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Euler Solver: NEARZEUSIN (with Inlets) /ZEUSBL

NEARZEUSIN is a CFD-level code for calculating the detailed aerodynamic loads and flow fields associated with configurations in supersonic and hypersonic flight. The original ZEUS (Zonal EUler Solver) code1,2 is a space-marching Euler solver which combines a semiautomatic, multiple zone, gridding technique and a second-order extension of Godunov's method. The Godunov method3 is an upwind scheme based on the Riemann problem for steady supersonic flow. It is cast in control volume form and consists of a predictor and corrector step. The predictor step advances the primitive variables using Euler's equations in nonconservation form. Derivatives are computed using a limited central differencing procedure. The corrector step modifies Godunov's method by assuming linear property variations within each control volume. Because the flow must remain supersonic in the axial direction, the flow conditions are typically limited to Mach numbers greater than 2 and angles of attack less than 30 deg. The code contains approximations to handle blunt leading edges of fins, and various starting solutions are incorporated for the body nose tip. Real gas effects applicable to very high Mach numbers are modeled4 by incorporating the high-temperature effects of air. Additionally, a body flow separation model5 is available in the ZEUS code.

The most recent version of the code is designated NEARZEUSIN. It is applicable to conventional missile-type configurations, as well as airbreathing missile configurations with two-dimensional, external-compression inlets for which the normal shock is at or downstream of the cowl lip.

A companion boundary layer module, ZEUSBL,6,7 contains an integral boundary layer method designed specifically to be used in tandem with the NEARZEUSIN code. It is based on the MEIT code8 which was originally designed for reentry vehicles. In the calculation procedure, NEARZEUSIN provides the inviscid solution to ZEUSBL, which performs boundary layer predictions using a two-dimensional formulation. Special procedures are included to account for transition, induced effects, shock-boundary layer interaction, and accurate computation of fin/wing leading edges.

The NEARZEUSIN/ZEUSBL codes are robust and capable of treating realistic configurations efficiently and accurately. Run times on a Pentium 3 PC are of the order of under a minute for a simple body-alone configuration, under five minutes for a body-canard-tail configuration at a high Mach number and including real gas effects, and under ten minutes for the 2-D inlet missile configurations described in Reference 9. Postprocessing capabilities include "generic" PLOT3D-type output for use with commercially available graphics programs such as TECPLOT. To date, NEARZEUS/ZEUSBL and NEARZEUSIN/ZEUSBL have been installed on the following computer platforms: SunSPARC, SunULTRA, HP, IBM 6000 IAX, SGI, DEC Alpha/VMS and Alpha/UNIX AXP, and PC.


During the development of ZEUS and NEARZEUS (and the companion boundary-layer module, ZEUSBL), comparisons were made4, 7, 10-14 for a wide range of supersonic configurations, from simple body-alone shapes at low supersonic Mach numbers to a wave-rider configuration at Mach number 20.

A recent application of the latest NEARZEUSIN/ZEUSBL codes to a two-dimensional, single-inlet, airbreathing missile configuration is shown below. Note that for the comparisons of measured and predicted aerodynamic characteristics, the axial force coefficient does not include base axial force; the measured axial force includes a correction for internal flow.

Additional applications of the NEARZEUSIN/ZEUSBL codes to conventional and to single- and twin-inlet airbreathing missile configurations are presented in Reference 9, which also contains further details about the software.


  1. Wardlaw, A. B., Jr., and Davis, S. F., "A Second Order Godunov Method for Tactical Missiles," Applications of Computational Fluid Dynamics in Aeronautics, AGARD CP 412, Apr. 1986.
  2. Wardlaw, A. B., Jr., and Davis, S. F., "A Second Order Godunov Method for Supersonic Tactical Missiles," NSWC TR 86-506, Dec. 1986.
  3. Wardlaw, A. B., Jr., Baltakis, F. P., Martin, F. M., Priolo, F. J., and Jettmar, R. U., "Godunov's Method for Supersonic Tactical Missile Computations," AIAA 85-1812, Aug. 1985.
  4. Priolo, F. J., Wardlaw, A. B., Jr., and Kuhn, G. D., "High-Temperature Effects for Missile-Type Bodies Using the Euler Solver, ZEUS," AIAA 91-3259, Sept. 1991.
  5. Priolo, F. J. and Wardlaw, A. B., "Euler Space-Marching Computations with Crossflow Separation for Missile-Type Bodies," AIAA 90-0616, Jan. 1990.
  6. Perkins, S. C., Jr., Wardlaw, A. B., Jr., Priolo, F., and Baltakis, F., "NEARZEUS User Manual, Vol. I, Operational Instructions; Vol. II, Sample Cases; Vol. III, Boundary Layer Code, ZEUSBL; Vol. IV, NEARZEUSIN, Application of NEARZEUS to Configurations with 2-D, External Compression Inlets," NEAR TR 459, Jan. 2002.
  7. Wardlaw, A. B., Jr., and Baltakis, F. P., "An Integral Boundary Layer Procedure for Tactical Missiles," AIAA 92-1024, Feb. 1992.
  8. Kwong, K., Suchsland, K., and Tong, H.,"Momentum/Energy Integral Technique (MEIT) User's Manual," Aerotherm UM-78-86, Feb. 1978.
  9. Perkins, S. C., Jr., Love, J. F., and Dillenius, M. F. E., "Recent Applications of Space- Marching Euler Solver NEARZEUSIN/ZEUSBL to Conventional and Airbreathing Missile Configurations," AIAA 2002-2717, June 2002.
  10. Priolo, F. J. and Wardlaw, A. B., Jr., "Induced Roll Computations for Conventional Missiles," AIAA 89-0331, Jan. 1989.
  11. Evans, J. and Wardlaw, A. B., Jr., "Prediction of Tubular Projectile Aerodynamics Using the ZEUS Euler Code," Journal of Spacecraft and Rockets, Vol. 26, No. 5, Sept./Oct. 1989, pp. 314-321.
  12. Priolo, F. J. and Wardlaw, A. B., Jr., "Supersonic Non-Circular Missile Computations," AIAA 88-0278, Jan. 1988.
  13. Priolo, F. J. and Wardlaw, A. B., Jr., "A Comparison of Inviscid Methods for Supersonic Tactical Missiles," AIAA 87-0113, Jan. 1987.
  14. Kuhn, G. D., "Application of a Supersonic Euler Method to Pegasus Aerodynamics," AIAA 93-0764, Jan. 1993.

    For software licensing information please contact:

    Aero Software Licensing and Training

    Missile Aerodynamics Prediction:  MISL3
    Detailed Missile Loads:  MISDL
    Euler Solver: NEARZEUSIN (with Inlets) /ZEUSBL
    Aircraft Store Separation and Carriage Loads Analysis: STRLNCH
    Aircraft Unsteady Maneuvering: SHAMAN
    Unsteady Hydrodynamic Analysis: SUBFLO_2
    User’s Training for all NEAR Software
    State Department Export License and TAA Preparation as Required



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