Free Access
| Issue |
ESAIM: M2AN
Volume 50, Number 6, November-December 2016
|
|
|---|---|---|
| Page(s) | 1887 - 1916 | |
| DOI | https://doi.org/10.1051/m2an/2016010 | |
| Published online | 21 October 2016 | |
- N. Aguillon, Capturing nonclassical shocks in nonlinear elastodynamic with a conservative finite volume scheme. Interfaces Free Bend. 18 (2016) 137–159. [CrossRef] [Google Scholar]
- N. Aguillon, A reconstruction scheme for the euler equations. Preprint hal-00967484 (2016). [Google Scholar]
- F. Alouges, F. De Vuyst, G. Le Coq and E. Lorin, The reservoir technique: a way to make Godunov-type schemes zero or very low diffuse. Application to Colella-Glaz solver. Eur. J. Mech. B Fluids 27 (2008) 643–664. [CrossRef] [Google Scholar]
- M. Arora and Ph.L. Roe, On postshock oscillations due to shock capturing schemes in unsteady flows. J. Comput. Phys. 130 (1997) 25–40. [CrossRef] [MathSciNet] [Google Scholar]
- M.B. Friess, B. Boutin, F. Caetano, G. Faccanoni, S. Kokh, F. Lagoutière and L. Navoret, A second order anti-diffusive Lagrange-remap scheme for two-component flows. In CEMRACS’10 research achievements: numerical modeling of fusion. Vol. 32 of ESAIM Proc. 32 (2011) 149–162. [Google Scholar]
- F. Bouchut, An antidiffusive entropy scheme for monotone scalar conservation laws. J. Sci. Comput. 21 (2004) 1–30. [CrossRef] [Google Scholar]
- F. Bouchut, A reduced stability condition for nonlinear relaxation to conservation laws. J. Hyperbolic Differ. Equ. 1 (2004) 149–170. [Google Scholar]
- F. Bouchut and T. Morales de Luna, Semi-discrete entropy satisfying approximate Riemann solvers. The case of the Suliciu relaxation approximation. J. Sci. Comput. 41 (2009) 483–509. [CrossRef] [Google Scholar]
- B. Boutin, Ch. Chalons, F. Lagoutière and Ph.G. LeFloch, Convergent and conservative schemes for nonclassical solutions based on kinetic relations. I. Interfaces Free Bound. 10 (2008) 399–421. [CrossRef] [MathSciNet] [Google Scholar]
- Ch. Chalons and F. Coquel, Navier-stokes equations with several independent pressure laws and explicit predictor-corrector schemes. Numer. Math. 101 (2005) 451–478. [CrossRef] [MathSciNet] [Google Scholar]
- Ch. Chalons and F. Coquel, Modified Suliciu relaxation system and exact resolution of isolated shock waves. Math. Models Methods Appl. Sci. 24 (2014) 937–971. [CrossRef] [Google Scholar]
- Ch. Chalons and J.-F. Coulombel, Relaxation approximation of the euler equations. J. Math. Anal. Appl. 348 (2008) 872–893. [CrossRef] [MathSciNet] [Google Scholar]
- Ch. Chalons, M. Laura Delle Monache and P. Goatin, A conservative scheme for non-classical solutions to a strongly coupled pde-ode problem. Preprint hal-01070262 (2014). [Google Scholar]
- G. Qiang Chen, C. David Levermore and Tai-Ping Liu, Hyperbolic conservation laws with stiff relaxation terms and entropy. Comm. Pure Appl. Math. 47 (1994) 787–830. [Google Scholar]
- F. Coquel, Shi Jin, Jian-Guo Liu and Li Wand, Entropic sub-cell shock capturing schemes via jin-xin relaxation and glimm front sampling for scalar hyperbolic conservation laws. Available at http://www.math.wisc.edu/˜jin/research.html (2016). [Google Scholar]
- B. Després and F. Lagoutière, Contact discontinuity capturing schemes for linear advection and compressible gas dynamics. J. Sci. Comput. 16 479–524 (2002), 2001. [CrossRef] [Google Scholar]
- E. Godlewski and P.-A. Raviart, Numerical approximation of hyperbolic systems of conservation laws, Vol. 118 of Appl. Math. Sci. Springer-Verlag, New York (1996). [Google Scholar]
- S.K. Godunov, A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics. Mat. Sb. (N.S.) 47 (1959) 271–306. [MathSciNet] [Google Scholar]
- A. Harten, ENO schemes with subcell resolution. J. Comput. Phys. 83 (1989) 148–184. [CrossRef] [Google Scholar]
- Sh. Jin and Z.P. Xin, The relaxation schemes for systems of conservation laws in arbitrary space dimensions. Comm. Pure Appl. Math. 48 (1995) 235–276. [Google Scholar]
- F. Lagoutière, Non-dissipative entropy satisfying discontinuous reconstruction schemes for hyperbolic conservation laws. Available at http://www.math.u-psud.fr/˜lagoutie/Papiers/disc˙reconst.pdf (2016). [Google Scholar]
- F. Lagoutière, Stability of reconstruction schemes for scalar hyperbolic conservation laws. Commun. Math. Sci. 6 (2008) 57–70. [CrossRef] [Google Scholar]
- H. Li, Zh. Wang and De-kang Mao, Numerically neither dissipative nor compressive scheme for linear advection equation and its application to the Euler system. J. Sci. Comput. 36 (2008) 285–331. [CrossRef] [Google Scholar]
- H. Nessyahu and E. Tadmor, Nonoscillatory central differencing for hyperbolic conservation laws. J. Comput. Phys. 87 (1990) 408–463. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
- I. Suliciu, On the thermodynamics of rate-type fluids and phase transitions. I. Rate-type fluids. Internat. J. Engrg. Sci. 36 (1998) 921–947. [Google Scholar]
- E.F. Toro. Riemann solvers and numerical methods for fluid dynamics. 3rd edition. Springer-Verlag, Berlin (2009). A practical introduction. [Google Scholar]
- B. van Leer, Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method. J. Comput. Phys. 135 (1997) 227–248. [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.