Article
Multidisciplinary Sciences
Azad Hussain, Muhammad Arsaln, Aysha Rehman, Fahad M. Alharbi, Nevzat Akkurt, Sayed M. Eldin, Saad Althobaiti
Summary: This study examines the unsteady compressible steam laminar flow in a squared cylinder using the CFD approach. The effects of time on velocity and pressure distributions are discussed, along with drag and lift coefficients and heat distributions. The study highlights the potential damage to materials caused by steam emission from furnaces, emphasizing the need for control of emission time and velocity.
SCIENTIFIC REPORTS
(2022)
Article
Computer Science, Interdisciplinary Applications
Hanahchim Choung, Vignesh Saravanan, Soogab Lee, Haeseong Cho
Summary: The study introduces a new ghost-cell approach, nonlinear-weighted IBM (NWIBM), which combines high-and low-order polynomials to enhance computational performance for addressing discontinuous and smoothly varying flow regions near the immersed boundary; The NWIBM showed more stable and accurate numerical solutions in compressible flow compared to conventional ghost cell approaches.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Mathematics, Applied
Gino I. Montecinos, Eleuterio F. Toro
Summary: High-order numerical methods for hyperbolic balance laws require non-linear spatial reconstruction. This paper proposes a new conservative ENO-type reconstruction method that overcomes the weaknesses of the classical ENO method and performs well in various test problems. The method achieves arbitrary order of accuracy in both space and time.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Meteorology & Atmospheric Sciences
Matthew R. Norman
Summary: A high-order-accurate WENO finite-volume scheme is detailed for compressible Euler equations, showing superior performance compared with second-order Strang dimensional splitting and achieving up to ninth-order accuracy.
QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY
(2021)
Article
Meteorology & Atmospheric Sciences
Matthew R. Norman, Christopher Eldred, Muralikrishnan Gopalakrishnan Meena
Summary: This study investigates inherent numerical dissipation in collocated Finite-Volume integration of the Euler equations, focusing on upwind fluxes and reconstruction strategies. The results show that using acoustic and advective upwinding methods can reduce data movement and computations, and automatically adapt to various factors such as grid spacing and flow smoothness. The study also suggests that using convex combinations of upwind and central solutions can reduce dissipation and extend the length scale range of the kinetic energy spectra.
JOURNAL OF ADVANCES IN MODELING EARTH SYSTEMS
(2023)
Article
Mathematics, Applied
I. S. Popov
Summary: This study used the space-time adaptive ADER finite element DG method with a posteriori correction technique of solutions on subcells by the finite-volume ADER-WENO limiter to simulate non-stationary compressible multicomponent reactive flows. The multicomponent composition and reactions in the reacting medium were described by expanding the original system of Euler equations into a system of non-stationary convection-reaction equations. The method is capable of simulating high stiff problems associated with reactions in a multicomponent medium by adaptively changing the time step. The results showed that it can simulate flows without the need for direction splitting and fractional step methods.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Computer Science, Interdisciplinary Applications
Zhilong Wei, Qin Jiang, Sihang Nie
Summary: This article presents a numerical scheme for two-phase flows, simplifying the previous unified governing equations for compressible-incompressible two-phase flows. The method is pressure-based and utilizes a fifth-order WENO scheme and the THINC scheme for capturing interface. The proposed scheme is validated for low Mach number compressible-incompressible two-phase flows, achieving first-order convergence and giving good results in simulations.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2021)
Article
Computer Science, Interdisciplinary Applications
Valerie Kulka, Patrick Jenny
Summary: An adaptive conservative time integration scheme (ACTI) is proposed for compressible flow simulations. By using decreasing time steps, conservation and periodic synchronization are guaranteed. Compared to previous methods, this new scheme has significant advantages in dealing with compressible flow, especially in the presence of shock waves. The accuracy and computational speedup of the scheme are demonstrated through 1D and 2D test cases.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Astronomy & Astrophysics
J. R. Canivete Cuissa, R. Teyssier
Summary: This study conducted three-dimensional numerical simulations of magneto-hydrodynamics in stellar interiors and demonstrated the feasibility of the simulation method. The results showed an exponential growth of magnetic energy and a decrease in power of acoustic and internal gravity waves. The study highlights the importance of including magnetic fields in the study of pressure waves.
ASTRONOMY & ASTROPHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Emmanuel Motheau, John Wakefield
Summary: The study investigates the impact of numerical schemes on data reconstruction in finite-volume methods and their interaction with quadrature rules for computing cell volume averages. Results show that the order of data reconstruction does not affect results in smooth solutions, but all methods collapse to first-order in shock-driven problems. High-order quadrature rules do not improve spectral accuracy in compressible turbulence decay, and the choice of numerical method for data reconstruction on cell faces is critical for capturing turbulent spectra accurately.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2021)
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
Thermodynamics
M. Priyadharsini, David Maxim A. Gururaj, Mohammed S. Ismail, Mikhail Sheremet
Summary: The research aims to investigate the dynamics of nanoparticle-mediated blood flow in the presence of bioconvection effects caused by microorganisms. The study focuses on the boundary layer problem of unsteady magnetohydrodynamic blood flow in the porous medium of tissues in stretching motion. The results show the effects of various physical parameters on the temperature and concentration distribution of blood, as well as the organism density profile in the boundary layer, with potential applications in targeted drug delivery, magnetic therapy, and therapeutic hyperthermia treatments.
INTERNATIONAL COMMUNICATIONS IN HEAT AND MASS TRANSFER
(2023)
Article
Mechanics
Bang Liang, Ming Li, Xiaoquan Yang, Xiaolong Tang, Jue Ding
Summary: A cell-centered spatiotemporal coupled method is proposed for solving the compressible Euler equations, featuring an improved weighted essentially non-oscillation scheme for spatial discretization and a two-stage fourth-order scheme for time advancement. The method achieves a large Courant-Friedrichs-Lewy (CFL) number and better captures small-scale flow structures compared to other studies using the two-stage fourth-order scheme. It can be generalized without using a case-dependent generalized Riemann problem solver.
Article
Mathematics
Iskandar Waini, Najiyah Safwa Khashi'ie, Abdul Rahman Mohd Kasim, Nurul Amira Zainal, Khairum Bin Hamzah, Norihan Md Arifin, Ioan Pop
Summary: This study discusses the impact of unsteady magnetohydrodynamics hybrid ferrofluid flow over a stretching/shrinking rotating disc. By transforming the mathematical model into ordinary differential equations and analyzing the solutions, it is found that both solutions are stable. The research also reveals that the unsteadiness parameter decreases the boundary layer thickness of velocity and temperature distribution, while the magnetic and mass flux parameters have a lowering effect on the skin friction coefficient and the unsteadiness parameter has a supportive effect on the heat transfer rate.
Article
Engineering, Mechanical
Yunqing Gu, Junjun Zhang, Songwei Yu, Chengqi Mou, Zhou Li, Chendong He, Denghao Wu, Jiegang Mou, Yun Ren
Summary: In this study, the grid irrelevance and discrete error in hydrofoil unsteady cavitation simulations were investigated using the GCI evaluation method to determine the optimal number of grids. Various turbulent viscosity correction approaches were employed to improve the turbulence model, and numerical simulations successfully captured the details of the hydrofoil cavity shape and shedding process, revealing the mechanism of hydrofoil cavitation.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2022)
Article
Mathematics, Applied
E. Guerrero Fernandez, M. J. Castro Diaz, M. Dumbser, T. Morales de Luna
Summary: In this paper, a novel numerical discretization method is proposed for simulating a variable pressure multilayer shallow water model. The method is capable of simulating density driven gravity currents in a shallow water framework and maintains high accuracy even in the presence of strong gradients or discontinuities.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
S. Busto, M. Dumbser
Summary: We present a novel staggered semi-implicit hybrid finite volume / finite element method for the numerical solution of the shallow water equations at all Froude numbers on unstructured meshes. The proposed algorithm is well-suited for low Froude number flows and can handle flows with shock waves, making it an all-Froude number solver.
APPLIED NUMERICAL MATHEMATICS
(2022)
Article
Physics, Mathematical
Walter Boscheri, Michael Dumbser, Elena Gaburro
Summary: In this paper, a new high order accurate nodal discontinuous Galerkin (DG) method is proposed for solving nonlinear hyperbolic systems of partial differential equations (PDE) on unstructured polygonal Voronoi meshes. The new approach represents the discrete solution using piecewise continuous polynomials of degree N within each Voronoi element, and uses a continuous finite element basis on a subgrid inside each polygon. The resulting subgrid basis allows for an efficient quadrature-free algorithm, and high accuracy in time is achieved using the ADER approach.
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics, Applied
Saray Busto, Michael Dumbser, Ilya Peshkov, Evgeniy Romenski
Summary: This paper presents a new family of finite volume schemes for solving overdetermined, hyperbolic, and thermodynamically compatible PDE systems. These schemes, known as HTC schemes, accurately conserve total energy and possess marginal stability and satisfy a discrete entropy inequality.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2022)
Article
Computer Science, Interdisciplinary Applications
Cristian Brutto, Michael Dumbser
Summary: A novel semi-implicit finite volume scheme is developed for simulating fluid-structure interaction problems involving free surface shallow water flow and floating rigid structures. The model is well-suited for geophysical flows and uses a nonlinear volume function to achieve coupling. Improved accuracy is achieved through subgrid volume computation and the application of the theta method for time accuracy.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2023)
Article
Mathematics, Applied
Saray Busto, Michael Dumbser
Summary: In this work, a new family of high order accurate semi-discrete discontinuous Galerkin finite element schemes is proposed for the thermodynamically compatible discretization of overdetermined first order hyperbolic systems. By mimicking and discretizing the entropy inequality, the new schemes achieve nonlinear stability in continuum mechanics.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
S. Busto, M. Dumbser, L. Rio-Martin
Summary: This paper presents a novel semi-implicit hybrid finite volume/finite element scheme for the numerical solution of the incompressible and weakly compressible Navier-Stokes equations on moving unstructured meshes. The scheme employs a suitable splitting of the equations, a staggered grid arrangement, and a space-time control volume approach. Numerical results demonstrate the high accuracy and computational efficiency of the proposed method.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Computer Science, Interdisciplinary Applications
Firas Dhaouadi, Michael Dumbser
Summary: In this paper, a novel first order hyperbolic reformulation is presented for the barotropic Navier-Stokes-Korteweg system, which allows the nonlinear dispersive systems to be rewritten in a first order hyperbolic form. The curl involutions introduced by the rewriting of the dispersive part are accounted for using a thermodynamically compatible generalized Lagrangian multiplier approach. The proposed mathematical model is able to restore hyperbolicity even for non-convex equations of state and is solved using a high order ADER discontinuous Galerkin finite element scheme. The paper provides an exact solution of the new mathematical model, demonstrates numerical convergence rates, and presents numerical results for various benchmark problems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics, Applied
Ferdinand Thein, Evgeniy Romenski, Michael Dumbser
Summary: This study investigates the solution of the Riemann problem for the barotropic version of the conservative symmetric hyperbolic and thermodynamically compatible (SHTC) two-phase flow model. Explicit expressions for the Riemann invariants and the Rankine-Hugoniot conditions are derived, and non-standard wave phenomena due to multiple characteristics in the system are discussed. The study highlights the advantages of the conservative form of the model and explores the relationships between different phase flow systems.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
Simone Chiocchetti, Michael Dumbser
Summary: In this paper, a pressure-based semi-implicit numerical scheme for a compressible two-phase flow is presented. The scheme addresses complexities presented by the governing equations, such as involution constraints, nonlinear stiff algebraic source terms, and efficiency and accuracy loss in the low-Mach number regime. The scheme utilizes compatible discrete operators, reliable analytical estimates, a novel semi-analytical technique, and a split treatment of acoustic and non-acoustic waves.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Mathematics, Applied
Remi Abgrall, Saray Busto, Michael Dumbser
Summary: We present a simple and general framework for constructing thermodynamically compatible schemes for overdetermined hyperbolic PDE systems. The proposed algorithms solve the entropy inequality as a primary evolution equation, leading to total energy conservation as a consequence of the compatible discretization. We apply the framework to the construction of three different numerical methods and demonstrate their stability and accuracy through numerical experiments.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Mathematics, Applied
Saray Busto, Michael Dumbser
Summary: In this paper, a novel thermodynamically compatible finite volume scheme is proposed for solving the equations of magnetohydrodynamics (MHD) in one and two space dimensions. The scheme directly discretizes the entropy inequality instead of the total energy conservation law, and achieves discrete total energy conservation through an appropriate linear combination. In multiple space dimensions, the scheme takes into account the divergence-free condition of the magnetic field via a new thermodynamically compatible generalized Lagrangian multiplier (GLM) divergence cleaning approach. The method's fundamental properties are mathematically proven, and it performs well on standard MHD benchmark problems.
SIAM JOURNAL ON NUMERICAL ANALYSIS
(2023)
Article
Mathematics, Applied
Alessia Lucca, Saray Busto, Michael Dumbser
Summary: We propose a new implicit hybrid finite volume/finite element method for incompressible flows. The method splits the incompressible Navier-Stokes equations into a pressure subsystem and a transport-diffusion subsystem. The pressure subsystem is efficiently solved using classical continuous Lagrange finite elements, while finite volume methods are employed for the convective subsystem.
EAST ASIAN JOURNAL ON APPLIED MATHEMATICS
(2023)
Article
Mathematics
Firas Dhaouadi, Michael Dumbser
Summary: In this paper, a new explicit second-order accurate structure-preserving finite volume scheme for the first-order hyperbolic reformulation of the Navier-Stokes-Korteweg equations is presented. The numerical scheme relies on vertex-based staggered grids and preserves the curl constraint exactly up to machine precision. Both theoretical proof and numerical tests are provided to demonstrate the effectiveness of the scheme, showing that failure to respect the curl-free constraint can lead to numerical solutions blowing up, especially for under-resolved simulations on coarse grids.
Article
Mathematics, Applied
Dinshaw S. Balsara, Roger Kaeppeli, Walter Boscheri, Michael Dumbser
Summary: This paper investigates the design of mimetic finite volume (FV) WENO-like schemes for PDEs that support a curl-preserving involution. It provides closed form expressions for reconstruction in two- and three-dimensional structured mesh problems, and emphasizes the importance of multidimensional Riemann solvers in facilitating the design process. The study also presents a von Neumann analysis of structure-preserving WENO-like schemes in two dimensions, showcasing their value in minimizing dissipation and dispersion.
COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION
(2023)
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)