Entropy Stability (Eitan Tadmor)

ENTROPY STABILITY

A collection of selected references on

Entropy conservative and entropy stable approximations
of nonlinear conservation laws and related problems

E. Tadmor Skew self-adjoint form for systems of conservation laws Journal of Mathematical Analysis and Applications 103(2) (1984) 428-442.
E. Tadmor Numerical viscosity and the entropy condition for conservative difference schemes Mathematics of Computation 43 (1984) 369-381.
E. Tadmor A minimum entropy principle in the gas dynamics equations Applied Numerical Mathematics 2 (1986) 211-219.
E. Tadmor Entropy conservative finite element schemes in "Numerical Methods for Compressible Flows - Finite Difference Element and Volume Techniques", Proceedings of the winter annual meeting of the American Society of Mechanical Engineering, Vol. AMD-Vol. 78 (T. E. Tezduyar and T.J.R. Hughes, eds.) (1986) 149-158..
E. Tadmor Entropy functions for symmetric systems of conservation laws Journal of Mathematical Analysis and Applications 122(2) (1987) 355-359.
E. Tadmor The entropy dissipation by numerical viscosity in nonlinear conservative difference schemes in "Nonlinear Hyperbolic Problems'", Proceedings of a 1986 Advanced Research Workshop in St. Etienne, Lecture Notes in Mathematics, Vol. Vol. 1270 (C. Carasso, P.-A. Raviart and D. Serre, eds.), Springer-Verlag (1987) 52-63..
E. Tadmor The numerical viscosity of entropy stable schemes for systems of conservation laws. I. Mathematics of Computation 49 (1987) 91-103.
M. Merriam An entropy based approach to nonlinear stability NASA Technical Memorandum 101086 (1989).
F. Dubois Concavity of thermostatic entropy and convexity of LAX's mathematical entropy La Recherche Aerospatiale (English Edition) (ISSN 0379-380X) 3 (1990) 77-80.
Brahim Khobalatte and Benoit Perthame Maximum principle on the entropy and second-order kinetic schemes Mathematics of Computation 62(205) (1994) 118-131.
F. Bouchut, Ch. Bourdarias and B. Perthame A MUSCL method satisfying all the numerical entropy inequalities Mathematics of Computation 65 (1996) 65 (1996), 1439-1461.
B. Hayes and P. LeFloch Nonclassical shocks and kinetic relations: finite difference schemes SIAM J. Numerical Analysis 35(6) (1998) 2169-2194.
C. Rhode and P. LeFloch High-order schemes, entropy inequalities, and nonclassical shocks SIAM J. Numerical Analysis 37(6) (2000) 2023-2060.
C. Chalons and P. LeFloch High-order entropy-conservative schemes and kinetic relations for van der Waals fluids Journal of Computational Physics 168(1) (2001) 184-206.
C. Chalons and P. LeFloch A fully discrete scheme for diffusive-dispersive conservation laws Numerische Mathematik 89(3) (2001) 493-509.
C. Chalons and P. G. LeFloch High-order entropy-conservative schemes and kinetic relations for van der Waals fluids Journal of Computational Physics 168(1) (2001) 184-2006.
P. LeFloch, J.M. Mercier and C. Rohde Fully discrete, entropy conservative schemes of arbitrary order SIAM J. Numerical Analysis 40(5) (2002) 1968-1992.
E. Tadmor Entropy stability theory for difference approximations of nonlinear conservation laws and related time dependent problems Acta Numerica 12 (2003) 451-512.
R. Abramov and J. Majda Discrete approximations with additional conserved quantities: deterministic and statistical behavior Methods and Applications in Analysis 10(2) (2003) 151-189.
G. F. Naterer and J. A. Camberos Entropy and the second law fluid flow and heat transfer simulation AIAA Journal of Thermophysics and Heat Transfer 17(3) (2003) 360-371.
E. Tadmor and W. Zhong Entropy stable approximations of Navier-Stokes equations with no artificial numerical viscosity J. of Hyperbolic Differential Equations 3(3) (2006) 529-559.
E. Tadmor On the entropy stability of difference schemes: a comparison principle and a homotopy approach in "Hyperbolic Problems: Theory, Numerics, Applications'", Proceedings of the 10th International Conference in 2004, Vol. vol. I (F. Asukura, H. Aiso, S. Kawashima, A. Matsumura, S. Nishibata & K. Nishihara, eds.), Yokohama Publishers, Osaka (2006) 195-204..
P. Roe Affordable, entropy-consistent, Euler flux functions (with applications to the carbuncle phenomenon) in "11th International Conference on `Hyperbolic Problems: Theory, Numerics, Applications'", Lyon (2006).
E. Tadmor and W. Zhong Novel entropy stable schemes for 1D and 2D fluid equations in "Hyperbolic Problems: Theory, Numerics, Applications", Proceedings of the 11th International Conference in Lyon in 2006 (S. Benzoni-Gavage and D. Serre, eds.), Springer (2007) 1111-1120..
J. Haink and C. Rohde Local discontinuous-Galerkin schemes for model problems in phase transition theory Communications in Computational Physics 4(4) (2008) 860-893.
P. LeFloch and M. Mohammadian Why many theories of shock waves are necessary: kinetic functions, equivalent equations, and fourth-order models J. Computational Physics 227(8) (2008) 4162-4189.
D. Kroner, P. LeFloch and M.-D. Thanh The minimum entropy principle for compressible fluid flows in a nozzle with discontinuous cross-section Mathematical Modeling & Numerical Analysis 42(3) (2008) 425-442.
E. Tadmor and W. Zhong Energy-preserving and stable approximations for the two-dimensional shallow water equations in "Mathematics and Computation - A Contemporary View", Proceedings of the Third Abel Symposium held in Alesund, Norway in 2006 (H. Munthe-Kaas & B. Owren eds.), Springer (2008) 67-94..
Jean-Luc Guermond and Richard Pasquetti Entropy-based nonlinear viscosity for Fourier approximations of conservation laws C. R. Acad. Sci. Paris, Ser. I 346 (2008) 801-806.
J. M. Mercier Optimally transported schemes: one dimensional case (2008).
P. LeFloch and S. Mishra Kinetic functions in magnetohydrodynamics with resistivity and Hall effect Acta Mathematica Scientia 29B(6) (2009) 1684-1702.
K. Kitamura, P. Roe and F. Ismail Evaluation of Euler fluxes for hypersomic flow computations AIAA 47(1) (2009) 44-53.
M. Lukacova- Medvidova and K. W. Morton Finite volume evolution Galerkin methods: A survey Indian J. Pure & Appl. Math. (2009).
B. Sjogreen and H. Yee On skew-symmetric splitting and entropy conservation for the Euler Equations in "Numerical Mathematics and Advanced Applications", Proc of ENUMATH2009 8th European Conference held in Uppsala in 2009 (G. Kreiss, P. Lotstedt, A. Malquist, M. Neytcheva eds.), Springer (2009) 817-827..
U. Fjordholm, S. Mishra and E. Tadmor Energy preserving and energy stable schemes for the shallow water equations in "Foundations of Computational Mathematics", Proc. FoCM in 2008 (F. Cucker, A. Pinkus & M. Todd, eds), London Math. Soc. Lecture Notes Ser. 363, Hong Kong (2009) 93-139..
M. Lukacova- Medvidova and E. Tadmor On the entropy stability of Roe-type finite volume methods in "Hyperbolic Problems: Theory, Numerics, Applications", Proceedings of the 12th International Conference in 2008, Vol. 67(2) (E. Tadmor, J.-G. Liu & A. Tzavaras, eds.), AMS Proc. Symp. Applied Math., University of Maryland (2009) 765-774..
Aziz Madrane and Eitan Tadmor Entropy stability of Roe-type upwind finite volume methods on unstructured grids in "Hyperbolic Problems: Theory, Numerics, Applications", Proceedings of the 12th International Conference in 2008, Vol. 67(2) (E. Tadmor, J.-G. Liu & A. Tzavaras, eds.), AMS Proc. Symp. Applied Math., University of Maryland (2009) 775-784..
Susana Serna A characteristic-based nonconvex entropy fix upwind scheme for the ideal magnetohydrodynamic equations Journal of Computational Physics 228 (2009) 4232-4247.
F. Ismail and P. L. Roe Affordable, entropy-consistent Euler flux functions II: Entropy production at shocks J. Computational Physics 228 (2009) 5410-5436.
Christos Arvanitis, Charalambos Makridakis and Nikolaos Sfakianakis Entropy conservative schemes and adapive mesh selection for hyperbolic conservation laws Journal of Hyperbolic Differential Equations 7(3) (2010) 383-404.
Jean-Luc Guermond and Richard Pasquetti Entropy viscosity method for high-order approximations of conservation laws in "Spectral and High Order Methods for Partial Differential Equations (ICOSAHOM)", Lecture Notes in computational Science and Engineering, Vol. 76 (Jan S. Hesthaven and Einar M. Ronquist, eds.), Springer, Trondheim, Norway, June 2009 (2011) 411-418..
U. Fjordholm, S. Mishra and E. Tadmor Well-balanced and energy stable schemes for the shallow water equations with discontinuous topography J. Computational Physics 230(14) (2011) 5587-5609.
Jean-Luc Guermond, Richard Pasquetti and Bojan Popov Entropy viscosity method for nonlinear conservation laws Journal of Computational Physics 230(11) (2011) 4248-4267.
Ulrik S. Fjordholm Energy conservative and stable schemes for the two-layer shallow water equations in "Hyperbolic problems: Theory, Numerics and Applications", Vol. 2 (Tatsien Li and Song Jiang, eds.), Higher Education Press, Beijing, June 2010 (2011) 414-421..
Gabriella Puppo and Matteo Semplice Numerical entropy and adaptivity for finite volume schemes Communications in Computational Physics 10(5) (2011) 1132-1160.
U. Fjordholm and S. Mishra Accurate numerical discretizations of non-conservative hyperbolic systems Mathematical Modelling and Numerical Analysis 46(1) (2011) 187-206.
Gabriella Puppo and Matteo Semplice Entropy and the numerical integration of conservation laws Physics Procedia (2011) 1-28.
H. Kumar and S. Mishra Enropy stable numerical schemes for two-fluid plasma equations Journal of Scientific Computing 52 (2011) 401-425.
Xiangxiong Zhang and Chi-Wang Shu A minimum entropy principle of high order schemes for gas dynamics equations Numerische Mathematik 121 (2011) 545-563.
U. Fjordholm, S. Mishra and E. Tadmor Arbitrarily high order accurate entropy stable essentially non-oscillatory schemes for systems of conservation laws SIAM Journal on Numerical Analysis 50(2) (2012) 544-573.
M. Svärd and S. Mishra Entropy stable schemes for initial-boundary-value conservation laws Zeitschrift für angewandte Mathematik und Physik (ZAMP) (2012).
A. Mardane, U. Fjordholm, S. Mishra and E. Tadmor Entropy conservative and entropy stable finite volume schemes for multi-dimensional conservation laws on unstructured meshes, in "European Congress Computational Methods Applied Sciences and Engineering", Prceedings of ECCOMAS 2012 (J. Eberhardsteiner et. al. eds.), held in Vienna (2012).
A. N. Mohammed and F. Ismail Study of an entropy-consistent Navier-Stokes flux International Journal of Computational Fluid Dynamics 27(1) (2012) 1-14.
Manuel J. Castro, Ulrik S. Fjordholm, Siddhartha Mishra and Carlos Parés Entropy conservative and entropy stable schemes for nonconservative hyperbolic systems SIAM J. Numerical Analysis 51(3) (2012) 1371-1391.
A. Hiltebrand and S. Mishra Entropy stable shock capturing space-time discontinuous Galerkin schemes for systems of conservation laws Numerische Mathematik 126(1) (2013) 103-151.
Mark H. Carpenter and Travis C. Fisher High-order entropy stable formulations for computational fluid dynamics in "21st AIAA Computational Fluid Dynamics Conference", San-Diego, CA (2013) AIAA 2013-2868..
Praveen Chandrashekar Kinetic energy preserving and entropy stable finite volume schemes for compressible Euler and Navier-Stokes equations Communications in Computational Physics 14(5) (2013) 1252-1286.
Magnus Svard and Hatice Ozcan Entropy-stable schemes for the Euler equations with far-field and wall boundary conditions Journal of Scientific Computing 58(1) (2014) 61-89.
Jean-Luc Guermond and Bojan Popov Viscous regularization of the Euler equations and entropy principles SIAM J. Applied Math 74(2) (2014) 284-305.
M. Lukacova-Medvidova and N. Sfakianakis Entropy dissipation of moving mesh adaptation J. Hyperbolic Differential Equations (2014).
Jean-Luc Guermond and Bojan Popov Entropy viscosity for the Euler equations and questions regarding parabolic regularization . in "Hyperbolic Problems: Hyperbolic Problems: Theory, Numerics, Applications", held in Padova in 2012 (Fabio Ancona, Alberto Bressan, Pierangelo Marcati, Andrea Marson eds.), AIMS on Applied Mathematics Vol. 8(1) (2014) 119-124..
Philippe LeFloch and Sid Mishra Numerical methods with controlled dissipation for small-scale dependent shocks Acta Numerica 23 (2014) 743-816.
A. N. Gorban and D. J. Packwood Enhancement of the stability of lattice Boltzmann methods by dissipation control Physica A 414 (2014) 285-299.
A. N. Mohammed and F. Ismail Entropy consistent methods for the Navier-Stokes equations. A first-order systems approach J. Scientific Computation 63 (2014) 612-631.
Laslo T. Diosadyand and Scott M. Murman and Scott M. Murman Higher-order methods for compressible turbulent flows using entropy variables in "53rd AIAA Aerospace Sciences Meeting" in 2015, Vol. 2015-0294, Kissimmee, FL (2015).
Yu Lv and Matthias Ihme Entropy-bounded discontinuous Galerkin scheme for Euler equations Journal of Computational Physics 295 (2015) 715739.
Siddhartha Mishra and Laura V. Spinolo Accurate numerical schemes for approximating initial-boundary value problems for systems of conservation laws Journal of Hyperbolic Differential Equations 12 (2015) 61-86.
U. Fjordholm, R. Kappeli, S. Mishra and E. Tadmor Construction of approximate entropy measure valued solutions for systems of conservation laws Foundations of Computational Mathematics 17 (2015) 763-827.
S. Lanthaler and S. Mishra Computation of measure valued solutions for the incompressible Euler equations Mathematical Models and Methods in Applied Sciences (2015).
M. Parsani, M. H. Carpenter and E. J. Nielsen Entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations Journal of Computational Physics 292 (2015) 88-113.
A. R. Winters and G. J. Gassner Affordable, entropy conserving and entropy stable flux functions for the ideal MHD equations Journal of Computational Physics 304 (2015) 72-108.
E. Tadmor Perfect derivatives, conservative differences and entropy stable computation of hyperbolic conservation laws Discrete and Continuous Dynamical Systems-A 36(8) (2016) 4579-4598.
M. Zakerzadeh and G. May On the convergence of a shock capturing discontinuous Galerkin method for nonlinear hyperbolic systems of conservation laws SIAM J. Numerical Analysis 54(2) (2016) 874-898.
D. Ray, P. Chandrashekar, U. S. Fjordholm and S. Mishra Entropy stable scheme on two-dimensional unstructured grids for Euler equations Communications in Computational Physics 19(5) (2016) 1111-1140.
U. S. Fjordholm, S. Mishra and E. Tadmor On the computation of measure-valued solutions Acta Numerica 25 (2016) 567-679.
Dominik Derigs, Andrew R. Winters, Gregor J. Gassner and Stefanie Walch A novel high-order, entropy stable, 3D AMR MHD solver with guaranteed positive pressure Journal of Computational Physics 317 (2016) 223-256.
Sudi Mungkasi Adaptive Finite Volume Method for the Shallow Water Equations on Triangular Grids Advances in Mathematical Physics 2016 (2016).
E. Tadmor Entropy stable schemes Handbook of Numerical Methods for Hyperbolic problems XVII (R. Abgrall and C.-W. Shu, eds.), Elsevier (2016) 467-493.
Dominik Derigs, Andrew R. Winters, Gregor J.Gassner and Stefanie Walch A novel averaging technique for discrete entropy-stable dissipation operators for ideal MHD Journal of Computational Physics 330 (2017) 624-632.
Birte Schmidtmann and Andrew R. Winters Hybrid entropy stable HLL-Type Riemann solvers for hyperbolic conservation laws Journal of Computational Physics 330 (2017) 566-570.
Deep Ray Entropy-stable finite difference and finite volume schemes for compressible flows Ph.D. Thesis, TIFR, Bangalore (2017) 1-233.
Tianheng Chen and Chi-Wang Shu Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws Journal of Computational Physics 345 (2017) 427-461.
Yong Liu,, Chi-Wang Shu and Mengping Zhang Entropy stable high order discontinuous Galerkin methods for ideal compressible MHD on structured meshes Journal of Computational Physics 354 (2017) 163-178.
J. Crean, J. E.Hicken, D. C.Del Rey Fernández, D.. W. Zingg and M. Carpenter Entropy-stable summation-by-parts discretization of the Euler equations on general curved elements Journal of Computational Physics 356(1) (2018) 410-438.
Hendrik Ranocha Comparison of some entropy conservative numerical fluxes for the Euler equations Journal of Scientific Computing 76/1 (2018) 216-242.
Ayoub Gouasmi, Scott Murman and Karthik Duraisamy Entropy conservative schemes and the receding flow problem Journal of Scientific Computing 78(2) (2018) 971-994.
Ayoub Gouasmi, Karthik Duraisamy and Scott Murman On entropy stable temporal fluxes ArXiv:1807.03483 (2018).
David Williams An analysis of discontinuous Galerkin methods for the compressible Euler equations: entropy and L2 stability Numerische Mathematik 141(4) (2019) 1079-1120.
Jan Hesthaven and Fabian Monkeberg Entropy stable essentially non-oscillatory methods based on RBF reconstructions Mathematical Modelling and Numerical Analysis 53 (2019) 925-958.
T. Chen and C.-W. Shu Review of entropy stable discontinuous Galerkin methods for systems of conservation laws on unstructured simplex meshes CSIAM Transactions on Applied Mathematics (CSAM). (2019).
K. Wu and C.-W. Shu Entropy symmetrization and high-order accurate entropy stable numerical schemes for relativistic MHD equations SIAM Journal on Scientific Computing (2019).
Deepak Bhoriya and Harish Kumar Entropy-stable schemes for relativistic hydrodynamics equations Z. Angew. Math. Phys. 71 (2020) 1-29.
Ayoub Gouasmi, Karthik Duraisamy and Scott M. Murman Formulation of entropy-stable schemes for the multicomponent compressible Euler equations Computer Methods in Applied Mechanics and Engineering 363(1) (2020).
Neelabja Chatterjee and Ulrik Skre Fjordholm Convergence of second-order, entropy stable methods for multi-dimensional conservation laws Mathematical Modelling and Numerical Analysis 54(4) (2020) 1415 - 1428.
Gregor J. Gassner, Magnus Svard and Florian J. Hindenlang Stability issues of entropy-stable and/or split-form high-order schemes ArXiv:2007.09026v1 (2020).
Philippe G. LeFloch and Hendrik Ranocha Kinetic functions for nonclassical shocks, entropy stability, and discrete summation by parts Journal of Scientific Computing 87:55 (2021).

ENTROPY STABILITY

A collection of selected references on

Entropy conservative and entropy stable approximations of nonlinear conservation laws and related problems

Entropy conservative and entropy stable approximations
of nonlinear conservation laws and related problems