The comparative analysis streamline finite-element schemes of the high order for a problem of the Navier-Stokes on the basis of modified SUPG-method |
V. K. Bulgakov, I. I. Potapov |
2003, issue 1, P. 5–17 |
Abstract |
In activity the class steady streamline finite-element schemes for the solution of a problem of the Navier-Stokes is offered. On the basis of a numerical modeling of a problem of the Navier-Stokes with the strongly expressed dominance of convective terms the comparative analysis of the offered schemes is conducted. |
Keywords: |
Download the article (PDF-file) |
References |
[1] K. Fletcher, Chislennye metody na osnove metoda Galerkina, Mir, M., 1988. [2] K. Fletcher, Vychislitel'nye metody v dinamike zhidkostej, Mir, M., 1991. [3] P. D. Rouch, Vychislitel'naya gidrodinamika, Mir, M., 1980. [4] S. Patankar, Chislennye metody resheniya zadach teploobmena i dinamiki zhidkosti, Mir, M., 1984. [5] J. W. Barrett, K. W. Morton, Optimal finite element approximation for diffusion-convection problems, Conf. on Math. of Finite Elements Trends and Appl. (Brunel Univ., May 1981). [6] V. K. Bulgakov, K. A. Chekhonin, I. I. Potapov, Optimal Coordination Coefficients Selection in Upwind Finite-Element Schemes, The Fourth International Symposium on Advances in Science and Technology in the Far East (February 10–15, 1995, Harbin, China). [7] D. F. Griffiths, A. R. Mitchell, Finite elements for convection dominated flows, AMD, 34 (1979), 91–104, New York. [8] O. C. Zeinkiewicz, The Finite Element Method, 2 ed., McGraw-Hill, London, 1977. [9] D. Anderson, Dzh. Tannexill, R. Pletcher, Vychislitel'naya gidrodinamika i teploobmen, v 2 t., t. 2, Mir, M., 1990. [10] C. Baiocchi, F. Brezzi, L. P. Franca, Virtual bubbles and Galerkin-Least-squares method, Comp. Methods Appl. Mech. Eng., 105 (1993), 125–141. [11] T. J. R. Hughes, L. P. Franca, G. M. Hulbert, A new finite element formulation for computational fluid dynamics: VIII. The Galerkin-least-squares method for advective-diffusive equations, Comp. Methods Appl. Mech. Eng., 73 (1989), 173–189. [12] F. Brezzi, M. O. Bristeau, L. P. Franca, M. Mallet, G. Roge, A relationship between stabilized finite element methods and the Galerkin method with bubble functions, Comp. Methods Appl. Mech. Eng., 96 (1992), 117–129. [13] F. Brezzi, L. P. Franca, T. J. R. Hughes, A. Russo, Stabilization techniques and subgrid scales capturing, Comp. Methods Appl. Mech. Eng., 145 (1997), 329–339. [14] A. N. Brooks, T. J. R. Hughes, Streamline upwind Retrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier – Stokes equations, Comp. Methods Appl. Mech. Eng., 32 (1982), 199–259. [15] L. P. Franca, S. L. Frey, T. J. R. Hughes, Stabilized finite element methods: I. Application to the advective-diffusive model, Comp. Methods Appl. Mech. Eng., 95 (1992), 253–276. [16] Metod konechnyx e'lementov v mexanike tverdyx tel, red. A. S. Saxarov, I. Al'tenbax, Vishha shkola, Kiev, 1982. [17] L. P. Franca, L. Michel, F. Charbel, Unusual stabilized finite element methods for second order linear differential equations, Proceedings of the Nintn International Conference on Finite Elements in Fluids - New Trends and Applications (Venezia, Italy, 15th–21st October, 1995). [18] G. Streng, Dzh. Fiks, Teoriya metoda konechnyx e'lementov, Mir, M., 1977. [19] F. Brezzi, D. Marini, A. Russo, Application of the Pseudo-Free Bubbles to the Stabilization of Convection-Diffusion Problems, Comp. Methods Appl. Mech. Eng., 166 (1998), 51–64. [20] V. T. Zhukov, L. G. Straxovskaya, R. P. Fedorenko, O. B. Fedoritova, Ob odnom napravlenii v konstruirovanii raznostnyx sxem, Zh. vychisl. matem. i matem. fiz., 42:2 (2002), 222–234. [21] L. P. Franca, R. L. Muller, Convergence analyses of Galerkin least-squares methods for symmetric advective-diffusive form of the Stokes and incompressible Navier – Stokes equations, Comp. Methods Appl. Mech. Eng., 105 (1993), 285–298. [22] V. K. Bulgakov, I. I. Potapov, Metod konechnyx e'lementov v zadachax gidrodinamiki, XGTU, Xabarovsk, 1999. [23] D. Dzhozef, Ustojchivost' dvizhenij zhidkosti, Mir, M., 1981. [24] Stefan Turek, Multilevel Pressure Schur Complement techniques for the numerical solution of the incompressible Navier – Stokes equations, Univ. Heidelberg, 1998. [25] V. V. Shajdurov, Mnogosetochnye metody konechnyx e'lementov, Nauka, M., 1989. [26] V. K. Bulgakov, I. I. Potapov, Sravnitel'nyj analiz konechno-e'lementnyx approksimacij vtorogo poryadka dlya zadachi Stoksa, Zh. vychisl. matem. i matem. fiz., 42:11 (2002), 1756–1761. [27] S. Pissanecki, Texnologiya razrezhennyx matric, Mir, M., 1988. [28] Dzh. Ortega, Vvedenie v parallel'nye i vektornye metody resheniya linejnyx sistem, Mir, M., 1991. |