EP1167865A1 - Method of automatic mesh generation of conduits to implement flow model coding - Google Patents

Abstract

Mapping conduits to enable flow modelling comprises the use of a series of networks having maximum and minimum sizes. A conduit is analyzed into sections separated by bends. Networks of maximum size are assigned to the central parts of the sections and networks of minimum size to the bends. Networks of increasing or decreasing size are assigned to the remainder of the conduit. Preferred Features: The topography of the conduit may be represented by a simplified graph of level against distance.

Description

The present invention relates to an automatic mesh method of conduits allowing the implementation of fluid modeling codes routed through these lines.

The method according to the invention finds applications in numerous areas. It can especially be used in the field of production of hydrocarbons for the implementation of flow simulation codes multiphase in oil lines from production sites to destination sites.

The mesh obtained by the method can be used in particular for the implementation of the TACITE modeling code (registered trademark) intended for simulate permanent or transient flows of hydrocarbons in pipes. Different algorithms to conduct the simulation of flows according to the TACITE code have been the subject of US Patents 5,550,761, FR 2,756,044 and FR 2,756,045 (US 5,960,187).

The flow modes of multiphase fluids in tubes are extremely varied and complex. Two-phase flows, for example, can be laminated, the liquid phase flowing in the lower part of the pipe, or intermittent with a succession of liquid and gaseous plugs, or still well dispersed, the liquid being entrained in the form of fine droplets. The flow mode varies in particular with the inclination of the pipes in relation to the horizontal and it depends on the flow rate of the gas phase, the temperature etc. The slip between the phases which varies according to whether one considers the sections of ascending or descending pipe, causes pressure variations without there always have compensation. The characteristics of the flow network (dimensioning, pressure, gas flow, etc.) must be determined with care.

The TACITE simulation code takes into account a number of parameters directly affecting the physics of the problem to be treated. Among these, we find the properties of fluids and flow modes, the variations topographic (variations in length, inclination, diameter etc.), roughness pipes, its thermal properties (number of layers of insulation and their nature) or the arrangement of equipment along the pipe (pumps, injectors, separators, etc.) that cause changes in physical flow.

State of the art

The mesh of a physical domain is an essential step during a Numerical simulation. On its quality depend the validity of the results and the times Calculation. It is therefore fundamental to provide the code with a correct mesh before start a simulation. We generally judge the quality of a mesh at its ability to properly describe physical phenomena without the simulation taking too much time, so there is always an optimal mesh for each problem studied. An unsuitable mesh can lead, in the execution of the numerical diagram which governs the simulation, with errors that are difficult to detect, at least at the first first, even make the calculation impossible and stop the execution of the code, if it is too aberrant. Code users do not necessarily have experience sufficient in numerical analysis for the realization of a correct mesh, susceptible to really account for the physical phenomena that we want to study.

The topography of a cylindrical pipe can be compared to a succession of line segments connecting successive points. In coordinates Cartesian, two successive points of the pipe on its vertical portions (ascending or descending) can have the same abscissa (curve A in Fig. 1). he it is therefore much better to represent the elevation of each point as a function of its curvilinear abscissa along the pipe. With this mode of representation, successive points of driving different elevations necessarily have two abscissas separate curves and the slope of the pipe sections is at most equal to 45 ° by horizontal relationship (case of ascending or descending sections absolutely vertical curve B in Fig. 1). An abscissa always corresponds to an ordinate and only one.

With a little physical sense, some mesh errors can be avoided. In places of the pipe likely to experience large variations physical parameters if we are able to predict them, we can impose a finer mesh than elsewhere. Thus, one carries out less computations with each step of time, while maintaining the desired finesse in important places. But in the optics of obtaining a continuous solution, the transition from a fine mesh to a mesh the coarser must also be continuous.

Fig. 2a shows for example a portion of W-shaped pipe with a length 2 km including four 500 m sections. If we discredit such conduct by stitches with a constant 40 m pitch from start to finish, leaving the stitches aside of the route at 500 m and 1500 m. The simulation will not render correctly account for the accumulation of liquid at these low points in the topography. More importantly, the calculation is distorted by the fact that the angles of the W by horizontal straight line segments (Fig. 2b). Physical phenomena do will not be those sought.

• 1 - Assurer la convergence du calcul ;
• 2 - Représenter au mieux les accumulations importantes de liquide dans les points bas de la conduite ;
• 3 - Placer les équipements sur un bord de maille ;
• 4 - Imposer à deux mailles consécutives d'avoir le même ordre de longueur ;
• 5 - Respecter la longueur totale de la conduite ;
• 6 - Limiter le nombre de mailles au minimum possible en respectant les contraintes précédentes, pour ne pas trop pénaliser la simulation avec le temps de calcul.

The method according to the invention makes it possible to automatically obtain a mesh or discretization of a pipe taking best account of the topography and the physical parameters affecting the physics of the flows, subject to the following constraints:

• 1 - Ensure the convergence of the calculation;
• 2 - Represent as much as possible the large accumulations of liquid in the low points of the pipe;
• 3 - Place the equipment on a mesh edge;
• 4 - Impose on two consecutive stitches to have the same order of length;
• 5 - Respect the total length of the pipe;
• 6 - Limit the number of meshes to the minimum possible while respecting the previous constraints, so as not to penalize the simulation too much over time.

Compliance with the previous six constraints is not an easy task, but it is the required passage to avoid meshing the conduct studied in a homogeneous way, without worry about the physics of the problem, as most meshers do automatic.

To limit the number of meshes, it is necessary to seek, if possible, to simplify the topography to retain only the only areas of the pipe where find significant variations in the profile likely to occur significant on physical phenomena.

The method according to the invention

The method according to the invention makes it possible to automatically mesh a 1D pipe with any topography or profile over its entire length in order to facilitate the implementation of flow modeling codes. The mesh obtained by the method presents a distribution of meshes of dimensions variables, appropriate to take best account of the physics of flows.

The method is characterized in that, having defined a minimum size of mesh and a maximum mesh size, the pipe is subdivided into sections delimited by elbows, we place a mesh of minimum size on the one hand and on the other of each elbow, we position large meshes of size at most equal to the maximum size in the central portion of each section, and we distribute increasing or decreasing mesh sizes on the intermediate portions of each section between each mesh of minimum size and the central portion.

The distribution of increasing or decreasing mesh sizes over the portions of each intermediate section between each mesh of minimum size and the central portion, is obtained for example by determining the points of intersection with each section of pipe, a bundle of straight lines competing at a point and forming a constant angle between them.

We determine for example the position of the vertex of the line bundle on an axis passing through a bend in the pipe and perpendicular to each section, a distance from it which is a function of the size of the extreme meshes of each intermediate portion and their gap.

Automatic mesh positioning with smaller meshes at proximity of the ends of each section allows greater care to be taken modeling of phenomena in the pipe sections with changes in direction (sag or elbow).

The method according to the invention preferably includes a simplification prior to the pipe topography so that the total number of meshes of the pipe mesh allow realistic modeling of the physics of phenomena in a fixed time.

According to a first mode of implementation, the method comprises a representation of the pipe in the form of a graph connecting the curvilinear abscissa and the level variation, and a simplification of the number of sections a) by affecting at each point between two successive sections a weight taking into account the length of the sections and their respective slopes, b) by selecting from the points arranged in ascending or descending weight order, those with the most weight high, the simplified topography being that of the graph passing through the points selected.

The selection of the most weighted pipe points is obtained for example by locating in the arrangement of points a discontinuity of weight greater than a certain fixed threshold.

According to another implementation mode, the method includes a representation of the pipe in the form of a graph connecting the curvilinear abscissa and the level variation, and a simplification of the number of sections by a) the formation of the frequency spectrum of the curve representative of the topography of the driving, b) the attenuation of the highest frequencies of the spectrum translating the most small variations in topography and c) reconstruction of a simplified topography corresponding to the rectified frequency spectrum.

The selection is made for example by a) a sampling of the curve representative of the topography of the pipe with a chosen sampling pitch so that the smallest section of the pipe contains at least two steps b) a determination of the frequency spectrum of the curve sampled by application, c) spectrum correction by low-pass filtering whose cutoff frequency is chosen according to a number of meshes maximum fixed to subdivide the pipe, and, d) a determination of the topography corresponding to the rectified frequency spectrum.

The two previous automatic simplification modes can be applied independently of one another or else successively, the second mode being applied preferably when the first mode does not allow for simplification notable of the topography.

Summary presentation of the figures

• -la Fig.1 montre deux modes de représentation schématique de la variation de l'élévation (E) d'une conduite en fonction de l'abscisse (A) selon que c'est une abscisse cartésienne (ca) ou curviligne (cu);
• les Fig.2a, 2b montrent respectivement la topographie schématique d'une conduite en forme de W en coordonnées curvilignes, et une partie agrandie de cette même topographie, discrétisée par un maillage approprié ;
• la Fig. 3 montre un mode d'attribution de poids (P) à des points de la topographie d'une conduite ;
• la Fig. 4 montre un exemple de spectre adimensionnel (PA) de poids en fonction de la longueur (L);
• la Fig. 5 montre un exemple d'arrangement des points par paliers de poids décroissants, permettant de repérer la position d'un seuil et de simplifier la topographie de la conduite ;
• la Fig. 6 montre un exemple de topographie d'une conduite marine (variation de l'élévation E en fonction de l'abscisse curviligne ca) comportant un « riser» à ses extrémités ;
• la Fig. 7 montre la topographie simplifiée de la même conduite, que l'on obtient par sélection des poids ;
• la Fig. 8 montre que, sans les « risers » terminaux, la forme générale de la même conduite est plus difficile à dégager ;
• la Fig.9 montre un spectre de fréquence typique d'une conduite ;
• la Fig. 10 montre un exemple de tronçon de conduite avec une distribution de mailles de différentes tailles, les plus petites M1 étant positionnées aux coudes, les plus grandes, M2 étant placées dans le tiers central, les mailles intermédiaires M3 étant interposées et résultant d'une interpolation I entre les unes et les autres ;
• la Fig. 11 montre un mode de formation de mailles de tailles croissantes ;
• la Fig. 12 illustre le mode de découpage angulaire d'une portion intermédiaire sur un tronçon de conduite ; et
• la Fig.13 montre le maillage obtenu par la mise en oeuvre de la méthode, sur une conduite sous-marine de 90km de longueur.

Other characteristics and advantages of the method according to the invention will appear on reading the following description of nonlimiting exemplary embodiments, with reference to the accompanying drawings in which:

• -Fig. 1 shows two modes of schematic representation of the variation in elevation (E) of a pipe as a function of the abscissa (A) depending on whether it is a Cartesian abscissa (ca) or curvilinear (cu) ;
• Fig.2a, 2b show respectively the schematic topography of a W-shaped pipe in curvilinear coordinates, and an enlarged part of this same topography, discretized by an appropriate mesh;
• Fig. 3 shows a method of assigning weight (P) to points on the topography of a pipe;
• Fig. 4 shows an example of an adimensional spectrum (PA) of weight as a function of length (L);
• Fig. 5 shows an example of arrangement of the points in decreasing weight steps, making it possible to identify the position of a threshold and to simplify the topography of the pipe;
• Fig. 6 shows an example of topography of a marine pipe (variation of the elevation E as a function of the curvilinear abscissa ca) comprising a "riser" at its ends;
• Fig. 7 shows the simplified topography of the same pipe, which is obtained by selection of the weights;
• Fig. 8 shows that, without the terminal “risers”, the general shape of the same pipe is more difficult to identify;
• Fig.9 shows a typical frequency spectrum of a pipe;
• Fig. 10 shows an example of a pipe section with a distribution of meshes of different sizes, the smallest M1 being positioned at the elbows, the largest, M2 being placed in the central third, the intermediate meshes M3 being interposed and resulting from an interpolation I between each other;
• Fig. 11 shows a mode of forming meshes of increasing sizes;
• Fig. 12 illustrates the mode of angular cutting of an intermediate portion on a pipe section; and
• Fig.13 shows the mesh obtained by the implementation of the method, on an underwater pipe of 90km in length.

DETAILED DESCRIPTION I) Simplification of the topography of a pipe

We generally have no difficulty in highlighting it at first glance the overall shape of any profile. The method according to the invention allows, by purely mathematical criteria, automatic identification of the configuration of a pipe, based on a spectral analysis of the curve representative of profile variations. Among all the spectra that can be associated with a topography given, we are looking for one that makes it possible to distinguish the portions of the profile to simplify and important profile portions.

I-1) First mode of simplification

In a topography, the only criteria ensuring that a point is simplifiable compared to another, can only be the lengths of the sections which surround it and the angular difference separating them (Fig. 3). When we build the two "Spectra" (Section indices) - (Section lengths) and (Curvilinear abscissa points) - (Angular difference between incoming and outgoing sections), we realize that they present significant differences in orders of magnitude but also that these two spectra are independent, so that by simplifying negligible points in one, important points may have been deleted in the other.

To group these two spectra into one, we will assign to each topographic point a weight taking into account the lengths of sections, and the angular differences which separate them. For example, the following weighting is used: Weight = The 1 . The 2 The 1 + The 2 ( P 2 - P 1 ) 2 where L ₁ and L ₂ are the lengths of the sections, and P 1 = there 1 x 1 and P 2 = there 2 x 2 are the slopes. Thus, at equal lengths, the sections separated by the smallest difference in slope will be simplified. And at equal angles, we will simplify the shortest lengths.

Spectrum construction

The spectrum (Curvilinear abscissa - Weight) presents in the majority of cases, a succession of peaks of all sizes. These spectra such as that of Fig. 4 cannot generally be analyzed directly. Under these conditions, the technique used here consists in classifying the weights (P) in ascending or descending order and in assigning to them each the corresponding classification index (CI) by weight from 1 to N. Preferably, we use a representation (Log Weight-Index) which brings out the orders of magnitude better because a jump of n on such a spectrum means a ratio of 10 ⁿ on the weights. All the weights having the same order of magnitude are classified on more or less horizontal bearings. Two weights of different orders of magnitude will be separated by a vertical line segment. This leads to a cascading spectrum, making it possible to easily read the different orders of magnitude present in the topography. In the example of Fig. 5 for example, the logarithmic spectrum Log P contains two very distinct steps separated by a vertical segment.

We are looking for the first triplet of consecutive points in the spectrum, defined for example by a threshold Δ P fixed on the logarithmic scale (Δ P = 1 for example) between the second and the third, which follows a jump less than Δ P between the first and second. The first two points are of the same order of magnitude. All the following points are of an order of magnitude negligible compared to the first two. In this way, we make sure that all the weights to the right of the triplet in question will be at least 10 times less than the weight of the second and therefore negligible compared to the points upstream. On the correspondence table (curvilinear abscissa weight index), select the curvilinear abscissa points corresponding to the strongest weights selected. The simplified topography will be the line passing through these points.

In the example of topography in Fig. 6, there are three parts distinct. It begins with a 3 km riser, followed by a horizontal part sawtooth over 20 km which ends with another 200m riser also in Sawtooth. Its spectrum is that of Fig. 5. The first triplet which obeys the criterion threshold is formed by points 4, 5 and 6. The simplification threshold is point index 6. A jump greater than 2 in the logarithmic scale separates the landings horizontal on either side of points 5 and 6. This ensures that the points to left of index 5 have weights at least 100 times greater than those found to the right of index 6.

In this example, we simplify the topography by keeping only the points of curvilinear abscissa corresponding to the weights greater than or equal to that of point 6. We obtain the simplified topography of Fig. 7. The overall shape is kept. All the small sawtooth variations on the horizontal part of 20 km have been deleted. The number of points increased from 43 initially (Fig. 6) to 6, i.e. a reduction of a factor of 7. This case lends itself particularly well to thresholding, since the different orders of magnitude are visible on the initial topography.

The first simplification mode which has just been described is easy to implement. work and based on relatively simple algorithms executable quickly. he is suitable for topographies with several orders of magnitude, such as previous topography which could have been considerably simplified because it contained points having negligible weights compared to others.

The problem is quite different if we are only interested in the central part of this topography, removing the risers at the ends because in this case, as shown in the Fig.8, the general shape of the pipe is more difficult to identify. Simplification of this topography by a straight line connecting the point of departure and that of arrival, is no more possible. Its spectrum is exactly the same as that of the topography initial, except that it starts at point 6. No threshold is present in this part of the spectrum, the points all have the same order of magnitude. And even if the weight the highest is more than 100 times the lowest, we go from one to the other so keep on going.

I-2) Second simplification mode

For topographies with points having the same order of magnitude, which cannot be processed by the previous thresholding method, we proceed to spectral filtering. Small variations in the driving profile are reflected by high frequencies in the Fourier spectrum of the representative function of topography. By cutting or attenuating the highest frequencies of sound frequency spectrum, it is possible to simplify the topography.

To do this, we sample the topographic function and determine its spectrum by the method known as FFT (Fast Fourier Transform). The sampling step must be small enough to properly account for all frequency ranges in avoiding aliasing. To do this, the number of sampling points is chosen so that the smallest section of pipe contains at least two subdivisions to ensure that the Fourier transform will act on all even the most insignificant parts of driving. Attenuation of high frequencies must of course be performed with discernment and adjusted so that the reconstructed topographic function remains representative of the initial function.

The simplest method of filtering is, for example, to apply a threshold, all Fourier coefficients (FC) whose amplitude A (FC) is less than this threshold being eliminated (coefficients less than 40 for example on the example of the Fig.9. Only the information contained in frequencies below this threshold is retained. We reconstitute by reverse transform the simplified typography corresponding.

By setting a cutoff frequency, we set the maximum number oscillations of the reconstructed signal. If we only keep the first ten frequencies, the reconstituted function will follow the general shape of the pipe, with a maximum of twenty extrema.

II) Selection of mesh sizes on each pipe section Principle

The principle of the mesh will consist in independently meshing the sections of conduct between two imposed edges. As the interest of a well made mesh is to ability to properly observe fluid build-up in elbows it is preferable that the mesh is refined at the points of the topography likely to see build up of liquid or gas. This is why, we are going to arrange to place a short stitch before and after each elbow and larger between the elbows. On the other hand, it is not useful to finely mesh the intermediate parts of the sections between the elbows.

The topography of the pipe having been previously (when it was necessary) simplified and reduced to a certain number of sections, we fix for meshes a minimum size and a maximum size. We first isolate the edges of each of them (their entry, their exit) by small cells and then we insert mesh edges on their central part which is longer. he it is generally not useful to refine the input and output mesh outside the portions at the ends of each section so we can insert on a good share of the length of each section (for example over 2/3 of the length) of the maximum size that we have set.

As distribution, one can choose for example that the size of the meshes after the one following a bend, gradually increases over a third of the length of the section, remains constant over the next third to finally decrease gradually over the last third before the final short stitch as shown in Fig. 10.

Definition of minimum and maximum cell lengths

We will define two cell lengths, a minimum length, which will serve to isolate the mesh edges imposed by small cells, and a maximum length, which will be used to mesh the midpoints of the sections between two short cells.

All the meshes which one inserts after these two stages are deduced from initial cells by interpolation between a short cell and a long cell. They therefore have intermediate sizes. This property is interesting. It indicates that the total number of meshes will necessarily be between the number we would have obtained by meshing homogeneously with the minimum length, and the number obtained in the same way but with the maximum length. So we can control the total number of stitches from minimum and maximum sizes.

One of the constraints of automatic meshing lies in the number of total mesh. This must generate the shortest possible simulation time, while allowing a good visualization of physical phenomena. experience shows on the one hand that a discretization of less than 40 meshes does not allow a good physical description of the problems. On the other hand, meshes of more than 150 meshes generate too long simulations. The default mesh must therefore be fairly flexible and have between 40 and 100 stitches.

Such a low number of meshes is not suitable for all cases. The ideal number of meshes for a specific case depends on several factors, coming into counts in the numerical scheme. With equal topography for example, a case with a large number of section changes will require more mesh end. The method according to the invention leaves a great latitude to the user to choose the total number of meshes which suits him.

From this number N, the code calculates the minimum lengths Min and maximum length Max as follows: Low = The NOT + P Max = The NOT - P

Parameter P makes it possible to reduce the difference between the minimum lengths and maximum so as to gradually make the mesh homogeneous for large numbers of meshes.

This parameter is defined for example as follows. For a number of meshes requested less than or equal to 60 for example, we set it for example to 60. This is the default mesh. The parameter is worth 40. The smallest mesh will be worth L / 100 and the larger L / 20. The total number of meshes will be between 20 and 100.

A number of meshes greater than or equal to 150 means that the modeling to be treated is certainly more delicate. The goal is then to build a homogeneous mesh. For this, the minimum and maximum sizes must be close to each other. We will therefore set the parameter at 10. The total number of meshes will then be between L / N +10 and L / N -10. We obtain the requested number of meshes, to within 20 meshes, over more than 150.

To make so that the mesh is gradually homogenized between 60 and 150 meshes, one will calculate the parameter by linear interpolation between the two fields, which is expressed in the following way: P = 40 if N <60 P = - 1 3 NOT + 60 if 60 <N <150 and P = 10 if N> 150

This parameter being determined, it is possible to isolate the edges imposed by short cells and to discretize the midpoints of the sections by cells long.

It only remains to find a way to gradually move from one cell short to long. We know the lengths of the three cells, and we are looking to insert mesh edges on the central part. The mesh sizes thus created must be between those of the extreme cells. Starting from the smallest, the next stitch should always be longer than the previous one, but shorter than the next one.

• la taille d'une maille se déduise de celle de la précédente en la multipliant par un facteur f.
• la somme des n longueurs ainsi créées soit égale à (L1+L2)
• la taille de la dernière cellule puisse s'exprimer sous la forme f^{n +1}.L ₁ f.

In the general case, there is no pair ( f, n ) ∈ (R, N) such that:

• the size of a mesh is deduced from that of the previous one by multiplying it by a factor f.
• the sum of the n lengths thus created is equal to (L1 + L2)
• the size of the last cell can be expressed as f ^{n +1} . L ₁ f.

The same goes for a possible linear interpolation between the two sts. Knowing the three lengths requires a glut of data compared to the unknowns. It is then impossible to satisfy all the constraints.

To overcome this difficulty, we propose a geometric type method where we use the property that the segments L1, L2, L3, L4 cut on an axis by the straight lines of a regular beam (angular spacing α constant with respect to each other to others) whose apex is outside this axis, gradually vary (Fig. 11).

We consider (Fig.12) a pipe section starting with a small mesh (0, x1) of length L1 and ending with a mesh (x2, x3) of length L3> L1. It can be shown that there is a point on a perpendicular to the pipe section at the abscissa 0 such that the meshes of lengths L1 and L3 are seen from this point at the same angle α. The y coordinate of this vertex is given by the relation: there = The 1 ( The 1 + The 2 ) ( The 1 + The 2 + The 3 ) ( The 3 - The 1 ) where L2 is the length of the segment (x1, x2).

It is then a question of cutting the angle β into N equal parts, N being equal to the integer division of β by α, that is N = E (β / α). Each of the N angles cutting β is always greater than or equal to α.

The principle used to carry out the insertion of the edges of meshes is at the same time simple and flexible. It allows, through a single parameter, to create a mesh either uniform or heterogeneous, refined in important places.

Claims (8)

Automatic mesh method of pipes allowing the implementation of modeling codes of fluids conveyed by these pipes, characterized in that , having defined a minimum mesh size and a maximum mesh size, the pipe is subdivided into sections delimited by elbows , we position a mesh of minimum size on each side of each elbow, we position large meshes of size at most equal to the maximum size in the central portion of each section, and we distribute meshes of increasing or decreasing sizes on the intermediate portions of each section between each mesh of minimum size and the central portion. Method according to claim 1, characterized in that increasing or decreasing meshes are distributed over the portions of each intermediate section between each minimum size mesh and the central portion by determining the points of intersection with each pipe section , of a bundle of lines competing at a point and forming between them a constant angle. Method according to claim 1, characterized in that the position of the apex of the straight line bundle is determined on an axis passing through an elbow of the pipe and perpendicular to each section, at a distance (y) from it which is function of the size (L1, L3) of the extreme meshes of each intermediate portion and their distance (L2). Mesh method according to one of claims 1 to 3, characterized in that it includes a prior simplification of the topography of the pipe. Mesh method according to claim 4, characterized in that it comprises a representation of the pipe in the form of a graph connecting the curvilinear abscissa and the level variation, and a simplification of the number of sections by assigning to each point between two successive sections a weight taking into account the length (L1, L2) of the sections and their respective slopes (P1, P2) and by selecting among the points arranged in order of increasing or decreasing weight, those whose weight is the highest . Mesh method according to claim 5, characterized in that the points of the pipe having the highest weight are selected by locating in the arrangement of points a weight discontinuity greater than a certain fixed threshold (Δ P ). Mesh method according to claim 5, characterized in that it comprises a representation of the pipe in the form of a graph connecting the curvilinear abscissa and the level variation, and a simplification of the number of sections by the formation of the spectrum of frequency of the curve representative of the topography of the pipe, the attenuation of the highest frequencies of the spectrum translating the smallest variations of topography and the reconstruction of a simplified topography corresponding to the rectified frequency spectrum. Mesh method according to claim 7, characterized in that it includes a sampling of the curve representative of the topography of the pipe with a sampling step chosen so that the smallest section of the pipe contains at least two steps of sampling, a determination of the frequency spectrum of the curve sampled by application, a correction of the spectrum by low-pass filtering, the cut-off frequency of which is chosen according to a maximum number of meshes fixed to subdivide the pipe, and the determination of the topography corresponding to the rectified frequency spectrum.

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