☆ 4.7 Article

A mass, energy, enstrophy and vorticity conserving (MEEVC) mimetic spectral element discretization for the 2D incompressible Navier-Stokes equations

JOURNAL OF COMPUTATIONAL PHYSICS (2017)

Journal

JOURNAL OF COMPUTATIONAL PHYSICS

Volume 328, Issue -, Pages 200-220

Publisher

ACADEMIC PRESS INC ELSEVIER SCIENCE

DOI: 10.1016/j.jcp.2016.10.009

Keywords

Energy conserving discretization; Mimetic discretization; Enstrophy conserving discretization; Spectral element method; Incompressible Navier-Stokes equations

Categories

Computer Science, Interdisciplinary Applications Physics, Mathematical

Ask authors/readers for more resources

Protocol

Community support

Reagent

Community support

Abstract

In this work we present a mimetic spectral element discretization for the 2D incompressible Navier-Stokes equations that in the limit of vanishing dissipation exactly preserves mass, kinetic energy, enstrophy and total vorticity on unstructured triangular grids. The essential ingredients to achieve this are: (i) a velocity-vorticity formulation in rotational form, (ii) a sequence of function spaces capable of exactly satisfying the divergence free nature of the velocity field, and (iii) a conserving time integrator. Proofs for the exact discrete conservation properties are presented together with numerical test cases on highly irregular triangular grids. (C) 2016 Elsevier Inc. All rights reserved.

Authors

I am an author on this paper

Click your name to claim this paper and add it to your profile.

Reviews

Primary Rating

4.7

Not enough ratings

Secondary Ratings

Novelty

-

Significance

-

Scientific rigor

-

Rate this paper

Recommended

Article Computer Science, Interdisciplinary Applications

A mass-, kinetic energy- and helicity-conserving mimetic dual-field discretization for three-dimensional incompressible Navier-Stokes equations, part I: Periodic domains

Yi Zhang, Artur Palha, Marc Gerritsma, Leo G. Rebholz

Summary: We introduce a mimetic dual-field discretization method for conserving mass, kinetic energy, and helicity in three-dimensional incompressible Navier-Stokes equations. The method utilizes a conservative dual-field mixed weak formulation and a discrete algebraic system that handles the nonlinearity. Conservation of mass, kinetic energy, and helicity is proven at the discrete level, along with proper dissipation rates in the viscous case.

JOURNAL OF COMPUTATIONAL PHYSICS (2022)

Add to Collection

Article Mathematics, Applied

Enstrophy dissipation and vortex thinning for the incompressible 2D Navier-Stokes equations

In-Jee Jeong, Tsuyoshi Yoneda

Summary: The study on vortex thinning mechanism in two-dimensional turbulence reveals that it may result in inverse energy cascade and enhanced dissipation rate. The research also demonstrates that the enhanced dissipation induced by vortex thinning has a vanishing order of enstrophy dissipation slower than Re-1.

NONLINEARITY (2021)

Add to Collection

Article Engineering, Multidisciplinary

On the influence of the nonlinear term in the numerical approximation of Incompressible Flows by means of proper orthogonal decomposition methods

Bosco Garcia-Archilla, Julia Novo, Samuele Rubino

Summary: In this article, we investigate the use of proper orthogonal decomposition (POD) methods for approximating the incompressible Navier-Stokes equations. We examine the effect of using different discretizations for the nonlinear term in the FOM and POD methods, and analyze the additional error term that arises. We also explore the impact of adding grad-div stabilization to both methods. Numerical experiments are conducted to validate the theoretical analysis.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2023)

Add to Collection

Article Engineering, Multidisciplinary

Full and reduced order model consistency of the nonlinearity discretization in incompressible flows

Sean Ingimarson, Leo G. Rebholz, Traian Iliescu

Summary: We investigate the consistency between nonlinear discretization in full order models (FOMs) and reduced order models (ROMs) for incompressible flows both theoretically and numerically. The study shows that consistent discretization yields more accurate results.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2022)

Add to Collection

Article Mathematics, Applied

Global solutions to 3D incompressible Navier-Stokes equations with some large initial data

Yanghai Yu, Jinlu Li, Zhaoyang Yin

Summary: In this paper, a new smallness hypothesis of initial data for the three-dimensional incompressible Navier-Stokes equations is derived and used to prove the existence of a unique global solution. Additionally, two examples of initial data satisfying the smallness condition are constructed, demonstrating that the norm of the initial data can be arbitrarily large.

APPLIED MATHEMATICS LETTERS (2022)

Add to Collection

Article Engineering, Multidisciplinary

Enabling convergence of the iterated penalty Picard iteration with O(1) penalty parameter for incompressible Navier-Stokes via Anderson acceleration

Leo G. Rebholz, Duygu Vargun, Mengying Xiao

Summary: This paper enhances the classical IPP method for incompressible NavierStokes equations by using Anderson acceleration to improve convergence properties. By analyzing the fixed point operator associated with IPP iteration and applying a general theory for AA, it is shown that the linear convergence rate of IPP can be significantly improved with AA enhancement. Numerical tests demonstrate the effectiveness of IPP with penalty parameter 1 enhanced by AA.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2021)

Add to Collection

Article Mathematics, Applied

HHO Methods for the Incompressible Navier-Stokes and the Incompressible Euler Equations

Lorenzo Botti, Francesco Carlo Massa

Summary: We propose two Hybrid High-Order (HHO) methods for the incompressible Navier-Stokes equations and investigate their robustness with respect to the Reynolds number. The two methods differ in their pressure-velocity coupling, but both have been numerically validated and shown to be effective and applicable.

JOURNAL OF SCIENTIFIC COMPUTING (2022)

Add to Collection

Article Mathematics, Applied

Well-posedness for incompressible fluid-solid interaction with vorticity

Wei Shi, Xin-Guang Yang, Lin Shen

Summary: This paper investigates the global well-posedness of a fluid-solid interaction model with vorticity, which is described as a hyperbolic-parabolic coupled system along the conjugate boundary. The fluid is governed by the incompressible Navier-Stokes equation with vorticity, while the elastic solid is modeled by the wave equation. The global existence of weak solution and uniqueness of the coupled system are proven using the energy method, delicate estimates, and the truncation-polishing technique to overcome the lack of smoothness in the variational form. (c) 2023 Elsevier B.V. All rights reserved.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION (2023)

Add to Collection

Article Engineering, Marine

Stabilization of a rigid body in a viscous incompressible fluid

K. D. Do

Summary: This paper addresses the problem of global asymptotic and local exponential stabilization of a rigid body inside a viscous incompressible fluid described by Navier-Stokes equations within a bounded domain in three dimensional space provided that there is no collision between the rigid body and the boundary of the fluid domain. Due to consideration of less regular initial values of the fluid velocity, the forces and moments induced by the fluid on the rigid body are not able to bound. Therefore, the paper handles fluid work and fluid power on the rigid body in stability and convergence analysis of the closed-loop system. The control design ensures global asymptotic and local exponential stability of the rigid body while the initial fluid velocity is not required to be small and regular but only under no collision between the rigid body and the boundary of the fluid domain.

OCEAN ENGINEERING (2023)

Add to Collection

Article Mechanics

Numerical evidence of anomalous energy dissipation in incompressible Euler flows: towards grid-converged results for the inviscid Taylor-Green problem

Niklas Fehn, Martin Kronbichler, Peter Munch, Wolfgang A. Wall

Summary: This study contributes to the investigation of the well-known energy dissipation anomaly in inviscid limit by conducting high-resolution numerical simulations of the three-dimensional Taylor-Green vortex problem. The interesting observation is made that the kinetic energy evolution does not tend towards exact energy conservation as the spatial resolution of numerical scheme increases. This raises the question of whether the results obtained can be seen as a numerical confirmation of the famous energy dissipation anomaly and elaborates on an indirect approach for the identification of finite-time singularities based on energy arguments.

JOURNAL OF FLUID MECHANICS (2021)

Add to Collection

Article Automation & Control Systems

Boundary stabilization of an elastic body surrounding a viscous incompressible fluid

K. D. Do

Summary: This paper considers the problem of boundary feedback stabilization of an elastic body surrounding a viscous incompressible fluid. It gives a proof of global existence of a weak solution of the closed-loop system and handles the issue of unbounded forces induced by the fluid on the elastic body due to less regular initial values of the fluid velocity.

AUTOMATICA (2022)

Add to Collection

Article Mathematics, Applied

Pullback dynamics for the 3-D incompressible Navier-Stokes equations with damping and delay

Xiaona Cui, Wei Shi, Xuezhi Li, Xin-Guang Yang

Summary: This paper investigates the tempered pullback dynamics of 3-D nonautonomous incompressible Navier-Stokes equations with nonlinear damping and delay in a bounded domain. It proves the existence and uniqueness of weak and strong solutions based on delicate priori estimates, and demonstrates the existence of the minimal family of pullback attractors under appropriate hypotheses on external forces.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES (2021)

Add to Collection

Article Mathematics, Applied

Robin-type domain decomposition with stabilized mixed approximation for incompressible flow

Yani Feng, Qifeng Liao, David Silvester

Summary: In this paper, a nonoverlapping Robin-type multi-domain decomposition method based on stabilized Q(1)-P-0 mixed approximation (RMDD-Q(1)-P-0) is presented for incompressible flow problems. The global equations are decomposed into local problems through Robin-type domain decomposition, which are solved using the local jump stabilized Q(1)-P-0 approximation. It is proven that the RMDD-Q(1)-P-0 solutions converge to the standard global Q(1)-P-0 solutions for the Stokes problem. Numerical experiments show that RMDD-Q(1)-P-0 significantly improves the scalability of the stabilized Q(1)-P-0 approximation. The codes used in the experiments are available online.

COMPUTERS & MATHEMATICS WITH APPLICATIONS (2023)

Add to Collection

Article Mathematics, Applied

A potential two-scale traveling wave singularity for 3D incompressible Euler equations

Thomas Y. Hou, De Huang

Summary: In this paper, the potential singularity behavior of the 3D incompressible axisymmetric Euler equations with smooth initial data of finite energy is investigated. It is found that the introduction of numerical viscosity leads to a locally self-similar blowup phenomenon.

PHYSICA D-NONLINEAR PHENOMENA (2022)

Add to Collection

Article Mathematics, Applied

Global weak solutions to the inhomogeneous incompressible Navier-Stokes-Vlasov-Boltzmann equations

Haibo Cui, Lei Yao

Summary: This paper considers the initial-boundary value problem of the coupled inhomogeneous incompressible Navier-Stokes equations and Vlasov-Boltzmann equation for the moderately thick spray in three-dimensional space. The global existence of weak solutions is established using an approximation scheme, a fixed point argument, and the weak convergence method.

APPLIED MATHEMATICS LETTERS (2021)

Add to Collection

Article Computer Science, Interdisciplinary Applications

Discrete conservation properties for shallow water flows using mixed mimetic spectral elements

D. Lee, A. Palha, M. Gerritsma

JOURNAL OF COMPUTATIONAL PHYSICS (2018)

Add to Collection

Article Computer Science, Interdisciplinary Applications

A mixed mimetic spectral element model of the rotating shallow water equations on the cubed sphere

D. Lee, A. Palha

JOURNAL OF COMPUTATIONAL PHYSICS (2018)

Add to Collection

Article Computer Science, Interdisciplinary Applications

Inclusion of no-slip boundary conditions in the MEEVC scheme

G. G. de Diego, A. Palha, M. Gerritsma

JOURNAL OF COMPUTATIONAL PHYSICS (2019)

Add to Collection

Article Physics, Fluids & Plasmas

Dependence on plasma shape and plasma fueling for small edge-localized mode regimes in TCV and ASDEX Upgrade

B. Labit, T. Eich, G. F. Harrer, E. Wolfrum, M. Bernert, M. G. Dunne, L. Frassinetti, P. Hennequin, R. Maurizio, A. Merle, H. Meyer, S. Saarelma, U. Sheikh, J. Adamek, M. Agostini, D. Aguiam, R. Akers, R. Albanese, C. Albert, E. Alessi, R. Ambrosino, Y. Andrebe, C. Angioni, G. Apruzzese, M. Aradi, H. Arnichand, F. Auriemma, G. Avdeeva, J. M. Ayllon-Guerola, F. Bagnato, V. K. Bandaru, M. Barnes, L. Barrera-Orte, P. Bettini, R. Bilato, O. Biletskyi, P. Bilkova, W. Bin, P. Blanchard, T. Blanken, V Bobkov, A. Bock, D. Boeyaert, K. Bogar, O. Bogar, P. Bohm, T. Bolzonella, F. Bombarda, L. Boncagni, F. Bouquey, C. Bowman, S. Brezinsek, D. Brida, D. Brunetti, J. Bucalossi, J. Buchanan, J. Buermans, H. Bufferand, S. Buller, P. Buratti, A. Burckhart, G. Calabro, L. Calacci, Y. Camenen, B. Cannas, P. Cano Megias, D. Carnevale, F. Carpanese, M. Carr, D. Carralero, L. Carraro, A. Casolari, A. Cathey, F. Causa, M. Cavedon, M. Cecconello, S. Ceccuzzi, J. Cerovsky, S. Chapman, P. Chmielewski, D. Choi, C. Cianfarani, G. Ciraolo, S. Coda, R. Coelho, L. Colas, D. Colette, L. Cordaro, F. Cordella, S. Costea, D. Coster, D. J. Cruz Zabala, G. Cseh, A. Czarnecka, I Cziegler, O. D'Arcangelo, A. Dal Molin, P. David, G. De Carolis, H. De Oliveira, J. Decker, R. Dejarnac, R. Delogu, N. den Harder, M. Dimitrova, F. Dolizy, J. J. Dominguez-Palacios Duran, D. Douai, A. Drenik, M. Dreval, B. Dudson, D. Dunai, B. P. Duval, R. Dux, S. Elmore, O. Embreus, B. Erdos, E. Fable, M. Faitsch, A. Fanni, M. Farnik, I Faust, J. Faustin, N. Fedorczak, F. Felici, S. Feng, X. Feng, J. Ferreira, G. Ferro, O. Fevrier, O. Ficker, L. Figini, A. Figueiredo, A. Fil, M. Fontana, M. Francesco, C. Fuchs, S. Futatani, L. Gabellieri, D. Gadariya, D. Gahle, D. Galassi, K. Galazka, J. Galdon-Quiroga, S. Galeani, D. Gallart, A. Gallo, C. Galperti, S. Garavaglia, J. Garcia, J. Garcia-Lopez, M. Garcia-Munoz, L. Garzotti, J. Gath, B. Geiger, L. Giacomelli, L. Giannone, S. Gibson, L. Gil, E. Giovannozzi, G. Giruzzi, M. Gobbin, J. Gonzalez-Martin, T. P. Goodman, G. Gorini, M. Gospodarczyk, G. Granucci, D. Grekov, G. Grenfell, M. Griener, M. Groth, O. Grover, M. Gruca, A. Gude, L. Guimarais, T. Gyergyek, P. Hacek, A. Hakola, C. Ham, T. Happel, J. Harrison, A. Havranek, J. Hawke, S. Henderson, L. Hesslow, F. Hitzler, B. Hnat, J. Hobirk, M. Hoelzl, D. Hogeweij, C. Hopf, M. Hoppe, J. Horacek, M. Hron, Z. Huang, A. Iantchenko, D. Iglesias, V Igochine, P. Innocente, C. Ionita-Schrittwieser, H. Isliker, I. Ivanova-Stanik, A. Jacobsen, M. Jakubowski, F. Janky, A. Jardin, F. Jaulmes, T. Jensen, T. Jonsson, A. Kallenbach, A. Kappatou, A. Karpushov, S. Kasilov, Y. Kazakov, P. Kazantzidis, D. Keeling, M. Kelemen, A. Kendl, W. Kernbichler, A. Kirk, G. Kocsis, M. Komm, M. Kong, V Korovin, M. Koubiti, J. Kovacic, N. Krawczyk, K. Krieger, L. Kripner, A. Krivska, O. Kudlacek, Y. Kulyk, T. Kurki-Suonio, R. Kwiatkowski, F. Laggner, L. Laguardia, A. Lahtinen, P. Lang, J. Likonen, B. Lipschultz, F. Liu, R. Lombroni, R. Lorenzini, V. P. Loschiavo, T. Lunt, E. Macusova, J. Madsen, R. Maggiora, B. Maljaars, P. Manas, P. Mantica, M. J. Mantsinen, P. Manz, M. Maraschek, V Marchenko, C. Marchetto, A. Mariani, C. Marini, T. Markovic, L. Marrelli, P. Martin, J. R. Martin Solis, A. Martitsch, S. Mastrostefano, F. Matos, G. Matthews, M-L Mayoral, D. Mazon, C. Mazzotta, P. Mc Carthy, K. McClements, R. McDermott, B. Mcmillan, C. Meineri, V Menkovski, D. Meshcheriakov, M. Messmer, D. Micheletti, D. Milanesio, F. Militello, I. G. Miron, J. Mlynar, V Moiseenko, P. A. Molina Cabrera, J. Morales, J-M Moret, A. Moro, D. Moulton, F. Nabais, V Naulin, D. Naydenkova, R. D. Nem, F. Nespoli, S. Newton, A. H. Nielsen, S. K. Nielsen, V Nikolaeva, M. Nocente, S. Nowak, M. Oberkofler, R. Ochoukov, P. Ollus, J. Olsen, J. Omotani, J. Ongena, F. Orain, F. P. Orsitto, R. Paccagnella, A. Palha, L. Panaccione, R. Panek, M. Panjan, G. Papp, I. Paradela Perez, F. Parra, M. Passeri, A. Pau, G. Pautasso, R. Pavlichenko, A. Perek, V. Pericoli Radolfini, F. Pesamosca, M. Peterka, V Petrzilka, V Piergotti, L. Pigatto, P. Piovesan, C. Piron, L. Piron, V Plyusnin, G. Pokol, E. Poli, P. Poloskei, T. Popov, Z. Popovic, G. Por, L. Porte, G. Pucella, M. E. Puiatti, T. Putterich, M. Rabinski, J. Juul Rasmussen, J. Rasmussen, G. A. Ratta, S. Ratynskaia, T. Ravensbergen, D. Refy, M. Reich, H. Reimerdes, F. Reimold, D. Reiser, C. Reux, S. Reznik, D. Ricci, N. Rispoli, J. F. Rivero-Rodriguez, G. Rocchi, M. Rodriguez-Ramos, A. Romano, J. Rosato, G. Rubinacci, G. Rubino, D. A. Ryan, M. Salewski, A. Salmi, D. Samaddar, L. Sanchis-Sanchez, J. Santos, K. Sarkimaki, M. Sassano, O. Sauter, R. Scannell, M. Scheffer, B. S. Schneider, P. Schneider, R. Schrittwieser, M. Schubert, J. Seidl, E. Seliunin, S. Sharapov, R. R. Sheeba, G. Sias, B. Sieglin, C. Silva, S. Sipila, S. Smith, A. Snicker, E. R. Solano, S. K. Hansen, C. Soria-Hoyo, E. Sorokovoy, C. Sozzi, A. Sperduti, G. Spizzo, M. Spolaore, M. Stejner, L. Stipani, J. Stober, P. Strand, H. Sun, W. Suttrop, D. Sytnykov, T. Szepesi, B. Tal, T. Tala, G. Tardini, M. Tardocchi, A. Teplukhina, D. Terranova, D. Testa, C. Theiler, E. Thoren, A. Thornton, B. Tilia, P. Tolias, M. Tomes, M. Toscano-Jimenez, C. Tsironis, C. Tsui, O. Tudisco, J. Urban, M. Valisa, M. Vallar, P. Vallejos Olivares, M. Valovic, D. Van Vugt, B. Vanovac, J. Varje, J. Varju, S. Varoutis, S. Vartanian, O. Vasilovici, J. Vega, G. Verdoolaege, K. Verhaegh, L. Vermare, N. Vianello, J. Vicente, E. Viezzer, F. Villone, I Voitsekhovitch, D. Voltolina, P. Vondracek, N. M. T. Vu, N. Walkden, T. Wauters, M. Weiland, V Weinzettl, M. Wensing, S. Wiesen, M. Wiesenberger, G. Wilkie, M. Willensdorfer, M. Wischmeier, K. Wu, L. Xiang, R. Zagorski, D. Zaloga, P. Zanca, R. Zaplotnik, J. Zebrowski, W. Zhang, A. Zisis, S. Zoletnik, M. Zuin

NUCLEAR FUSION (2019)

Add to Collection

Article Mathematics, Applied

The Discrete Steklov-Poincare Operator Using Algebraic Dual Polynomials

Yi Zhang, Varun Jain, Artur Palha, Marc Gerritsma

COMPUTATIONAL METHODS IN APPLIED MATHEMATICS (2019)

Add to Collection

Article Physics, Fluids & Plasmas

Physics research on the TCV tokamak facility: from conventional to alternative scenarios and beyond

S. Coda, M. Agostini, R. Albanese, S. Alberti, E. Alessi, S. Allan, J. Allcock, R. Ambrosino, H. Anand, Y. Andrebe, H. Arnichand, F. Auriemma, J. M. Ayllon-Guerola, F. Bagnato, J. Ball, M. Baquero-Ruiz, A. A. Beletskii, M. Bernert, W. Bin, P. Blanchard, T. C. Blanken, J. A. Boedo, O. Bogar, T. Bolzonella, F. Bombarda, N. Bonanomi, F. Bouquey, C. Bowman, D. Brida, J. Bucalossi, J. Buermans, H. Bufferand, P. Buratti, G. Calabro, L. Calacci, Y. Camenen, D. Carnevale, F. Carpanese, M. Carr, L. Carraro, A. Casolari, F. Causa, J. Cerovsky, O. Chellai, P. Chmielewski, D. Choi, N. Christen, G. Ciraolo, L. Cordaro, S. Costea, N. Cruz, A. Czarnecka, A. Dal Molin, P. David, J. Decker, H. De Oliveira, D. Douai, M. B. Dreval, B. Dudson, M. Dunne, B. P. Duval, T. Eich, S. Elmore, O. Embreus, B. Esposito, M. Faitsch, M. Farnik, A. Fasoli, N. Fedorczak, F. Felici, S. Feng, X. Feng, G. Ferro, O. Fevrier, O. Ficker, A. Fil, M. Fontana, L. Frassinetti, I Furno, D. S. Gahle, D. Galassi, K. Galazka, A. Gallo, C. Galperti, S. Garavaglia, J. Garcia, M. Garcia-Munoz, A. J. Garrido, I Garrido, J. Gath, B. Geiger, G. Giruzzi, M. Gobbin, T. P. Goodman, G. Gorini, M. Gospodarczyk, G. Granucci, J. P. Graves, M. Gruca, T. Gyergyek, A. Hakola, T. Happel, G. F. Harrer, J. Harrison, E. Havlickova, J. Hawke, S. Henderson, P. Hennequin, L. Hesslow, D. Hogeweij, J-Ph Hogge, C. Hopf, M. Hoppe, J. Horacek, Z. Huang, A. Hubbard, A. Iantchenko, V Igochine, P. Innocente, C. Ionita Schrittwieser, H. Isliker, R. Jacquier, A. Jardin, A. Kappatou, A. Karpushov, P- Kazantzidis, D. Keeling, N. Kirneva, M. Komm, M. Kong, J. Kovacic, N. Krawczyk, O. Kudlacek, T. Kurki-Suonio, R. Kwiatkowski, B. Labit, E. Lazzaro, B. Linehan, B. Lipschultz, X. Llobet, R. Lombroni, V. P. Loschiavo, T. Lunt, E. Macusova, J. Madsen, E. Maljaars, P. Mantica, M. Maraschek, C. Marchetto, A. Marco, A. Mariani, C. Marini, Y. Martin, F. Matos, R. Maurizio, B. Mavkov, D. Mazon, P. McCarthy, R. McDermott, V Menkovski, A. Merle, H. Meyer, D. Micheletti, F. Militello, K. Mitosinkova, J. Mlyn, V Moiseenko, P. A. Molina Cabrera, J. Morales, J-M Moret, A. Moro, R. T. Mumgaard, V Naulin, R. D. Nem, F. Nespoli, A. H. Nielsen, S. K. Nielsen, M. Nocente, S. Nowak, N. Offeddu, F. P. Orsitto, R. Paccagnella, A. Palha, G. Papp, A. Pau, R. O. Pavlichenko, A. Perek, V. Pericoli Ridolfini, F. Pesamosca, V Piergotti, L. Pigatto, P. Piovesan, C. Piron, V Plyusnin, E. Poli, L. Porte, G. Pucella, M. E. Puiatti, T. Puetterich, M. Rabinski, J. Juul Rasmussen, T. Ravensbergen, M. Reich, H. Reimerdes, F. Reimold, C. Reux, D. Ricci, P. Ricci, N. Rispoli, J. Rosato, S. Saarelma, M. Salewski, A. Salmi, O. Sauter, M. Scheffer, Ch Schlatter, B. S. Schneider, R. Schrittwieser, S. Sharapov, R. R. Sheeba, U. Sheikh, R. Shousha, M. Silva, J. Sinha, C. Sozzi, M. Spolaore, L. Stipani, P. Strand, T. Tala, A. S. Tema Biwole, A. A. Teplukhina, D. Testa, C. Theiler, A. Thornton, G. Tomaz, M. Tomes, M. Q. Tran, C. Tsironis, C. K. Tsui, J. Urban, M. Valisa, M. Vallar, D. Van Vugt, S. Vartanian, O. Vasilovici, K. Verhaegh, L. Vermare, N. Vianello, E. Viezzer, W. A. J. Vijvers, F. Villone, I Voitsekhovitch, N. M. T. Vu, N. Walkden, T. Wauters, M. Weiland, H. Weisen, M. Wensing, M. Wiesenberger, G. Wilkie, M. Wischmeier, K. Wu, M. Yoshida, R. Zagorski, P. Zanca, J. Zebrowski, A. Zisis, M. Zuin

NUCLEAR FUSION (2019)

Add to Collection

Article Computer Science, Interdisciplinary Applications

A mixed mimetic spectral element model of the 3D compressible Euler equations on the cubed sphere

D. Lee, A. Palha

JOURNAL OF COMPUTATIONAL PHYSICS (2020)

Add to Collection

Article Mathematics, Applied

Non-conforming least-squares spectral element method for Stokes equations on non-smooth domains

S. Mohapatra, P. Dutt, B. V. Rathish Kumar, Marc Gerritsma

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS (2020)

Add to Collection

Article Computer Science, Interdisciplinary Applications

Exact spatial and temporal balance of energy exchanges within a horizontally explicit/vertically implicit non-hydrostatic atmosphere

David Lee, Artur Palha

Summary: The new HEVI scheme achieves a balance of energy exchanges in space and time, but still exhibits a temporal energy conservation error, showing good stability and accuracy in tests.

JOURNAL OF COMPUTATIONAL PHYSICS (2021)

Add to Collection

Article Mathematics, Applied

Construction and application of algebraic dual polynomial representations for finite element methods on quadrilateral and hexahedral meshes

V. Jain, Y. Zhang, A. Palha, M. Gerritsma

Summary: This passage discusses the construction of dual representations in a sequence of finite element spaces, along with the use of differential operators to connect these spaces. The dual representations must also satisfy the required conditions on the domain boundary, with the matrix converting primal representations to dual representations known as the Hodge matrix. Additionally, it is demonstrated that the bilinear form of primal and dual representations equates to the vector inner product of their expansion coefficients, resulting in sparse system matrices.

COMPUTERS & MATHEMATICS WITH APPLICATIONS (2021)

Add to Collection

Article Computer Science, Interdisciplinary Applications

A mass-, kinetic energy- and helicity-conserving mimetic dual-field discretization for three-dimensional incompressible Navier-Stokes equations, part I: Periodic domains

Yi Zhang, Artur Palha, Marc Gerritsma, Leo G. Rebholz

Summary: We introduce a mimetic dual-field discretization method for conserving mass, kinetic energy, and helicity in three-dimensional incompressible Navier-Stokes equations. The method utilizes a conservative dual-field mixed weak formulation and a discrete algebraic system that handles the nonlinearity. Conservation of mass, kinetic energy, and helicity is proven at the discrete level, along with proper dissipation rates in the viscous case.

JOURNAL OF COMPUTATIONAL PHYSICS (2022)

Add to Collection

Article Engineering, Multidisciplinary

Use of algebraic dual spaces in domain decomposition methods for Darcy flow in 3D domains

V. Jain, A. Palha, M. Gerritsma

Summary: In this work, algebraic dual spaces are used with a domain decomposition method to solve the Darcy equations. Broken Sobolev spaces and their finite dimensional counterparts are defined, along with a global trace space that connects the solution between broken spaces. The use of algebraic dual spaces allows for a sparse, metric-free representation of the incompressibility constraint, pressure gradient term, and continuity constraint between subdomains. Test cases demonstrate the effectiveness of the dual spaces in domain decomposition formulation, resulting in less simulation time compared to the continuous Galerkin formulation without sacrificing solution accuracy.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2023)

Add to Collection

Article Computer Science, Interdisciplinary Applications

A new type of non-polynomial based TENO scheme for hyperbolic conservation laws

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)

Add to Collection

Article Computer Science, Interdisciplinary Applications

A high-order residual-based viscosity finite element method for incompressible variable density flow

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)

Add to Collection

Article Computer Science, Interdisciplinary Applications

Convergence analysis and optimization of a Robin Schwarz waveform relaxation method for time-periodic parabolic optimal control problems

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)

Add to Collection

Article Computer Science, Interdisciplinary Applications

Data-driven Whitney forms for structure-preserving control volume analysis

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)

Add to Collection

Article Computer Science, Interdisciplinary Applications

Higher-continuity s-version of finite element method with B-spline functions

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)

Add to Collection

Article Computer Science, Interdisciplinary Applications

A cell-centred Eulerian volume-of-fluid method for compressible multi-material flows

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)

Add to Collection

Article Computer Science, Interdisciplinary Applications

Two-step multi-resolution reconstruction-based compact gas-kinetic scheme on tetrahedral mesh

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)

Add to Collection

Article Computer Science, Interdisciplinary Applications

Multiscale sampling for the inverse modeling of partial differential equations

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)

Add to Collection

Article Computer Science, Interdisciplinary Applications

Constrained optimized dynamic mode decomposition with control for physically stable systems with exogeneous inputs

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)

Add to Collection

Article Computer Science, Interdisciplinary Applications

A hybridizable discontinuous Galerkin formulation for the Euler-Maxwell plasma model

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)

Add to Collection

Article Computer Science, Interdisciplinary Applications

Numerical solution of the cavity scattering problem for flexural waves on thin plates: Linear finite element methods

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)

Add to Collection

Article Computer Science, Interdisciplinary Applications

Fast and scalable computation of shape-morphing nonlinear solutions with application to evolutional neural networks

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)

Add to Collection

Article Computer Science, Interdisciplinary Applications

A second order directional split exponential integrator for systems of advection-diffusion-reaction equations

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)

Add to Collection

Article Computer Science, Interdisciplinary Applications

A conservative semi-Lagrangian method for inhomogeneous Boltzmann equation

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)

Add to Collection

Article Computer Science, Interdisciplinary Applications

Uniqueness and numerical scheme for spherical shell-structured sources from the far field patterns with at most two frequencies

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)

Add to Collection

© Peeref 2019-2024. All rights reserved.