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NUMERICAL SOLUTION OF THE EULER EQUATIONS BY FINITE VOLUME METHODS: Central versus Upwind Schemes

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Abstract (2. Language): 
Euler equations are solved by means of three efficient and robust finite volume schemes, namely, central scheme of Jameson-Schmidt-Turkel (JST) and upwind schemes of Roe’s Approximate Riemann Solver and Convective Upwind Split Pressure (CUSP) Scheme. Cell-centered discretization technique is employed. Multistage timestepping algorithm is used to advance the solution in time. Acceleration techniques including local time stepping and implicit residual smoothing are applied for faster convergence to steady state. The flux at the cell faces is computed using MUSCL approach in upwind schemes and simple averaging procedure in JST scheme. MUSCL is enhanced by employing Van Albada limiter to suppress oscillations in regions of sharp gradients. Attention is directed towards the accuracy, convergence, and computational performance of the schemes. All schemes yield good convergence rates for a wide range of flow speeds.
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REFERENCES

References: 

[1] Jameson, A., Schmidt, W., Turkel, E., 1981,
“Numerical Solutions of the Euler Equations by
Finite Volume Methods Using Runge-Kutta
Time-Stepping Schemes,” AIAA Paper 81-
1259.
[2] Roe, P.L., 1981, “Approximate Riemann
Solvers, Parameter Vectors, and Difference
Schemes,” Journal of Computational Physics,
43: 357-372.
[3] Jameson, A., 1993, “Artificial Diffusion,
Upwind Biasing, Limiters and Their Effect on
Accuracy and Multigrid Convergence in
Transonic and Hypersonic Flow,” AIAA Paper
93-3559.
[4] Warming, R.F., and Beam, R.W., 1976,
“Upwind Second Order Difference Schemes and
Applications in Aerodynamic Flows,” AIAA
Journal, Vol. 24, pp. 1241-1249.
[5] Leer, B. V., 1977, “Towards the Ultimate
Conservation Difference Scheme IV; A New
Approach to Numerical Convection,” Journal of
Computational Physics, 23: 276-299.
[6] Albada, G.D., Leer, B. V., and Roberts, W.W.,
1982, “A Comparative Study of Computational
Methods in Cosmic Gas Dynamics,” Astron.
Astrophysics, 108:76-84.
[7] Godunov, S.K., 1959, “A difference Scheme for
Numerical Computation Discontinuous Solution
of Hydrodynamic Equations,” Math. Sbornik (in
Russian), 47, pp. 271-306.
[8] Roe, P.L.; Pike, J., “Efficient Construction and
Utilization of Approximate Riemann Solutions,”
Computing Methods in Applied Sciences and
Engineering, R. Glowinski, J.L. Lions (eds.),
Numerical Solution of the Euler Equations by Finite Volume Methods: Central versus Upwind Schemes
UYGUN, KIRKKÖPRÜ
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North Holland Publishing, The Netherlands,
1984.
[9] Harten, A., Lax, P.D., Van Leer, B., 1983, “On
Upstream Differencing and Godunov-Type
Schemes for Hyperbolic Conservation Laws,”
Soc. Indust. and Appl. Math. Rev., 25, No.1.
[10] Jameson, A., 1995, “Positive Schemes and
Shock Modeling for Compressible Flows,”
Inter. J. Numerical Methods Engineering,
20:743-776.
[11] Jameson, A., 1995, “Analysis and Design of
Numerical Schemes for Gas Dynamics II:
Artificial Diffusion and Discrete Shock
Structure,” Int. J. Computational Fluid
Dynamics, Vol. 5, pp. 1-38.
[12] Tatsumi, S., Martinelli, L. and Jameson, 1994,
“A Design, Implementation and Validation of
Flux Limited Schemes for the Solution of the
Compressible Navier-Stokes Equations,” AIAA
Paper 94-0647.
[13] Tatsumi, S., Martinelli, L., Jameson, A., 1995,
“A New High Resolution Scheme for
Compressible Viscous Flow with Shocks,”
AIAA Paper 95-0466.
[14] Venkatakrishnan, V., 1993, “On the Accuracy of
Limiters and Convergence to Steady State
Solutions,” AIAA Paper 93-0880
[15] Jameson, A., Baker, T.J., 1983, “Solution of the
Euler Equations for Complex Configurations,”
AIAA paper 83-1929.
[16] Rho-Ho, Ni, 1982, “A Multiple Grid Scheme
For Solving the Euler Equations,” AIAA
Journal, Vol. 20, No. 11.
[17] Moretti, G., 1981, “Experiments on Initial and
Boundary Conditions,” Paper Presented At
Symposium on Numerical and Physical Aspects
of Aerodynamic Flow.

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