Open Access
| Issue |
ESAIM: M2AN
Volume 57, Number 2, March-April 2023
|
|
|---|---|---|
| Page(s) | 991 - 1027 | |
| DOI | https://doi.org/10.1051/m2an/2023004 | |
| Published online | 07 April 2023 | |
- R. Abgrall, A combination of residual distribution and the active flux formulations or a new class of schemes that can combine several writings of the same hyperbolic problem: application to the 1d Euler equations. Commun. Appl. Math. Comput. (2022) 1–33. DOI: 10.1007/s42967-021-00175-w. [Google Scholar]
- W. Barsukow, The active flux scheme for nonlinear problems. J. Sci. Comput. 86 (2021) 1–34. [CrossRef] [MathSciNet] [Google Scholar]
- W. Barsukow and J. Berberich, A well-balanced Active Flux scheme for the shallow water equations with wetting and drying. submitted to J. Sci. Comput (2020). [Google Scholar]
- W. Barsukow and C. Klingenberg, Exact solution and a truly multidimensional Godunov scheme for the acoustic equations. ESAIM M2AN 56 (2022). [Google Scholar]
- W. Barsukow, J. Hohm, C. Klingenberg and P.L. Roe, The active flux scheme on Cartesian grids and its low Mach number limit. J. Sci. Comput. 81 (2019) 594–622. [CrossRef] [MathSciNet] [Google Scholar]
- W. Barsukow, J.P. Berberich and C. Klingenberg, On the Active Flux scheme for hyperbolic PDEs with source terms. SIAM J. Sci. Comput. 43 (2021) A4015–A4042. [CrossRef] [Google Scholar]
- E. Chudzik, C. Helzel and D. Kerkmann, The cartesian grid active flux method: linear stability and bound preserving limiting. Appl. Math. Comput. 393 (2021) 125501. [CrossRef] [Google Scholar]
- A. Cohn, Über die Anzahl der Wurzeln einer algebraischen Gleichung in einem Kreise. Math. Z. 14 (1922) 110–148. [CrossRef] [MathSciNet] [Google Scholar]
- B. Cockburn and C.-W. Shu, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: general framework, Math. Comput. 52 (1989) 411–435. [Google Scholar]
- B. Cockburn and C.-W. Shu, The Runge-Kutta local projection P1-discontinuous-Galerkin finite element method for scalar conservation laws. ESAIM: Math. Modell. Numer. Anal.-Modél. Math. Anal. Numér. 25 (1991) 337–361. [CrossRef] [EDP Sciences] [Google Scholar]
- B. Cockburn, S.-Y. Lin and C.-W. Shu, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: one-dimensional systems. J. Comput. Phys. 84 (1989) 90–113. [CrossRef] [MathSciNet] [Google Scholar]
- T.A. Eymann and P.L. Roe, Active flux schemes for systems, in 20th AIAA Computational Fluid Dynamics Conference (2011). [Google Scholar]
- T.A. Eymann and P.L. Roe, Multidimensional active flux schemes, in 21st AIAA Computational Fluid Dynamics Conference (2013). [Google Scholar]
- D. Fan, On the acoustic component of active flux schemes for nonlinear hyperbolic conservation laws. Ph.D. thesis, University of Michigan (2017). [Google Scholar]
- S.K. Godunov, A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics. Matematicheskii Sbornik 89 (1959) 271–306. [Google Scholar]
- H. Guillard and A. Murrone, On the behavior of upwind schemes in the low Mach number limit: II. Godunov type schemes. Comput. Fluids 33 (2004) 655–675. [Google Scholar]
- F. He, Towards a new-generation numerical scheme for the compressible Navier–Stokes equations with the active flux method. Ph.D. thesis University of Michigan Library (2021). [Google Scholar]
- C. Helzel, D. Kerkmann and L. Scandurra, A new ADER method inspired by the active flux method. J. Sci. Comput. 80 (2019) 1463–1497. [CrossRef] [MathSciNet] [Google Scholar]
- A. Iserles, Order stars and a saturation theorem for first-order hyperbolics. IMA J. Numer. Anal. 2 (1982) 49–61. [CrossRef] [MathSciNet] [Google Scholar]
- P. Lesaint and P.-A. Raviart, On a finite element method for solving the neutron transport equation. Publications mathématiques et informatique de Rennes S 4 (1974) 1–40. [Google Scholar]
- J.J.H. Miller, On the location of zeros of certain classes of polynomials with applications to numerical analysis. IMA J. Appl. Math. 8 (1971) 397–406. [CrossRef] [Google Scholar]
- P. Roe, Did numerical methods for hyperbolic problems take a wrong turning? in XVI International Conference on Hyperbolic Problems: Theory, Numerics, Applications. Springer (2016) 517–534. [Google Scholar]
- P. Roe, Is discontinuous reconstruction really a good idea? J. Sci. Comput. 73 (2017) 1094–1114. [CrossRef] [MathSciNet] [Google Scholar]
- P. Roe, Designing CFD methods for bandwidth – a physical approach. Comput. Fluids 214 (2021) 104774. [CrossRef] [Google Scholar]
- P.L. Roe, T. Lung and J. Maeng, New approaches to limiting, in 22nd AIAA Computational Fluid Dynamics Conference (2015) 2913. DOI: 10.2514/6.2015-2913. [Google Scholar]
- I. Schur, Über Potenzreihen, die im Innern des Einheitskreises beschränkt sind. Journal für die reine und angewandte Mathematik 147 (1917) 205–232. [CrossRef] [Google Scholar]
- I. Schur, Über Potenzreihen, die im Innern des Einheitskreises beschränkt sind. Part II. J. Reine Angew. Math. 148 (1918) 122–145. [CrossRef] [Google Scholar]
- G.A. Sod, A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws. J. Comput. Phys. 27 (1978) 1–31. [CrossRef] [MathSciNet] [Google Scholar]
- B. van Leer, Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection. J. Comput. Phys. 23 (1977) 276–299. [NASA ADS] [CrossRef] [Google Scholar]
- X.X. Zhang and C.-W. Shu, On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes. J. Comput. Phys. 229 (2010) 8918–8934. [CrossRef] [MathSciNet] [Google Scholar]
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