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TECHNICAL PAPERS

Numerical Solutions of Cauchy-Riemann Equations for Two and Three-Dimensional Flows

[+] Author and Article Information
M. Hafez, J. Housman

Department of Mechanics and Aerospace Engineering, University of California, Davis, CA 95616

J. Appl. Mech 70(1), 27-31 (Jan 23, 2003) (5 pages) doi:10.1115/1.1530632 History: Received August 24, 2001; Revised June 11, 2002; Online January 23, 2003
Copyright © 2003 by ASME
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References

Tang, C., and Hafez, M., 2003, “Numerical Simulation of Steady Compressible Flows Using a Zonal Formulation,” Comput. Fluids, to appear.
Hughes,  T.J.R., Franca,  L.P., and Hulbert,  G.M., 1989, “A New Finite Element Formulation for Computational Fluid Dynamics: VIII. The Galerkin/Least Squares Method for Advective-Diffusive Equations,” Comput. Methods Appl. Mech. Eng., 73, pp. 173–189.
Tezduyar, T.E., and Hughes, T.J.R., 1983, “Finite Element Formulations for Convection Dominated Flows With Particular Emphasis on the Compressible Euler Equations,” AIAA (83-0125), January Paper No. 83-0125.
Lerat, A., and Corre, C., 2003, “Residual-Based Compact Schemes for Multidimensional Hyperbolic Systems of Conservation Laws,” Comput. Fluids, to appear.
McCormack,  R.W., and Paullay,  A.J., 1974, “The Influence of the Computational Mesh on Accuracy for Initial Value Problems With Discontinuous or Non-linear Solutions,” Comput. Fluids, 2, pp. 339–361.
Jameson, A., Schmidt, W., and Turkel, E., 1981, “Numerical Solutions for the Euler Equations by Finite Volume Methods Using Runge-Kutta Time-Stepping Schemes.” AIAA Paper No. 81-1259.
Roy, J., Hafez, M., and Chattot, J., 2003, “Explicit Methods for the Solution of the Generalized Cauchy Riemann Equations and Simulation of Invicid Rotational Flows,” Comput. Fluids, to appear.
Bachelor, G.K., 1967, An Introduction to Fluid Dynamics. Cambridge University Press, Cambridge, UK.
Briggs, W.L., Hensen, V.E., and McCormick, S.F., 2000, A Multigrid Tutorial. SIAM.

Figures

Grahic Jump Location
(a) Plot of the local Mach number for compressible flow around a cylinder with M=0.2. (b) Plot of the local Mach number for compressible flow over sphere with M=0.2. (c) Example 2: Convergence history for the ‖r‖ norm for systems 1 and 2. (d) Convergence history for the ‖r‖ norm for systems 1 and 2.
Grahic Jump Location
(a) Streamlines for incompressible flow over a cylinder with ωz=0. (b) Streamlines for incompressible axisymmetric flow around a sphere with ωϕ=0.

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