# US 2014/0195210 A1 · Simulation method for determining aerodynamic coefficients of an aircraft

> Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt

- Number: US 2014/0195210 A1
- Document ID: US20140195210A1
- Status: Published application
- Kind: A1
- Application number: 13/882,446
- Filed: 2011-11-02
- Published: 2014-07-10
- Earliest claimed: 2010-11-03
- Assignees: Airbus Operations GmbH
- Inventors: Benoit Calmels
- Web page: https://patentgrep.com/patent/US20140195210A1

## CPC

- G06F 30/28: using fluid dynamics, e.g. using Navier-Stokes equations or computational fluid dynamics [CFD]
- G01M 9/08: Aerodynamic models
- G06F 30/20: Design optimisation, verification or simulation (optimisation, verification or simulation of circuit designs G06F30/30)
- G05D 1/0808: {specially adapted for aircraft}
- G06F 30/15: Vehicle, aircraft or watercraft design
- G06F 2111/10: Numerical modelling
- Y02T 90/00: Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)
- G01M: TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G05D: SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- Y02T: CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION

## Abstract

A computer method of simulating a fluid flow in an aircraft environment to determine at least one aerodynamic coefficient, comprising obtaining a first series of values of the aerodynamic coefficient. The method also includes defining a criterion for convergence of said aerodynamic coefficient, selecting a determined set of terms belonging to said first series, defining a monotonic function configured to make a relatively expanding transformation in said determined set relative to the complement of said set, applying said monotonic function on said first series to form a second series of values of the aerodynamic coefficient, determining said aerodynamic coefficient by plotting a variation curve representative of said second series of values of the aerodynamic coefficient, and displaying said variation curve including an intrinsic zoom of the convergence zone of said aerodynamic coefficient.

## Claims

### Claim at position 1

1-13. (canceled)

### Claim 14

A computer method of simulating a fluid flow in an aircraft environment to determine at least one aerodynamic coefficient characterising the aerodynamic behaviour of at least one element of the aircraft, said method comprising a digital solution of equations modelling the fluid flow in said environment, according to a model configured using physical parameters of the fluid, said digital solution being made iteratively to obtain a first series of values of the aerodynamic coefficient indexed by the number of iterations, the method comprising the steps:
defining a criterion for convergence of said aerodynamic coefficient using processing means,
selecting a determined set of terms belonging to said first series of values of the aerodynamic coefficient, as a function of said convergence criterion, using the processing means,
defining a monotonic function configured to make a relatively expanding transformation in said determined set relative to the complement of said set, using the processing means,
applying said monotonic function on said first series to form a second series of values of the aerodynamic coefficient, said second series defining a global change to said aerodynamic coefficient with a local expansion in a convergence zone corresponding to said determined set, using the processing means,
determining said aerodynamic coefficient by plotting a variation curve representative of said second series of values of the aerodynamic coefficient as a function of the number of iterations, using the processing means and,
displaying said variation curve including an intrinsic zoom of said convergence zone giving details of the convergence of said aerodynamic coefficient, on output means.

### Claim 15 (depends on 14)

The method according to claim 14, wherein said convergence criterion is defined as a function of a predetermined number of iterations.

### Claim 16 (depends on 15)

The method according to claim 15, wherein the predetermined number of iterations corresponds to a total number of iterations.

### Claim 17 (depends on 14)

The method according to claim 14, wherein the cardinality of said determined set is defined as a function of a predetermined order of magnitude of the aerodynamic coefficient.

### Claim 18 (depends on 14)

The method according to claim 14, wherein said monotonic function corresponds to a mixed linear-logarithmic transformation with a linear behaviour in said determined set and a logarithmic behaviour outside said set, defined as follows:
F(x)=x/10psi|x|≦10p and
F(x)=sign(x)·log10(|x|/10p−1)si|x|>10p,
where p is an order of magnitude of precision.

### Claim 19 (depends on 15)

The method according to claim 15, further comprising adding a constant to each term in the first series before application of said monotonic function, said constant being equal to the value of the aerodynamic coefficient at said determined number of iterations.

### Claim 20 (depends on 19)

The method according to claim 19, further comprising applying an absolute value operation on the terms of said second series to form a third series of positive terms.

### Claim 21 (depends on 20)

The method according to claim 20, further comprising the following steps:
applying an oscillation filtering operation on said third series to form a fourth monotonic series; and
plotting a positive and monotonic variation curve representative of said fourth series.

### Claim 22 (depends on 18)

The method according to claim 18, further comprising the following steps:
plotting a preliminary variation curve C0(I) representative of said first series of values of the aerodynamic coefficient as a function of the number of iterations,
defining at least one interval of values of the aerodynamic coefficient corresponding to said determined set,
applying said mixed linear-logarithmic monotonic function on said preliminary variation curve operating a linear transformation inside said interval and a logarithmic transformation outside said interval to form said variation curve.

### Claim 23 (depends on 22)

The method according to claim 22, further comprising the steps:
calculating a final value C0final=C0(Imax), a maximum value C0max=max(C0(I)), and a minimum value C0min=min(C0(I)) of said preliminary variation curve C0(I),
recursively defining a fifth decreasing series I0p, I0p+1, . . . , I0i, . . . , I0m−1, I0m such that I0i>C0min∀iε[p, m−1], I0m≦C0min, I0p=M0p−10p, and M0p≈C0final to the nearest 10p, where p is an order of magnitude of precision,
recursively defining a sixth increasing series S0p, S0p+1, . . . , S0i, . . . , S0n−1, S0n, such that S0i<C0max∀iε[p, n−1], S0n≧C0max, and S0p=M0p+10p,
defining a seventh ordered series as a function of said fifth and sixth series: I0m<I0m−1< . . . <I0i< . . . <I0p+1<I0p<M0p<S0p<S0p+1 . . . <S0i< . . . S0n−1<S0n,
defining a lower interval [I0m, I0p], a median interval [I0p, S0p], and an upper interval [S0p, S0n],
applying said mixed linear-logarithmic monotonic function on said preliminary variation curve using said seventh ordered series to form said variation curve as follows:
C2′(I)=F(C0(I)−M0p)
I2i=F(I0i−M0p)∀iε[p,m]
S2i=F(S0i−M0p)∀iε[p,n]
M2p=F(M0p−M0p)=F(0)=0.

### Claim 24 (depends on 22)

The method according to claim 22, wherein defining said interval comprises the steps:
translating said preliminary variation curve by the value of the aerodynamic coefficient at the total number of iterations to form an intermediate variation curve,
determining a high order of magnitude m relative to said intermediate variation curve, defined as being the relative integer m such that:
10m−1<max|C1(I)|≦10m, and
defining said interval by extremities equal to −10p and 10p where p is an order of magnitude of precision that is strictly less than said high order of magnitude m, and
applying said mixed linear-logarithmic monotonic function on said intermediate variation curve using said ordered series to form said variation curve as follows:
C2′(I)=C1(I)·10−p for |C1(I)≦10p, and
C2′(I)=sign(C1(I))·[log10(|C1(I)|)−p+1] for |C1(I)|>10p.

### Claim 25 (depends on 22)

The method according to claim 22, further comprising the steps:
applying an absolute value on said variation curve to form a positive variation curve C3(I), and
plotting a positive monotonic variation curve C4(I) using a recurrence calculation for I decreasing between Imax and 1, according to the following equations:
C4(Imax)=C3(Imax)
C4(I)=max(C3(I),C4(I+1))pour I≠Imax

### Claim 26 (depends on 14)

A computer program comprising code instructions stored in non-transient memory for use of the simulation method according to claim 14 when it is run on a computer.