Year: 2011
Communications in Computational Physics, Vol. 10 (2011), Iss. 3 : pp. 635–671
Abstract
This paper is concerned with a new version of the Osher-Solomon Riemann solver and is based on a numerical integration of the path-dependent dissipation matrix. The resulting scheme is much simpler than the original one and is applicable to general hyperbolic conservation laws, while retaining the attractive features of the original solver: the method is entropy-satisfying, differentiable and complete in the sense that it attributes a different numerical viscosity to each characteristic field, in particular to the intermediate ones, since the full eigenstructure of the underlying hyperbolic system is used. To illustrate the potential of the proposed scheme we show applications to the following hyperbolic conservation laws: Euler equations of compressible gasdynamics with ideal gas and real gas equation of state, classical and relativistic MHD equations as well as the equations of nonlinear elasticity. To the knowledge of the authors, apart from the Euler equations with ideal gas, an Osher-type scheme has never been devised before for any of these complicated PDE systems. Since our new general Riemann solver can be directly used as a building block of high order finite volume and discontinuous Galerkin schemes we also show the extension to higher order of accuracy and multiple space dimensions in the new framework of PNPM schemes on unstructured meshes recently proposed in [9].
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.170610.021210a
Communications in Computational Physics, Vol. 10 (2011), Iss. 3 : pp. 635–671
Published online: 2011-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 37
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A well balanced diffuse interface method for complex nonhydrostatic free surface flows
Gaburro, Elena | Castro, Manuel J. | Dumbser, MichaelComputers & Fluids, Vol. 175 (2018), Iss. P.180
https://doi.org/10.1016/j.compfluid.2018.08.013 [Citations: 27] -
A Computational Model for the Dynamics of Cerebrospinal Fluid in the Spinal Subarachnoid Space
Toro, Eleuterio F. | Thornber, Ben | Zhang, Qinghui | Scoz, Alessia | Contarino, ChristianJournal of Biomechanical Engineering, Vol. 141 (2019), Iss. 1
https://doi.org/10.1115/1.4041551 [Citations: 5] -
Application of Osher and PRICE-C schemes to solve compressible isothermal two-fluid models of two-phase flow
Shekari, Younes | Hajidavalloo, EbrahimComputers & Fluids, Vol. 86 (2013), Iss. P.363
https://doi.org/10.1016/j.compfluid.2013.07.018 [Citations: 8] -
High-Order and High Accurate CFD Methods and Their Applications for Complex Grid Problems
Deng, Xiaogang | Mao, Meiliang | Tu, Guohua | Zhang, Hanxin | Zhang, YifengCommunications in Computational Physics, Vol. 11 (2012), Iss. 4 P.1081
https://doi.org/10.4208/cicp.100510.150511s [Citations: 59] -
Non-Newtonian Fluid Mechanics and Complex Flows
Lectures on Hyperbolic Equations and Their Numerical Approximation
Toro, Eleuterio F.
2018
https://doi.org/10.1007/978-3-319-74796-5_3 [Citations: 2] -
Low-dissipation centred schemes for hyperbolic equations in conservative and non-conservative form
Toro, E.F. | Saggiorato, B. | Tokareva, S. | Hidalgo, A.Journal of Computational Physics, Vol. 416 (2020), Iss. P.109545
https://doi.org/10.1016/j.jcp.2020.109545 [Citations: 12] -
Adaptive Osher-type scheme for the Euler equations with highly nonlinear equations of state
Lee, Bok Jik | Toro, Eleuterio F. | Castro, Cristóbal E. | Nikiforakis, NikolaosJournal of Computational Physics, Vol. 246 (2013), Iss. P.165
https://doi.org/10.1016/j.jcp.2013.03.046 [Citations: 26] -
Numerical methods for hydraulic transients in visco-elastic pipes
Bertaglia, Giulia | Ioriatti, Matteo | Valiani, Alessandro | Dumbser, Michael | Caleffi, ValerioJournal of Fluids and Structures, Vol. 81 (2018), Iss. P.230
https://doi.org/10.1016/j.jfluidstructs.2018.05.004 [Citations: 40] -
Central Weighted ENO Schemes for Hyperbolic Conservation Laws on Fixed and Moving Unstructured Meshes
Dumbser, Michael | Boscheri, Walter | Semplice, Matteo | Russo, GiovanniSIAM Journal on Scientific Computing, Vol. 39 (2017), Iss. 6 P.A2564
https://doi.org/10.1137/17M1111036 [Citations: 75] -
DOT-type schemes for hybrid hyperbolic problems arising from free-surface, mobile-bed, shallow-flow models
Zugliani, Daniel | Rosatti, GiorgioJournal of Computational Physics, Vol. 507 (2024), Iss. P.112975
https://doi.org/10.1016/j.jcp.2024.112975 [Citations: 0] -
Uncertainty quantification of viscoelastic parameters in arterial hemodynamics with the a-FSI blood flow model
Bertaglia, Giulia | Caleffi, Valerio | Pareschi, Lorenzo | Valiani, AlessandroJournal of Computational Physics, Vol. 430 (2021), Iss. P.110102
https://doi.org/10.1016/j.jcp.2020.110102 [Citations: 14] -
A new smoothed particle hydrodynamics method based on high-order moving-least-square targeted essentially non-oscillatory scheme for compressible flows
Gao, Tianrun | Liang, Tian | Fu, LinJournal of Computational Physics, Vol. 489 (2023), Iss. P.112270
https://doi.org/10.1016/j.jcp.2023.112270 [Citations: 11] -
Recent Advances in Numerical Methods for Hyperbolic PDE Systems
Incomplete Riemann Solvers Based on Functional Approximations to the Absolute Value Function
Gallardo, José M. | Castro, Manuel J. | Marquina, Antonio2021
https://doi.org/10.1007/978-3-030-72850-2_1 [Citations: 0] -
Theory, Numerics and Applications of Hyperbolic Problems I
Jacobian-Free Incomplete Riemann Solvers
Castro, Manuel J. | Gallardo, José M. | Marquina, Antonio2018
https://doi.org/10.1007/978-3-319-91545-6_24 [Citations: 0] -
Space-time adaptive ADER discontinuous Galerkin schemes for nonlinear hyperelasticity with material failure
Tavelli, Maurizio | Chiocchetti, Simone | Romenski, Evgeniy | Gabriel, Alice-Agnes | Dumbser, MichaelJournal of Computational Physics, Vol. 422 (2020), Iss. P.109758
https://doi.org/10.1016/j.jcp.2020.109758 [Citations: 21] -
Approximate Osher–Solomon schemes for hyperbolic systems
Castro, Manuel J. | Gallardo, José M. | Marquina, AntonioApplied Mathematics and Computation, Vol. 272 (2016), Iss. P.347
https://doi.org/10.1016/j.amc.2015.06.104 [Citations: 15] -
Computational Algorithms for Shallow Water Equations
Approximate Riemann Solvers
Toro, Eleuterio F.
2024
https://doi.org/10.1007/978-3-031-61395-1_11 [Citations: 0] -
A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws
Dumbser, Michael | Zanotti, Olindo | Loubère, Raphaël | Diot, StevenJournal of Computational Physics, Vol. 278 (2014), Iss. P.47
https://doi.org/10.1016/j.jcp.2014.08.009 [Citations: 259] -
Efficient conservative ADER schemes based on WENO reconstruction and space-time predictor in primitive variables
Zanotti, Olindo | Dumbser, MichaelComputational Astrophysics and Cosmology, Vol. 3 (2016), Iss. 1
https://doi.org/10.1186/s40668-015-0014-x [Citations: 35] -
Space–time adaptive ADER discontinuous Galerkin finite element schemes with a posteriori sub-cell finite volume limiting
Zanotti, Olindo | Fambri, Francesco | Dumbser, Michael | Hidalgo, ArturoComputers & Fluids, Vol. 118 (2015), Iss. P.204
https://doi.org/10.1016/j.compfluid.2015.06.020 [Citations: 118] -
A Unified Framework for the Solution of Hyperbolic PDE Systems Using High Order Direct Arbitrary-Lagrangian–Eulerian Schemes on Moving Unstructured Meshes with Topology Change
Gaburro, Elena
Archives of Computational Methods in Engineering, Vol. 28 (2021), Iss. 3 P.1249
https://doi.org/10.1007/s11831-020-09411-7 [Citations: 21] -
A novel numerical flux for the 3D Euler equations with general equation of state
Toro, Eleuterio F. | Castro, Cristóbal E. | Lee, Bok JikJournal of Computational Physics, Vol. 303 (2015), Iss. P.80
https://doi.org/10.1016/j.jcp.2015.09.037 [Citations: 25] -
High order cell-centered Lagrangian-type finite volume schemes with time-accurate local time stepping on unstructured triangular meshes
Boscheri, Walter | Dumbser, Michael | Zanotti, OlindoJournal of Computational Physics, Vol. 291 (2015), Iss. P.120
https://doi.org/10.1016/j.jcp.2015.02.052 [Citations: 26] -
High order ADER schemes for a unified first order hyperbolic formulation of continuum mechanics: Viscous heat-conducting fluids and elastic solids
Dumbser, Michael | Peshkov, Ilya | Romenski, Evgeniy | Zanotti, OlindoJournal of Computational Physics, Vol. 314 (2016), Iss. P.824
https://doi.org/10.1016/j.jcp.2016.02.015 [Citations: 138] -
A universal centred high-order method based on implicit Taylor series expansion with fast second order evolution of spatial derivatives
Montecinos, Gino I.
Journal of Computational Physics, Vol. 443 (2021), Iss. P.110535
https://doi.org/10.1016/j.jcp.2021.110535 [Citations: 5] -
A Stability Analysis of Hybrid Schemes to Cure Shock Instability
Shen, Zhijun | Yan, Wei | Yuan, GuangweiCommunications in Computational Physics, Vol. 15 (2014), Iss. 5 P.1320
https://doi.org/10.4208/cicp.210513.091013a [Citations: 29] -
An Efficient Quadrature-Free Formulation for High Order Arbitrary-Lagrangian–Eulerian ADER-WENO Finite Volume Schemes on Unstructured Meshes
Boscheri, W. | Dumbser, M.Journal of Scientific Computing, Vol. 66 (2016), Iss. 1 P.240
https://doi.org/10.1007/s10915-015-0019-2 [Citations: 15] -
Multidimensional Riemann problem with self-similar internal structure. Part I – Application to hyperbolic conservation laws on structured meshes
Balsara, Dinshaw S.
Journal of Computational Physics, Vol. 277 (2014), Iss. P.163
https://doi.org/10.1016/j.jcp.2014.07.053 [Citations: 94] -
Shear shock formation in incompressible viscoelastic solids
Berjamin, H. | Chockalingam, S.Wave Motion, Vol. 110 (2022), Iss. P.102899
https://doi.org/10.1016/j.wavemoti.2022.102899 [Citations: 8] -
An efficient lattice Boltzmann method for compressible aerodynamics on D3Q19 lattice
Guo, S. | Feng, Y. | Jacob, J. | Renard, F. | Sagaut, P.Journal of Computational Physics, Vol. 418 (2020), Iss. P.109570
https://doi.org/10.1016/j.jcp.2020.109570 [Citations: 55] -
A splitting scheme for the coupled Saint-Venant-Exner model
Siviglia, A. | Vanzo, D. | Toro, E.F.Advances in Water Resources, Vol. 159 (2022), Iss. P.104062
https://doi.org/10.1016/j.advwatres.2021.104062 [Citations: 9] -
An efficient high order direct ALE ADER finite volume scheme with a posteriori limiting for hydrodynamics and magnetohydrodynamics
Boscheri, Walter
International Journal for Numerical Methods in Fluids, Vol. 84 (2017), Iss. 2 P.76
https://doi.org/10.1002/fld.4342 [Citations: 7] -
High‐order ADER‐WENO ALE schemes on unstructured triangular meshes—application of several node solvers to hydrodynamics and magnetohydrodynamics
Boscheri, W. | Dumbser, M. | Balsara, D. S.International Journal for Numerical Methods in Fluids, Vol. 76 (2014), Iss. 10 P.737
https://doi.org/10.1002/fld.3947 [Citations: 63] -
A staggered semi-implicit spectral discontinuous Galerkin scheme for the shallow water equations
Dumbser, Michael | Casulli, VincenzoApplied Mathematics and Computation, Vol. 219 (2013), Iss. 15 P.8057
https://doi.org/10.1016/j.amc.2013.02.041 [Citations: 25] -
High order space–time adaptive ADER-WENO finite volume schemes for non-conservative hyperbolic systems
Dumbser, Michael | Hidalgo, Arturo | Zanotti, OlindoComputer Methods in Applied Mechanics and Engineering, Vol. 268 (2014), Iss. P.359
https://doi.org/10.1016/j.cma.2013.09.022 [Citations: 78] -
A mathematical framework for modelling rock–ice avalanches
Sansone, Stefania | Zugliani, D. | Rosatti, G.Journal of Fluid Mechanics, Vol. 919 (2021), Iss.
https://doi.org/10.1017/jfm.2021.348 [Citations: 13] -
A novel structure preserving semi‐implicit finite volume method for viscous and resistive magnetohydrodynamics
Fambri, Francesco
International Journal for Numerical Methods in Fluids, Vol. 93 (2021), Iss. 12 P.3447
https://doi.org/10.1002/fld.5041 [Citations: 17] -
High order direct Arbitrary-Lagrangian-Eulerian (ALE) PP schemes with WENO Adaptive-Order reconstruction on unstructured meshes
Boscheri, Walter | Balsara, Dinshaw S.Journal of Computational Physics, Vol. 398 (2019), Iss. P.108899
https://doi.org/10.1016/j.jcp.2019.108899 [Citations: 24] -
High order ADER schemes for a unified first order hyperbolic formulation of Newtonian continuum mechanics coupled with electro-dynamics
Dumbser, Michael | Peshkov, Ilya | Romenski, Evgeniy | Zanotti, OlindoJournal of Computational Physics, Vol. 348 (2017), Iss. P.298
https://doi.org/10.1016/j.jcp.2017.07.020 [Citations: 56] -
A divergence‐free semi‐implicit finite volume scheme for ideal, viscous, and resistive magnetohydrodynamics
Dumbser, M. | Balsara, D.S. | Tavelli, M. | Fambri, F.International Journal for Numerical Methods in Fluids, Vol. 89 (2019), Iss. 1-2 P.16
https://doi.org/10.1002/fld.4681 [Citations: 48] -
A generalized Rusanov method for the Baer‐Nunziato equations with application to DDT processes in condensed porous explosives
Menshov, Igor | Serezhkin, AlexeyInternational Journal for Numerical Methods in Fluids, Vol. 86 (2018), Iss. 5 P.346
https://doi.org/10.1002/fld.4419 [Citations: 14]