CFD Effectiveness = Quality x Acceptance

where,

Quality – Fidelity of Data

Acceptance – Timeliness of Data

CFD should essentially meet 3 requirements:

*I. Rapid Turnaround.*

II. Reliable Accuracy.

III. Affordable Cost.

A typical design process includes:

i. Pre-conceptual

ii. Conceptual

iii. Preliminary

iv. Critical

v. Production

**I. Linear Potential Methods**

- Solve 1st order PDE
- Based on Prandtl-Glauert /Laplace equation.
- Green’s Theorem
- Surface Discretization
- Vortex-Lattice Methods (VORLAX code). Mean surface representation of geometry & vortex filaments as singularities.
- Panel Methods (Actual surface geometry discretized)
- Purely Subsonic & Supersonic flows.
- Good estimate of F & M and distributed air loads for steady-level flight.
- 1960’s, established 1980’s.

**II. Non-Linear Potential Methods**

- Solver 2nd order PDE
- Based on Transonic Small Perturbation (TSP) or Full Potential Equation ( FPE).
- Benefit of modelling transonic flows with Shocks.
- Need to solve non-linear PDE’s.

**III. Euler Methods**

- Highest level of Inviscid approximations.
- Subsonic to Hypersonic regimes.
- Captures Potential flow regimes (Wake sheds from wing & leading edges)
- Solving atleast 4 and generally 5 coupled 1st order PDE’s instead of one 2nd order PDE.
- 1980’s : Structured Grid Generation, Patched Multiblock, Overset Mesh
- Mid 1980’s : Unstructured grid generation.
- Convergence acceleration techniques- i) Local time-stepping, ii) Multi-Grid (FMG)
- Explicit and Implicit time-marching schemes.
- Time dependent equations
- Codes didnot provide Total Drag (incl. Skin Friction) and thus N-S codes were pursued in parallel.

**IV. Navier-Stokes Method**

- Same equation except the diffusion terms in N-S solver
- Elimination of the diffusion term converts the N-S equations to Euler equations as they both share some convective terms.
- RANS- Turbulence Model – Simple algebraic model to sophisticated Reynolds’ Stress model.

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