RUS  ENG
Full version
JOURNALS // Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences

Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2014, Issue 1(34), Pages 156–167 (Mi vsgtu1233)

On the accuracy of difference scheme for Navier–Stokes equations
N. I. Sidnyaev, N. M. Gordeeva

References

1. L. G. Loitsyansky, Fluid and Gas Mechanics, Nauka, Moscow, 1970, 904 pp. (In Russian)  mathscinet
2. V. Ya. Neiland, V. V. Bogolepov, G. N. Dudin, I. I. Lipatov, Asymptotic Theory of Supersonic Viscous Gas Flows, Elsiever, Oxford, The Netherlands, 2008, xxv+536 pp.
3. V. V. Bogolepov, “Small perturbations of a laminar boundary layer”, J. Appl. Mech. Tech. Phys., 28:5 (1987), 706–716  crossref  adsnasa
4. V. A. Bashkin, G. N. Dudin, 3-Dimensional Hypersonic Viscous Flow, Fizmatlit, Moscow, 2000, 288 pp. (In Russian)
5. J. Gazdag, “Numerical convective schemes based on accurate computation of space derivatives”, J. Comput. Phys., 13:1 (1973), 100–113  crossref  zmath  adsnasa
6. J. Gazdag, “Time-differencing schemes and transform methods”, J. Comput. Phys., 20:2 (1976), 196–207  crossref  mathscinet  zmath  adsnasa
7. N. I. Sidnyaev, “Calculation method of unstable external flow past rotation body with surface injection in three dimensional parabolized Navier–Stokes code”, Matem. Mod., 16:5 (2004), 55–65 (In Russian)  mathnet
8. N. I. Sidnyaev, D. A. Sirotovskiy, “On the accuracy of difference schemes for Burgers and Navier–Stokes equations”, Neobratimyye protsessy v prirode i tekhnike [Irreversible Processes in Nature and Technology. 3rd All-Russ. Conf. Abstr.], Bauman MSTU Publ., Moscow, 2005, 132–133 pp. (In Russian)
9. Y. Morchoisne, “Résolution des équations de Navier-Stokes par une méthode pseudo-spectrale en espace-temps”, Rech. Aérosp., 5 (1979), 293–306 (In French)  mathscinet  zmath
10. Ph. Roy, “Résolution des équations de Navier–Stokes par un schema de haute précision en espace et en temps”, Rech. Aérosp., 6 (1980), 373–385 (In French)  mathscinet  zmath
11. Ya. I. Belopolskaya, “Generalized Solutions of Nonlinear Parabolic Systems and the Vanishing Viscosity Method”, J. Math. Sci. (N. Y.), 133:3 (2006), 1207–1223  mathnet  crossref  mathscinet  zmath
12. L. Bertini, N. Cancrini, G. Jona-Lasinio, “The stochastic Burgers Equation”, Comm. Math. Phys., 165:2 (1994), 211–232  crossref  mathscinet  zmath  adsnasa  isi
13. I. M. Davies, A. Truman, H. Zhao, “Stochastic heat and Burgers equations and their singularities. I. Geometrical properties”, J. Math. Phys., 43:6 (2002), 3293–3328  crossref  mathscinet  zmath  adsnasa  isi
14. O. O. Obrezkov, “The Proof of the Feynman–Kac Formula for Heat Equation on a Compact Riemannian Manifold”, Infin. Dimens. Anal. Quantum. Probab. Relat. Top., 6:2 (2003), 311–320  crossref  mathscinet  zmath  isi
15. O. G. Smolyanov, H. von Weizsäcker, “Smooth probability measures and associated differential operators”, Infin. Dimens. Anal. Quantum. Probab. Relat. Top., 2:1 (1999), 51–78  crossref  mathscinet  zmath  isi
16. O. G. Smolyanov, H. von Weizsäcker, O. Wittich, “Brownian motion on a manifold as a limit of stepwise conditioned standard Brownian motions”, Canadian Mathematical Society, Conference Proceedings, v. 29, ed. J. Jost, 2000, 589–602  mathscinet  zmath
17. O. G. Smolyanov, H. von Weizsäcker, O. Wittich, “Surface Measures and Initial Boundary Value Problems Generated by Diffusions with Drift”, Doklady Mathematics, 76:1 (2007), 606–610  mathnet  crossref  mathscinet  zmath  isi  elib  elib
18. A. Truman, H. Z. Zhao, “On stochastic diffusion equations and stochastic Burgers' equations”, J. Math. Phys., 37:1 (1996), 283–307  crossref  mathscinet  zmath  adsnasa  isi
19. H. J. Wospakrik, F. P. Zen, Inhomogeneous Burgers Equation and the Feynman-Kac Path Integral, 1998, 12 pp., arXiv: solv-int/9812014
20. S. E. Matskevich, “Burgers equation and Kolmogorov–Petrovsky–Piskunov equation on manifolds”, Infin. Dimens. Anal. Quantum. Probab. Relat. Top., 14:2 (2011), 199–208  crossref  mathscinet  zmath  isi  elib


© Steklov Math. Inst. of RAS, 2026