideal equation of state. Entropy stability is achieved by using two types of numerical fluxes and time discretization is performed using SSP Runge-Kutta methods. Several numerical test cases validate the accuracy and stability of the proposed schemes.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Computer Science, Interdisciplinary Applications
Wei Tong, Ruifang Yan, Guoxian Chen
Summary: This paper introduces sharp stability conditions for the single-stage MUSCL-Hancock root scheme: 1) the CFL number is (3-1)/2 which allows nearly 73 percent of the time step of the classical two-stage MUSCL scheme, resulting in a significant speed-up; 2) The preliminary TVD reconstruction is modified, when necessary, by a bound-preserving slope limiter to maintain higher resolution. The extension to the 2D nonlinear Euler system achieves a positivity-preserving scheme. Numerical examples confirm the sharpness of these settings and demonstrate the robustness of the scheme for different types of problems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Physics, Multidisciplinary
Prashant Kumar Pandey, Ritesh Kumar Dubey
Summary: In this paper, an efficient scaling method for WENO-JS weights is proposed, leading to robust and accuracy preserving high resolution WENO-JS schemes. The proposed scaling makes the schemes robust regardless of the choice for the parameter in classical WENO-JS weights to prevent division by zero. In smooth solution regions, the scaled WENO weights are kept close to critical weights, resulting in a scheme with formal accuracy. Numerical experiments demonstrate that the WENO schemes with scaled weights provide higher resolution for discontinuities and smooth solutions with high gradients.
Article
Computer Science, Interdisciplinary Applications
Zhenyu Cai, Decai Li, Yang Hu, Mingjun Li, Xiangshen Meng
Summary: A new high resolution central-upwind scheme for hyperbolic conservation laws is proposed in this paper, which incorporates a new upwind biased slope limiter for better accuracy and stability. The scheme maintains the efficiency and simplicity of central scheme, while also exhibiting total-variation diminishing (TVD) property and maximum principle. Numerical experiments demonstrate the desired resolution and robustness of the new scheme for various Riemann and Euler equation problems.
COMPUTERS & FLUIDS
(2021)
Article
Mathematics, Applied
S. Mousavi Yeganeh, J. Farzi
Summary: This paper utilizes MPP and PP parametrized flux limiters to achieve strict maximum principle and positivity-preserving property for solving hyperbolic conservation laws, demonstrating efficiency and effectiveness through high-order MPP RK-SV and PP RK-SV schemes. The proposed schemes maintain the maximum principle without additional time step restrictions and preserve the high-order accuracy for linear advection problems.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
A. J. Kriel
Summary: This study introduces a general condition for numerical schemes to mimic the properties of exact solutions of scalar conservation laws. By applying this condition to various schemes, different CFL-like conditions are derived to ensure the accuracy and reliability of the numerical simulations.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Wasilij Barsukow
Summary: The Active Flux scheme is a third order accurate finite volume scheme suitable for solving nonlinear hyperbolic systems and nonlinear scalar equations. It obtains approximate evolution operators by estimating wave speeds and demonstrates flexibility and effectiveness in evaluations.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Mathematics, Applied
Megala Anandan, S. V. Raghurama Rao
Summary: This paper investigates the entropy conserving scheme for vector kinetic model and its corresponding entropy stable scheme for macroscopic model, filling the gap in numerical methods. The schemes are validated through benchmark tests, demonstrating the conservation/stability of both the kinetic and macroscopic entropies.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Ke Xu, Zhenxun Gao, Zhansen Qian, Chongwen Jiang, Chun-Hian Lee
Summary: This paper focuses on the discontinuities capturing problems in nonconservative and nonconvex conservative hyperbolic systems. It analyzes the numerical dissipation at discontinuous points in the simulation process for the Godunov scheme of nonconservative hyperbolic systems. The paper proposes a novel numerical path preserving (NPP) method to modify the original Godunov schemes for accurately capturing the discontinuous structures.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics, Applied
Prashant Kumar Pandey, Farzad Ismail, Ritesh Kumar Dubey
Summary: This paper proposes a novel WENO scheme with a new smoothness indicator to improve the resolution of the solution while maintaining high-order accuracy and non-oscillatory property. Computational results demonstrate the effectiveness of this new scheme compared to other state-of-the-art WENO schemes.
COMPUTATIONAL & APPLIED MATHEMATICS
(2022)
Article
Engineering, Multidisciplinary
Ritesh Kumar Dubey, Vikas Gupta
INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS
(2020)
Article
Computer Science, Interdisciplinary Applications
Sabana Parvin, Ritesh Kumar Dubey
Summary: A new framework is proposed for constructing nonlinear weights to design third-order WENO schemes, ensuring third-order accurate nonoscillatory reconstructions. By analyzing various weight limiter functions, this method achieves third-order accuracy on smooth solutions and resolves discontinuities.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2021)
Article
Mathematics, Applied
Biswarup Biswas, Ritesh Kumar Dubey
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2020)
Article
Computer Science, Interdisciplinary Applications
Biswarup Biswas, Harish Kumar, Anshu Yadav
Summary: In this article, high order discontinuous Galerkin entropy stable schemes are proposed for ten-moment Gaussian closure equations, utilizing entropy conservative numerical flux and appropriate entropy stable numerical flux for stability. These schemes are extended to model plasma laser interaction source term and tested for stability, accuracy and robustness on several test cases using strong stability preserving methods.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Mathematics, Applied
Vikas Gupta, Sanjay K. Sahoo, Ritesh K. Dubey
Summary: A parameter-uniform fitted mesh finite difference scheme is proposed and analyzed for singularly perturbed interior turning point problems, showing second-order uniform convergence with respect to the singular perturbation parameter. The proposed method is validated through theoretical bounds and numerical experiments, demonstrating competitive results compared to existing methods in literature.
COMPUTATIONAL & APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Ritesh Kumar Dubey, Prabhat Mishra
Summary: This article presents an entirely new approach for constructing locally adaptive mesh to compute nonoscillatory solutions using representative second order schemes. The method uses modified equation analysis and a notion of data dependent stability of schemes to identify the solution regions for local mesh adaptation.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Applied
Biswarup Biswas, Harish Kumar, Deepak Bhoriya
Summary: This article presents entropy stable discontinuous Galerkin numerical schemes for special relativistic hydrodynamics equations with the ideal equation of state. Entropy stability is achieved by using two types of numerical fluxes and time discretization is performed using SSP Runge-Kutta methods. Several numerical test cases validate the accuracy and stability of the proposed schemes.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Physics, Multidisciplinary
C. R. Jisha, Ritesh Kumar Dubey, Dudley Benton, A. Rashid
Summary: This study constructs exact solutions for the KS equation using the generalized unified method, which have important applications in mathematical physics and applied science. The study also proposes using the bilinear form related to the Hirota method to discuss wave interactions and structures.
Article
Mathematics, Applied
Prashant Kumar Pandey, Farzad Ismail, Ritesh Kumar Dubey
Summary: This paper proposes a novel WENO scheme with a new smoothness indicator to improve the resolution of the solution while maintaining high-order accuracy and non-oscillatory property. Computational results demonstrate the effectiveness of this new scheme compared to other state-of-the-art WENO schemes.
COMPUTATIONAL & APPLIED MATHEMATICS
(2022)
Article
Engineering, Mechanical
C. R. Jisha, Ritesh Kumar Dubey
Summary: This article characterizes nonlinear wave propagation in an incompressible fluid by investigating an exact unique solution of the (4+1)-dimensional Boiti-Leon-Manna-Pempinelli (BLMP) equation. The study provides various wave structures and wave interaction phenomena, which are important for understanding physical phenomena in many areas of applied physics, especially nonlinear optics and acoustics waves.
NONLINEAR DYNAMICS
(2022)
Article
Computer Science, Interdisciplinary Applications
C. R. Jisha, T. K. Riyasudheen, Ritesh Kumar Dubey
Summary: This work presents a novel numerical viscosity for constructing fourth-order hybrid entropy stable schemes for convection-diffusion equations, and its effectiveness and stability are demonstrated through numerical experiments.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics, Applied
Prabhat Mishra, Vikas Gupta, Ritesh Kumar Dubey
Summary: A novel mesh adaptation technique is proposed in this work to approximate discontinuous or boundary layer solutions of partial differential equations. It introduces new estimators and monitor functions to detect solution regions containing discontinuity and layered regions, which are then utilized with the equi-distribution principle to adapt the mesh locally. The numerical tests demonstrate the robustness of this method and the non-oscillatory nature of the computed solutions.
NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION
(2022)
Article
Mathematics, Applied
Rathan Samala, Biswarup Biswas
Summary: This article presents novel smoothness indicators for calculating the nonlinear weights in order to improve the accuracy of viscosity numerical solutions of Hamilton-Jacobi equations. Extensive numerical tests are conducted to compare the proposed scheme with the classical WENO scheme, showing its performance capability and numerical accuracy.
COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Mathematics, Applied
Neelesh Kumar, Ritesh Kumar Dubey
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2020)
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)
