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  • Missile Aerodynamics
  • Transonic Aerodynamics
  • Unsteady Aerodynamics

Models active in this Demonstration Case

  • Compressible flow
  • Turbulence models
  • Energy models
  • Ideal gasses
  • Double Precision


To profile the accuracy and performance of Envenio’s EXN/Aero manycore CFD solver on a challenging missile aerodynamics test case.

Case Description

A generic missile geometry is considered in the present study with the canards at 15o angle of attack. The geometry of the missile configuration is shown in Fig. 1. The dimensions of the missile are as follows:


Length 1.4 m

Missile body diameter 0.07 m

Tail body diameter 0.04 m

Canard length 0.03 m

Canard span 0.04 m

Canard thickness 0.003 m

Angle of attack for the canards 15o

Tail fin length 0.05 m

Tail fin height 0.05 m

Tail fin max thickness 0.005 m


The free flow conditions employed in the present study correspond to sea level conditions and to a free stream Mach number of 0.5.

The Reynolds number with respect to the missile length is 2849872. No shock waves are developed around the missile.


Screen Shot 2018-01-09 at 16.48.13.png

Figure 1: Missile geometry. 


Screen Shot 2018-01-09 at 16.49.05.png

Figure 2: Tail fins geometry.


Mesh Description

The surface mesh is shown in the following figures where it is seen that a mixed element type mesh has been generated. Specifically, the cylindrical body of the missile was meshed with triangular elements while the canards and tail fins were meshed with quadrilateral elements. The mesh was refined at the missile nose, where the flow stagnates, in order to resolve the high local flow gradients.


Screen Shot 2018-01-09 at 16.49.37.png



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Screen Shot 2018-01-09 at 16.51.01.png


Figure 3. Surface mesh


The volume mesh is depicted in Fig. 4 for the configuration with the canards at 15o AoA. The volume mesh is comprised of pentas, hexahedral and tetrahedral elements and has about 2.7 million elements. The  distribution is as follows:

Screen Shot 2018-01-09 at 16.53.28.pngScreen Shot 2018-01-09 at 16.53.10.png



Screen Shot 2018-01-09 at 16.54.25.png


 Figure 4. Hybrid volume mesh


Simulation Setup

Solver Control for the canards at 15 o AoA

Steady state and Transient simulation


For the steady state we start with a CFL of 2 and progressively increased it to 50000.

For the transient simulation a constant dt of 1.0e-5 sec


Convergence criteria: 1.0e-4 RMS and 1e-2 Max

Coefficient loops 10


Advection scheme: 1st run first order Upwind (steady state)

Advection scheme: 2nd run second order TVD  (restart from 1st run - unsteady)


EXN GPU Allocation     1 Nvidia K40

EXN CPU Allocation     2 Intel Xeon 2.6GHz


X-axis orientation         Longitudinal axis

Y-axis orientation         Yaw axis

Z-axis orientation         Pitch axis

Boundary Conditions

Turbulence Kinetic Energy       0.0001 m2/s2

Turbulence K Dissipation          0.0003 m2/s3

Wall model                               Smooth wall

Outlet                                       Constant Specified Pressure


Initial Velocity                           [170.1,  0,  0] m/s

Angle of Attack                        0.0

Mach Number                           0.5

Temperature                            300 Kelvin

Pressure                                  101.325 kPa

Fluid Settings

Initial Velocity                                       [170.1,  0,  0] m/s

Initial Turbulence Kinetic Energy                      0.0001 m2/s2

Initial Turbulence K Dissipation             0.0003 m2/s3


Turbulence Model        RANS SST k-ω

Flow type                     Compressible air, Ideal Gas (R = 286.9 J/kg K)

Constant Viscosity        1.715 x 10-5 kg/m s

Precision                      Double precision


Simulation Outcomes, Timing, and External Factors

The Mach number distribution is shown in Fig. 5. The pressure distribution on the missile surface is shown in Fig. 6. A vortex ring is formed at the tail of the missile and it is resolved quote well by EXN/Aero as it is shown in Fig. 7. Moreover, flow separation takes place over the canards and the separation bubble is resolved quite well also, as it is seen in Fig. 8.

Screen Shot 2018-01-09 at 16.55.34.png



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Screen Shot 2018-01-09 at 16.56.43.png


Figure 5. Mach number distribution

 Screen Shot 2018-01-09 at 16.57.27.png

Figure 6. Pressure distribution over the missile

 Screen Shot 2018-01-09 at 16.57.56.png

Figure 7. Vortex ring at the tail of the missile

 Screen Shot 2018-01-09 at 16.58.28.png

Figure 8. Separation bubble over the canards.


Table 1: Simulation performance outcomes

Reporting Item


Simulation starting conditions

Transient simulation initial conditions corresponded to steady state calculation.

Time to 1st wash-through

Simulated time of 0.0082 sec requires 820 time steps.

This is equivalent to a wall clock-time of ~8.9hrs.

Real time per time step


CPU type

Intel Xeon @ 2.6GHz

CPU cores


GPU type

NVIDIA Tesla K40



  • External Unsteady Flow
  • RANS SST k-ω
  • Compressibility
  • Energy Models
  • Double Precision
2018-01-9 | Categories: CFD

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