Chapter 6 – The Contribution of Modeling to the Knowledge and Management of Cave Climates: the Example of Lascaux
p. 143-167
Texte intégral
6.1 Introduction
1This document follows on from Philippe Malaurent’s article, “Climatology of the Subterranean Environment at Lascaux: from a Global Study to the Microclimatology of the Cave Walls” (cf. chapter 5). The climatological data are used here as boundary and initial conditions for the simulation. The synergistic work between the instruments, knowledge of the subterranean environment and simulation will lead to a better understanding of how to manage the climate at Lascaux.
2We will first give a brief outline of what simulation and digital simulation are in fluid mechanics. The contributions of simulation to heritage conservation will then be examined generally before turning more specifically to the Lascaux simulator, which is a preventive conservation tool. Finally, we will consider the contributions of simulation to the knowledge and management of the climate at Lascaux. Among other things, the impact of temperature inversion on climate change in the cave, the influence of human impact and the different possible modifications to the climate-assistance system will be studied.
6.2 Simulation and digital simulation in fluid mechanics
3Simulation is used extensively in many fields, such as the aeronautics, space, automobile and steel industries, areas, as well as in the fields of environment and sustainable development.
4Experimentation and theories have allowed scientific concepts to be constructed. Despite everything, it is still difficult to access very small scales in space, such as the atomic scale (10‑10 m), for calculations in molecular dynamics. In the same way, very large scales are also more easily accessible by means of simulation, especially in astronomical calculations (light years). The problem also exists for time scales: very short times (shorter than 10‑15 s) or very long times, up to geological scales, are very difficult to access other than by simulation. Industrial processes that are very difficult to measure using instruments, and which involve very high temperatures (the steel industry) or hazardous products (the chemicals industry) can also be studied using simulation. Finally, simulation is crucial to the non-destructive control or study of fragile environments, such as Lascaux Cave. Environmental simulation is useful for determining pollutant dispersal—the movements of air masses or oceans, for example—and provides weather forecasts.
5Simulation therefore concerns very diverse fields. In the context of Lascaux, we are more particularly interested in numerical simulation in fluid mechanics. This relates to the study of air flows, heat and mass transfers, and particle transport, which are all phenomena present in Lascaux Cave.
6.3 The contributions of simulation to heritage conservation
6The main interest of simulation is that it is non-intrusive. It is thus a very important aid for making decisions in heritage conservation. Modifications can be tested virtually, using laboratory computer simulation, to evaluate their impact and help to decide if they can and should be applied to the cave.
7Basic research in fluid mechanics
8The simulator must be state-of-the-art, rely on the best digital tools for solving equations, the best digital diagrams, as well as the best models, implying a physical study, for example, on transfers of heat and mass to the walls. It must also be concerned with subjects that are rarely addressed, such as the projection of a complex object onto a Cartesian grid, thus raising new and complex problems for the community of digital experts.
9Research in archaeology and conservation
10It is possible to use simulation to modify the geometry of the cave and to study the repercussions of these modifications on its climate. We therefore plan to virtually replace the archaeological floor in order to deduce the flow during different periods, depending on the initial temperature conditions. The opening of the Oculus, the Shaft where the discovery was made, has been simulated in order to visualize the development of flows within this geometric configuration.
11Simulation of scenarios
12The Lascaux simulator was designed to respond to the questions of the International Lascaux Cave Scientific Committee. It addresses spontaneous interrogations depending on the condition of the cave and projected modifications. A typical example is the creation of scenarios showing the impact of modifications to the cave (partitioning, scaffolding), or even the distribution of human presence in space (the different chambers) and through time (per week, per day), depending on the envisaged climatic configuration.
13Understanding the climate
14Simulation is used to validate or invalidate hypotheses concerning modifications to the thermal and hydrological conditions, and thus contributes to improving our understanding of the climate of the cave. A typical example is temperature inversions and their impact on flows in the cave.
15Integration of microbiological data
16The longer-term objective is to find correlations between the cave climate, the microclimate of the walls and biological developments, to make the Lascaux simulator a tool for predicting the appearance of microorganisms and to avoid creating conditions that are favorable to them.
6.4 The Lascaux simulator: a tool for preventative conservation
17The Lascaux simulator is based on a fluid mechanics code and takes the complex geometry of the cave into account using a fictitious domain approach (Lacanette et al. 2006; Lacanette, Caltagirone 2006). The main interest of modeling lies in its predictive aspect. It is possible to evaluate the short-term consequences of modifying installations in the cave or making changes to the climatic assistance system. The first simulations using digital models have validated the results of the first scientific committee of 1963. The different stages of this work have allowed us to develop a methodology to help with conservation: by simulating scenarios that have already occurred, the hypotheses proposed by observation or data analysis are digitally validated or invalidated.
186.4.1 Objectives
19Taking measurements in the cave is very important. However, the limits of the measuring equipment, in terms of sensitivity and reliability, are sometimes attained. We must remember that the physical and environmental conditions (thermal and hydrological) in the cave are hard on measuring instruments: the humidity is greater than 98% and the temperature has fluctuated between 11°C and 13°C over the years, with annual variations of only a few tenths of a degree maximum; the atmosphere is oxidant and microorganisms develop very easily on and in the equipment.
20The Lascaux simulator is used to create scenarios such as the impact of modifications (scaffolding, partitions and machinery), the impact of the climate (introduction of unstable conditions) and the impact of human presence (improvement in the distribution of the time of human presence).
21Finally, the simulator was designed to be easily adaptable to other decorated caves. The models used at Lascaux are common to all subterranean environments, and the geometry is the only parameter that must be modified in the simulator.
6.4.2 The grid: structure of the simulator
22The first stage of the simulation is to generate the grid that forms the structure of the simulator. A 3D laser recording was made by the Cabinet Guy Perazio. It is depicted in fig. 61a using 3D Studio Max image synthesis software. The 3D reproduction is triangulated on its surface, as can be seen in fig. 61b. Each triangle comprises three nodes. Each node is then projected onto a cubic grid of the structured Cartesian grid, and the new grid is shown on the same view as the previous one, in fig. 61c. Finally, the projection in our calculation code, Aquilon1, developed by the TREFLE Laboratory, is presented in fig. 61d.

FIG. 61 – 3D laser reproduction of the cave: a general view; b detailed view. Aquilon projection: c detailed view; d general view.
Fig. 61a-b © cabinet Guy Perazio; fig. 61c-d image réalisée sur le logiciel Thétis (Aquilon) : © université Bordeaux 1, laboratoire Trefle.
23The constituent equations for the fluid mechanics are solved on each node of the Cartesian grid and the important parameters (temperature, speed, humidity levels) are also calculated on these nodes.
6.4.3 Constituent equations and models
24In a fluid environment, the conservation equations that describe the incompressible, unstable convection flows of a Newtonian fluid and the evolution of the concentration of humidity, according to the Boussinesq hypothesis, are the incompressible Navier-Stokes equations (1-2) [Khadra et al. 2000], of energy (3) and the transport of the humidity concentration (4), written as speed and temperature: where u is the speed vector, r the density, t the time, g the gravity vector, p the pressure, m the dynamic viscosity, CP the calorific capacity, l the conductivity, f the rate of absolute humidity and D the coefficient of diffusion.

25The humidity has an initial value of 98% relative humidity throughout the cave. The calculations are made using the level of absolute humidity, which is given by the temperature at each point using the psychrometric diagram (fig. 62). The psychrometric diagram shows the relationship between the air temperature and the level of absolute humidity in graphic form. The circled area refers to the conditions found in the cave.

FIG. 62 –Psychrometric diagram.
© Université Bordeaux 1, laboratoire Trefle.
6.4.4 View of Lascaux Cave in the simulator
26Lascaux Cave is shown in fig. 63 as it perceived by the simulator. Markers indicating the different chambers have been placed to locate the areas relative to the two-dimensional plan that is more frequently presented in publications.

FIG. 63 – General view of Lascaux Cave in the simulator.
Image réalisée sur le logiciel Thétis (Aquilon) : © université Bordeaux 1, laboratoire Trefle.
6.4.5 Temperature limits
27The boundary conditions must be added to the simulator in order to recreate the actual temperature conditions in the cave. Lascaux Cave is located at between 10 and 20 m and the maximum temperature amplitude is approximately 0.6°C throughout the year. The phase difference is at least 6 months. The highest temperatures in the Hall of the Bulls occur in winter, when the outside temperatures are at their lowest.
28In order to be as accurate as possible regarding the boundary conditions on the walls of the cave, we consider the adjacent hill and initialize a temperature gradient from measurements based on measures made inside the cave. Each point of the cave wall will therefore be associated with the temperature value that corresponds to its depth.
29The depth-based temperature profile input into the simulator has been calculated using a theoretical model (Fourier’s Law) based on temperatures measured at the surface of the hill above the cave (fig. 64).

FIG. 64 – Temperature profile (°C) depending on the depth in the hill surrounding Lascaux Cave.
Image réalisée sur le logiciel Thétis (Aquilon) : © université Bordeaux 1, laboratoire Trefle
6.5 Contribution of simulation to the knowledge and management of the climate of Lascaux Cave
6.5.1 Impact of temperature inversions on knowledge of the climate
30The temperatures in the cave have been inverted since the mid-1980s (cf. chapiter 5) under the influence of the climate change above the cave, resulting in two very distinct periods of thermal behavior: from 1963 to 1981 and from 1982 until today. We have made an arbitrary selection of dates within these two periods. To illustrate the first, the thermal configuration for September 1981 was chosen. For the second, the configurations for December 1999 and February 2008 have been studied (to include more recent modifications and in the interest of being closer to the phenomena that are present today).
31Figure 65 shows the development of these temperatures in the ground, depending on the depth, for the two thermal configurations envisaged: September 1981 and December 1999. The cave is located at a depth of between 10 and 20 m in this section. The depth-related temperature gradients are the reverse of each other: in September 1981, the air was hotter when people went into the cave, whereas it has been colder more recently.

FIG. 65 – Temperature variation depending on the depth for two thermal configurations (sept. 1981: in red; dec. 1999: in green).
© Université Bordeaux 1, laboratoire Trefle.
32This temperature inversion influences the air speeds, as we see in figs 66 and 67. In fact, the convection currents form when the floor is warmer than the ceilings: the hot air is lighter and it rises, cools, and falls back down to the ground under the influence of gravity, where it reheats and rises again; this is what causes the air movements, especially in the thermal configuration of September 1981. In December 1999, the air at the floor level is colder than the hotter air at the ceiling level: the convection current is not created and the air stays as it is, stratified. The corresponding speeds were therefore lower in December 1999 than in September 1981.

FIG. 66 – Temperature profiles (°C) (left) and speed profiles (right) on a cross-section in the Passageway and the Mondmilch Gallery, in the thermal configuration of September 1981 (top) and December 1999 (bottom): the speeds were roughly 0.01 m·s‑1 in September 1981 and roughly 0.001 m s‑1 in December 1999.
Image réalisée sur le logiciel Thétis (Aquilon) : © université Bordeaux 1, laboratoire Trefle.

FIG. 67 – Temperature distribution (°C) on a cross-section in the Hall of the Bulls and the Axial Gallery for the thermal configurations of September 1981 (top) and December 1999 (bottom): the speeds were roughly 0.01 m·s‑1 in September 1981 and roughly 0.001 m·s‑1 in December 1999.
Image réalisée sur le logiciel Thétis (Aquilon) : © université Bordeaux 1, laboratoire Trefle.
6.5.2 Influence of the climate configuration on air movements
33The phenomenon of temperature inversion has an impact on the movements of fluids, which take different directions. The air movement is shown by arrows in figures 68 and 69. In September 1981, in the right gallery of the cave, the air was directed naturally from the deepest parts (the Mondmilch Gallery) to the shallowest parts (the Passageway) and to the Hall of the Bulls, whereas in December 1999 it came from the Hall of the Bulls and went from the Passageway to the Mondmilch Gallery.

FIG. 68 – Flow direction in the Right Gallery in the climatic configuration of September 1981 (left), and December 1999 (right).
Image réalisée sur le logiciel Thétis (Aquilon) : © université Bordeaux 1, laboratoire Trefle.

FIG. 69 – Flow direction in the Passageway in the climatic configuration of September 1981 (left), and December 1999 (right).
Image réalisée sur le logiciel Thétis (Aquilon): © université Bordeaux 1, laboratoire Trefle
34Figures 68 and 69 highlight the trajectory of a virtual particle released in the same place for two simulations corresponding to two thermal configurations. In fig. 70, the particle is released at the bottom of the Mondmilch Gallery, and in fig. 71 it is released at the bottom of the Axial Gallery. In both cases, the particle was directed towards the cave entrance in September, whereas in December 1999 it was directed towards the bottom of the Right Gallery.

FIG. 70 – Trajectory of a virtual particle released at the end of the Mondmilch Gallery in the climate configuration of September 1981 (left), and December 1999 (right).
Image réalisée sur le logiciel Thétis (Aquilon) : © université Bordeaux 1, laboratoire Trefle.

FIG. 71 – Trajectory of a virtual particle released at the end of the Axial Gallery in the climatic configuration of September 1981 (left), and December 1999 (right).
Image réalisée sur le logiciel Thétis (Aquilon): © université Bordeaux 1, laboratoire Trefle.
35With regard to the evacuation of virtual particles, the flow in the cave was favorable in the thermal configuration of 1981 and unfavorable in that of December 1999. The analysis corresponds to the observations made in the cave during these periods (Malaurent et al. 2006; Lacanette et al. 2007), and to the experiences of H. Schoeller (cf. chapiter 5).
6.5.3 Impact of human presence
36The aim of the simulation is to provide information about the exact locations of the areas with a high risk of condensation due to the presence of human activity in the cave. The case presented in figure 72 corresponds to a configuration that has no human-made effects. It is intended to serve as the basis for future studies, such as the introduction of an air regulation system, exceptional human presence, and the introduction of hot or cold spots in the cave. This figure shows the distribution of the levels of absolute humidity for the two thermal configurations of September 1981 and December 1999. With regard to the humidity levels on the walls of the cave, it was globally higher in December 1999, due to the increase in temperature inside the cave. Furthermore, it was concentrated at ceiling level in September 1981 and at floor level in December 1999. This fact is proven by the weekly records of S. Géraud, B. Desplat and P. Buraud.

FIG. 72 – Humidity distribution (g/kg of dry air) for the thermal configurations of September 1981 (left) and December 1999 (right).
Image réalisée sur le logiciel Thétis (Aquilon) : © université Bordeaux 1, laboratoire Trefle.
37Human presence is modeled by taking account of the thermal and hydrological impact of three people and two neon lights located in the Apse for 7 hours, i.e. a total of 21 hours of presence, 500 W and 840 g of vapor.
38One human is put in the Passageway close to the Apse for the two thermal configurations, as shown in figure 73.

FIG. 73 – Humidity distribution (g/kg of dry air) on the cave walls with human presence (indicated by an arrow) for the thermal configurations of September 1981 (left) and December 1999 (right).
Image réalisée sur le logiciel Thétis (Aquilon) : © université Bordeaux 1, laboratoire Trefle.
39If we look at the humidity distribution in more detail on the crosssections, we find (fig. 74) that in September 1981 human presence increased the level of absolute humidity in the Passageway and a small part of the Nave, whereas in December 1999 (fig. 75) human presence increased the level of absolute humidity in much greater proportions and in a larger impact zone (up to the Hall of the Bulls). In a comparison of the two thermal configurations with human presence, the humidity level was much higher in December 1999, and the disruption caused was greater.

FIG. 74 – Visualization of absolute humidity (g/kg of dry air) on a cross-section of the Passageway and Mondmilch Gallery for the thermal configuration of September 1981, without human presence (top) and with it (bottom).
Image réalisée sur le logiciel Thétis (Aquilon) : © université Bordeaux 1, laboratoire Trefle.

FIG. 75 – Visualisation of absolute humidity (g/kg of dry air) on a cross-section of the Passageway and Mondmilch Gallery for the thermal configuration of December 1999, without human presence (top) and with it (bottom).
Image réalisée sur le logiciel Thétis (Aquilon) : © université Bordeaux 1, laboratoire Trefle.
40Figure 76 shows the same configuration as the previous one, from a different perspective. The level of absolute humidity remained much higher in December 1999. The speeds in the Apse were almost the same in both configurations, which is linked to the proximity of the source of the disruption: the presence of humans. The speed generated by humans is equal to the speed in the cave in September 1981 without any humans, and 10 times greater than that of December 1999 without any humans.

FIG. 76 – Visualisation of absolute humidity (g/kg of dry air) and speeds on a cross-section of the Apse and Shaft with human presence for the thermal configuration of September 1981 (left) and December 1999 (right).
Image réalisée sur le logiciel Thétis (Aquilon) : © université Bordeaux 1, laboratoire Trefle.
41Figure 77a shows that the presence of humans in the Passageway at the level of the Apse did not have any impact on the flows in the Hall of the Bulls and in the Axial Gallery in September 1981. The value of the speed generated by the disruption – the presence of humans – is therefore equal to the value of the speeds without any disruption, i.e. approximately 0.01 m·s-1. On the contrary, in fig. 77b, for the thermal configuration of December 1999, the presence of humans had an impact on the level of absolute humidity in the Hall of the Bulls. The temperature and humidity level were stratified during this period. The introduction of a heat source increased the speeds and dispersed the humidity level throughout a large area. The value of the speed generated by the disruption – the presence of humans – is 10 times higher than the value of the speeds without any disruption.
6.5.4 Correspondence between the temperature inversions that occurred in the history of the cave after its discovery and periods of conservation problems
42Finally, a relationship appeared between local climate change and conservation problems (fig. 78). Every time a deep area was colder than a shallower area, a conservation problem was found in the archives. This temperature inversion involves stratification of the air, as has been seen previously; air does not blow in the cave and any particles that may be present cannot be evacuated. If there had been stratification without the disruption, would there have been fewer conservation problems? It is the presence of humans combined with stratification that causes the conservation problems: the humidity level, carbon dioxide, pollution, etc. generated by visitors are no longer evacuated to the outside in this case, and they must be dispersed on the walls.

FIG. 78 – Correlation between climatic changes and the conservation problems.
© P. Sin / université Bordeaux 1, laboratoire Ghymac.
6.5.5 Impact of hot and cold spots and combined effects of human presence
6.5.5.1 “Natural” functioning of the cave
43Cold floor
44In the past, the rimstones were filled with water (cf. chapiter 5). We are attempting to recreate this “natural” hygrothermic state of the cave by means of simulation in order to determine its impact on the cave climate. The position of the cold floor corresponds to that of the rimstones on the ground in the Hall of the Bulls and the Passageway. The temperature taken was 0.5°C lower than the average temperature in the Hall of the Bulls. In the 1981 configuration, it was 11.7°C; that of the floor itself was therefore taken as 11.2°C. It was 12.2°C in the 2008 configuration, and that of the floor was 11.7°C (fig. 79).

FIG. 79 – View from below showing the position of the cold floor and temperature: thermal configuration of September 1981 (left) and February 2008 (right).
Image réalisée sur le logiciel Thétis (Aquilon) : © université Bordeaux 1, laboratoire Trefle.
45Figures 80 and 81 show the distribution of humidity and speeds in two places in Lascaux Cave: on a cross-section of the Hall of the Bulls and the Axial Gallery (fig. 80), and on a cross-section of the Passageway and the Mondmilch Gallery (fig. 81), for the two climate configurations of September 1981 and February 2008, in both cases with and without a cold floor. In fig. 80, we find the influence of the cold floor in both configurations: in the configuration of September 1981, the cold floor does not change the speed intensity, whereas in February 2008 it accelerates it considerably. From the perspective of humidity variations, the cold floor dries the cave considerably in the two climatic configurations. The same observations apply to the section of the cave (fig. 81) in which the cold floor acts to perform localized drying: the Passageway.
46A cold floor is interesting from the perspective of the creation of convections, but it causes significant drying.

FIG. 80 – Cross-section of the Hall of the Bulls and the Axial Gallery, showing absolute humidity (g/kg of dry air) and speeds in the thermal configuration of 1981 (left) and of 2008 (right), without a cold floor (top) and with one (bottom).
Image réalisée sur le logiciel Thétis (Aquilon) : © université Bordeaux 1, laboratoire Trefle.

FIG. 81 – Cross-section of the Passageway and the Mondmilch Gallery, showing absolute humidity (g/kg of dry air) and speeds in the thermal configuration of 1981 (left) and of 2008 (right), without a cold floor (top) and with one (bottom).
Image réalisée sur le logiciel Thétis (Aquilon) : © université Bordeaux 1, laboratoire Trefle.
47Hot floor
48When the rimstones were filled with water, this water was colder than the ambient air for part of the year (in winter), and hotter than the air during another part of the year (late summer or autumn). This is the situation that we would now like to simulate. The position is the same as previously (fig. 79). The temperature of the cold floor is set at 0.5°C higher than the average temperature in the Hall of the Bulls, i.e. 12.2°C in the thermal configuration of September 1981 and 12.7°C in that of February 2008.
49Figures 82 and 83 show the distribution of humidity and speeds in two places in Lascaux Cave, on a cross-section of the Hall of the Bulls and the Axial Gallery (fig. 82) and on a cross-section of the Passageway and the Mondmilch Gallery (fig. 83), for the two climate configurations of September 1981 and February 2008, in both cases with and without a hot floor.

FIG. 82 – Cross-section of the Hall of the Bulls and the Axial Gallery: absolute humidity (g/kg of dry air) and speeds in the thermal configuration of 1981 (left) and of 2008 (right), without a hot floor (top) and with one (bottom).
Image réalisée sur le logiciel Thétis (Aquilon) :© université Bordeaux 1, laboratoire Trefle.

FIG. 83 – Cross-section of the Passageway and the Mondmilch Gallery: absolute humidity (g/kg of dry air) and speeds in the thermal configuration of 1981 (left) and of 2008 (right), without a hot floor (top) and with one (bottom).
Image réalisée sur le logiciel Thétis (Aquilon) : © université Bordeaux 1, laboratoire Trefle.
50We find that the influence of the hot floor is even more localized than for the cold floor. The hot floor induces an increase in the speeds and humidity in the Hall of the Bulls and in the Passageway. A vertical thermal plume develops at the level of the hot floor, so the cold floor causes more horizontal air movements.
51The hot floor must be eliminated, since its action in the creation of convections is too localized and it generates air humidity saturation that has the risk of producing condensation on the coldest remote walls.
6.5.5.2 Artificial cold point at the entrance to the Hall of the Bulls
52The current air-conditioning system corresponds to a cold point situated at the entrance to the Hall of the Bulls. We would like to test this configuration by means of a simulation. The position of this cold point is given in figure 84. This cold point is, as in the case of the cold floor, set at a temperature lower than 0.5°C of the average temperature in the Hall of the Bulls, i.e. 11.2°C in the climate configuration of 1981 and 11.7°C in that of 2008.

FIG. 84 – Position of cold points at the entrance to the Hall of the Bulls.
Image réalisée sur le logiciel Thétis (Aquilon) : © université Bordeaux 1, laboratoire Trefle.
53Figure 85 shows the very localized action of the cold points, contained a few meters inside the Hall of the Bulls. The speeds are very slightly modified and the air is a little drier than the configuration of February 2008.

FIG. 85 – Cross-section of the Hall of the Bulls and the Axial Gallery: absolute humidity (g/kg of dry air) and speeds in the thermal configuration of 1981 (left) and of 2008 (right), without a cold point (top) and with one (bottom).
Image réalisée sur le logiciel Thétis (Aquilon) : © université Bordeaux 1, laboratoire Trefle.
54Figure 86 shows a practically negligible influence of the cold point at the entrance to the Hall of the Bulls on the local climate in the Right Diverticulum of the cave.

FIG. 86 – Cross-section of the Passageway and the Mondmilch Gallery: absolute humidity (g/kg of dry air) and speeds in the thermal configuration of 1981 (left) and of 2008 (right), without a cold point (top) and with one (bottom).
Image réalisée sur le logiciel Thétis (Aquilon) : © université Bordeaux 1, laboratoire Trefle.
55The cold point at the entrance to the Hall of the Bulls does not have any significant influence on either the convection movements or the humidity values.
6.5.5.3 Hot point at the bottom of the Axial Gallery
56We intend to simulate the influence of the hot points (fig. 87) in order to recreate the convections and try, as near as possible, to simulate the favorable thermal configuration of 1981, in which the soil was warmer than the ceilings. Figures 88 and 89 show the distribution of humidity and speeds in two places in Lascaux Cave, on a cross-section of the Hall of the Bulls and the Axial Gallery (fig. 88) and on a cross-section of the Passageway and the Mondmilch Gallery (fig. 89), for the two climate configurations of September 1981 and February 2008, in both cases with and without a hot point at the bottom of the Axial Gallery. Figure 88 shows another localized influence of the hot point, with vertical rising speeds and air humidity saturation. The hot point at the bottom of the Axial Gallery has no impact on the right section of the cave (fig. 89).

FIG. 87 – Position of the hot point at the end of the Axial Gallery.
Image réalisée sur le logiciel Thétis (Aquilon) : © université Bordeaux 1, laboratoire Trefle.

FIG. 88 – Cross-section of the Hall of the Bulls and the Axial Gallery: absolute humidity (g/kg of dry air) and speeds in the thermal configuration of 1981 (left) and of 2008 (right), without a hot point (top) and with one (bottom).
Image réalisée sur le logiciel Thétis (Aquilon) : © université Bordeaux 1, laboratoire Trefle.

FIG. 89 – Cross-section of the Passageway and the,Mondmilch Gallery: absolute humidity (g/kg of dry air) and speeds in the thermal configuration of 1981 (left) and of 2008 (right), without a hot point (top) and with one (bottom).
Image réalisée sur le logiciel Thétis (Aquilon) : © université Bordeaux 1, laboratoire Trefle.
57The positioning of a hot point at the bottom of the Axial Gallery must be disregarded, since its influence is excessively localized in the area in which it is situated.
6.5.5.4 Hot point in the Mondmilch Gallery (fig. 90)
58Figures 91 and 92 show the distribution of humidity and speeds in two places in Lascaux Cave, on a cross-section of the Hall of the Bulls and the Axial Gallery (fig. 91) and on a cross-section of the Passageway and the Mondmilch Gallery (fig. 92), for the two climate configurations of September 1981 and February 2008, in both cases with and without a hot point in the Mondmilch Gallery. The cold point in the Mondmilch Gallery has no impact on the central section of the cave (fig. 91). Figure 92 shows that the influence of the hot point in the Mondmilch Gallery is restricted to the area in which it is situated. It brings humidity and creates convections in a very narrow perimeter.

FIG. 91 – Cross-section of the Hall of the Bulls and the Axial Gallery: absolute humidity (g/kg of dry air) and speeds in the thermal configuration of 1981 (left) and of 2008 (right), without a hot point (top) and with one (bottom).
Image réalisée sur le logiciel Thétis (Aquilon) : © université Bordeaux 1, laboratoire Trefle.

FIG. 92 – Cross-section of the Passageway and the Mondmilch Gallery: absolute humidity (g/kg of dry air) and speeds in the thermal configuration of 1981 (left) and of 2008 (right), without a hot point (top) and with one (bottom).
Image réalisée sur le logiciel Thétis (Aquilon) : © université Bordeaux 1, laboratoire Trefle.
59The hot point in the Mondmilch Gallery is not an option for recreating convections in the cave.
6.5.5.5 Comparison between relaxation and human presence (middle of the Passageway, bottom of the Axial Gallery), with and without cold points
60We have shown the influence of a cold floor at 11.7°C (0.5°C less than the ambient temperature in the Hall of the Bulls), resulting in the filling of the rimstones, on the thermoaeraulic equilibrium in the cave. We add a disruption to this cold source, represented by 3 people for 7 hours with 2 neon lights, i.e. a contribution of 500 W and 840 g of water vapor. After these 7 hours, the human disruption is removed we observe the relaxation under the influence of the cold floor.
61The residual humidity disappears rapidly and after 1 hour there are few traces of the disruption. This disappearance is sudden and could cause the walls to dry out. The positioning of two cold points, situated in the Hall of the Bulls and in the Passageway (fig. 93) and maintained at a temperature of 11.7°C, seems more judicious and will be tested by simulation.

FIG. 93 – View from below the cave, showing the position of the two cold points.
Image réalisée sur le logiciel Thétis (Aquilon): © université Bordeaux 1, laboratoire Trefle.
62Relaxation after disruption in the Passageway
63We find that the cave relaxes following the same disruption as described above, when there are two cold points. The drying out is less sudden than in the presence of the cold floor and the residual humidity practically disappears after 2 hours. In order to evaluate the value of using two cold points to eliminate humidity, we compare this case with relaxation in the absence of cold points (fig. 94) after the same time period (1 hour 23 minutes). The evacuation of humidity by the cold points is visible. Their presence allows the detrimental impact of any introduction of humans into the cave to be reduced by eliminating it more quickly.

FIG. 94 – Humidity distribution (g/kg of dry air) after 1 hour 23 minutes of relaxation in the presence of the two cold points (left) and without a cold point (right).
Image réalisée sur le logiciel Thétis (Aquilon) : © université Bordeaux 1, laboratoire Trefle.
64Figures 95 and 96 show the distribution of humid air and the speeds on a cross-section of the Passageway towards the Mondmilch Gallery, and they show the reduction in the humidity level and the recreation of convection currents.

FIG. 95 – Humidity distribution (g/kg of dry air) after 1 hour 23 minutes of relaxation on the cross-sections of the Passageway towards the Mondmilch Gallery, in the presence of the two cold points (left) and without a cold point (right).
Image réalisée sur le logiciel Thétis (Aquilon) : © université Bordeaux 1, laboratoire Trefle.

FIG. 96 – Comparison of speeds in the Passageway and the Mondmilch Gallery in the presence of the two cold points (left) and without a cold point (right).
Image réalisée sur le logiciel Thétis (Aquilon) : © université Bordeaux 1, laboratoire Trefle
65Relaxation after disruption at the bottom of the Axial Gallery
66The same calculation is done by positioning the disruption at the bottom of the Axial Gallery and not in the Passageway. We find that the cold point situated in the Hall of the Bulls is effective in eliminating the humidity generated by the presence of humans.
6.5.5.6 Conclusion: the impact of hot and cold points on relaxation following disruption
67The positioning of two cold points in the Hall of the Bulls and the Passageway allows the humidity to be lowered and the convections to be recreated locally, thereby “ironing out” the problems caused by disruption (presence of humans). This solution seems to be the best one among the configurations studied through simulation and presented in this document.
6.6 Conclusions and perspectives
68The Lascaux simulator is a preventive conservation tool. It has contributed new elements to our knowledge of the climate in Lascaux Cave. In particular, it has recently contributed to the proposition of an alternative to the climatic assistance system in the cave, which could be adapted to the current climate configuration.
69Research on digital simulation in fluid mechanics is continuously progressing from the perspective of physical models and digital methods. Furthermore, the TREFLE Laboratory, where the simulator is housed, has recently been equipped with a super-calculator of 256 processors and has thus doubled its calculation capacity, allowing calculations to be made in half the time. These advances in simulation will help to make decisions concerning the constantly developing conservation of decorated caves.
70References
71Khadra et al. 2000 : KHADRA (K.), ANGOT (P.), PARNEIX (S.), CALTAGIRONE (J.‑P.). — Fictitious domain approach for numerical modelling of Navier-Stokes équations. International journal for numerical methods in fluids, 34, 2000, p. 651-684.
72Lacanette, Caltagirone 2006 : LACANETTE (D.), CALTAGIRONE (J.‑P.). — Le simulateur Lascaux : un outil d’aide à la décision pour l’avenir de la préhistoire. Monumental, 2006, 2, p. 94-97.
73Lacanette et al. 2006 : LACANETTE (D.), MALAURENT (P.), CALTAGIRONE (J.‑P.), VINCENT (S.). — A model of thermal and aeraulic flows in the cave of Lascaux. In INTERNATIONAL ASSOCIATION FOR MATHEMATICAL GEOLOGY — Quantitative geology from multiple sources : IAMG 06. Congrès international (11 ; Liège ; 2006). Publication électronique = digital journal.
74Lacanette et al. 2007 : LACANETTE (D.), MALAURENT (P.), CALTAGIRONE (J.‑P.), BRUNET (J.). — Étude des transferts de masse et de chaleur dans la grotte de Lascaux : le suivi climatique et le simulateur. Karstologia, 50, 2007, p. 19-30.
75Malaurent et al. 2006 : MALAURENT (P.), BRUNET (J.), LACANETTE (D.), CALTAGIRONE (J.‑P.). — Contribution of numerical modelling of environmental parameters to the conservation of prehistoric cave paintings : the example of Lascaux Cave. Conservation and management of archaeological sites, 8, 2006, p. 1‑11.
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