Gauge-Uzawa methods for incompressible flows with variable density

Journal of Computational Physics

Volumn 221, Issue 1, 2007, Pages 181-197

  Pyo, Jae Hong ^a   Shen, Jie ^b  

^a Yonsei University   (South Korea)

^b PURDUE UNIVERSITY   (United States)

Author keywords

Finite element method; Gauge Uzawa method; Incompressible flows with variable density; Projection methods; Stability

Indexed keywords

FINITE ELEMENT METHOD; GAGES;

CONVERGENCE RATES; FIRST ORDER; GAUGE-UZAWUM METHOD; INCOMPRESSIBLE FLOW WITH VARIABLE DENSITY; NUMERICAL EXPERIMENTS; PROJECTION METHOD; SECOND ORDER CONVERGENCE; SECOND ORDERS; UNCONDITIONALLY STABLE; VARIABLE DENSITY;

INCOMPRESSIBLE FLOW;

EID: 33846182594     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2006.06.013     Document Type: Article

References (14)

1. Almgren A.S., Bell J.B., Colella P., Howell L.H., and Welcome M.L. A conservative adaptive projection method for the variable density incompressible Navier-Stokes equations. J. Comput. Phys. 142 1 (1998) 1-46
2. Chorin A.J. Numerical solution of the Navier-Stokes equations. Math. Comput. 22 (1968) 745-762
3. Weinan E., and Liu J.-G. Gauge method for viscous incompressible flows. Commun. Math. Sci. 1 2 (2003) 317-332
4. Ern A., and Guermond J.-L. Theory and practice of finite elements. Applied Mathematical Sciences vol. 159 (2004), Springer, New York
5. J.L. Guermond, P. Minev, J. Shen, An overview of projection methods for incompressible flows. Comput. Methods Appl. Mech. Eng., in press, doi:10.1016/j.cma.2005.10.010.
6. Guermond J.-L., and Quartapelle L. A projection FEM for variable density incompressible flows. J. Comput. Phys. 165 1 (2000) 167-188
7. Johnson C. Numerical Solution of Partial Differential Equations by the Finite Element Method (1987), Cambridge University Press, Cambridge
8. Johnston H., and Liu J.-G. Finite difference schemes for incompressible flow based on local pressure boundary conditions. J. Comput. Phys. 180 1 (2002) 120-154
9. Pierre-Louis Lions. Mathematical topics in fluid mechanics. Vol. 1, volume 3 of Oxford Lecture Series in Mathematics and its Applications. The Clarendon Press Oxford University Press, New York, 1996. Incompressible models, Oxford Science Publications.
10. Nochetto R., and Pyo J.-H. The Gauge-Uzawa finite element method part I: the Navier-Stokes equations. SIAM J. Numer. Anal. 43 (2005) 1043-1068
11. R. Nochetto, J.-H. Pyo, The Gauge-Uzawa finite element method part II: Boussinesq equations. Math. Models Methods Appl. Sci., to appear.
12. J.-H. Pyo, The Gauge-Uzawa and related projection finite element methods for the evolution Navier-Stokes equations. Ph.D Dissertation, 2002.
13. Pyo J.-H., and Shen J. Normal mode analysis of second-order projection methods for incompressible flows. Discrete Contin. Dyn. Syst. Ser. B 5 3 (2005) 817-840
14. Temam R. Sur l'approximation de la solution des equations de Navier-Stokes par la methode des pas fractionnaires. II. Arch. Rational Mech. Anal. 33 (1969) 377-385