Flight Loads


ZEUS - Euler Unsteady Aerodynamic Solver


ZEUS is ZONA’s Euler Unsteady Aerodynamic Solver that integrates the essential disciplines required for aeroelastic design/analysis. It uses an Euler equation solver as the underlying aerodynamic force generator coupled with structural finite element modal solution to solve various aeroelastic problems such as flutter, maneuver loads, gust loads, and static aeroelastic/trim analysis. Structural nonlinearities can also be included to perform a nonlinear aeroelastic analysis.

The Euler equation solver solves the Euler equations on a Cartesian grid system using a cell-centered finite volume method with dual-time stepping algorithm for unsteady solutions. The viscous effects are included by coupling the Euler solution with a steady boundary-layer equation. For turbulence closure, the Green’s lag entrainment is employed. Because ZEUS solves the Euler equations with boundary layer coupling, the requirement of large computing resources by a Navier-Stokes code can be avoided. Therefore, ZEUS provides a good balance between the complete modeling of the flow physics and the computational efficiency.

Completely Automated Mesh Generation Scheme

Y-Zone Technique For Automated Mesh Generation
All components within each block are projected on an X-Y plane. On this X-Y plane, all components are divided into several spanwise zones, called the Y-Zones. The Y-Zone technique can automatically generate the mesh by a line-tracing method that spans across all Y-Zones. An example of division of an aircraft model into spanwise zones is shown at right with descriptions of each zone listed below.

ZONE 1: Left launcher
ZONE 2: Outboard left wing
ZONE 3: Inboard left wing and outboard left horizontal tail
ZONE 4: Outboard left strake and inboard left horizontal tail
ZONE 5: Inboard left strake
ZONE 6: Fuselage
ZONE 7: Inboard right strake
ZONE 8: Outboard right strake and inboard right horizontal tail
ZONE 9: Inboard right wing and outboard right horizontal tail
ZONE 10: Outboard right wing
ZONE 11: Right launcher

Overset Mesh for Complex Configuartions
  • Complex configurations can be modeled by multiple blocks of mesh with over-lapping regions; the overset mesh.
  • Communication of flow solutions among blocks is through the interpolation of solutions in the overlapping regions.
  • Solution convergence is acheived by sub-iterations.

3D Spline Module
The 3D Spline module establishes the displacement/force transferal between the structural Finite Element Method (FEM) module and the ZEUS surface panel model.

It consists of four spline methods that jointly assemble a spline matrix. These four spline methods include:

  • Thin Plate Spline
  • Infinite Plate Spline
  • Beam Spline
  • Rigid Body Attachment methods

The spline matrix provides the x, y and z displacements and slopes in three dimensions at all aerodynamic grids.
Displacement of ZEUS Panel Model Splined to FEM Model

Click here to view Validation Test Cases

ZEUS Licensing Information

ZEUS is available for annual licensing (1 token = 1 license).

Features included with the ZEUS License:

  • A CFD code whose program architecture is specially designed for aeroelasticians.
  • Euler solver with boundary layer option to provide an appropriate balance between the complete modeling of flow physics and computational efficency.
  • Automated mesh generation requiring only the surface panel model as input.
  • Overset mesh scheme for modeling of complex configurations such as whole aircraft with external stores.
  • Includes ZAERO 3D spline module and FEM modal solution importer.
  • Supports parallel computation using OpenMP.
  • Generates time-domain aeroelastic response or frequency-domain generalized aerodynamic forces for flutter, LCO and static/trim aeroelastic analysis.
  • ZONA will assist the new user by telephone/fax/email consultation to successfully run test cases in the documentation (i.e., turn-key operation) at no cost to the user.
  • Customer service is included in the annual license fee (up to 20 hours per year by telephone, fax, email, etc.) Additional support will be charged at ZONA’s T&M rate.
  • Includes software upgrades as they become available.

System Requirements and Platform


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