# Marx Chhay's research while affiliated with Université Savoie Mont Blanc and other places

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## Publications (41)

The stability and dynamics of a falling liquid film over an anisotropic porous medium are studied using a one-domain approach. Our stability analysis shows a significant departure from the effective no-slip boundary condition in the isotropic case. Anisotropy does not affect the threshold of linear instability. However, a non-trivial dual effect of...

Back Matter (Pages 233-245) of the book: "Numerical Methods for Diffusion Phenomena in Building Physics: A Practical Introduction" by Nathan Mendes, Marx Chhay, Julien Berger and Denys Dutykh

Front Matter (Pages i-xviii) of the book: "Numerical Methods for Diffusion Phenomena in Building Physics: A Practical Introduction" by Nathan Mendes, Marx Chhay, Julien Berger and Denys Dutykh

This book is the second edition of Numerical methods for diffusion phenomena in building physics: a practical introduction originally published by PUCPRESS (2016). It intends to stimulate research in simulation of diffusion problems in building physics, by providing an overview of mathematical models and numerical techniques such as the finite diff...

This chapter is organized as follows. First, we present some theoretical bases behind spectral discretizations in Sect. 8.1. An application to a problem stemming from the building physics is given in Sect. 8.3. Finally, we give some indications for the further reading in Sect. 8.4. This document contains also a certain number of Appendices directly...

In building physics, as mentioned in Chaps. 2 and 3, numerical models used to predict heat and moisture transfer involve different characteristic time and lengths. Simulation of building behavior is generally analyzed on a time scale of 1 year (or more). However, the phenomena and particularly the boundary conditions evolve in seconds. The geometri...

In the field of building physics, diffusion phenomena started to be extensively modeled in the 70s (because of the oil crisis) to develop building-performance-simulation programs for the adoption of rational policies of energy conservation. However, existing tools might still present inconsistent scenarios of the actual occurrences in buildings, es...

Above in Chap. 3 the basic finite differences approaches were presented. In particular, it was shown that explicit discretizations are subject to some additional constraints if one wants to have a stable numerical scheme. These restrictions are known in the literature under the name of Courant–Friedrichs–Lewy conditions [43]. For parabolic diffusio...

This chapter is entirely devoted to numerical methods, keeping in mind that the main application is on diffusion processes in building physics. However, the presentation is oriented to the practical construction of numerical schemes with an overview of their elementary numerical properties.

This chapter is devoted to a practical presentation of the finite-element method (FEM). The focus is on the construction of numerical schemes rather than on the numerical properties that this approach benefits; References [5, 106] provide an introduction. A very large literature survey, sorted by fundamental references, mathematical foundations, ap...

The first two parts of this book provided some theoretical background for solving diffusion problems in building physics and presented traditional (finite differences and finite elements) and nontraditional numerical methods (boundary integral approach, reduced order methods, and spectral methods). In addition, some practical examples were provided...

Since the main focus of the Ph.D. school is set on the diffusion processes (molecular diffusion, heat and moisture conduction through the walls, etc.), it is desirable to explain how this research started and why the diffusion is generally modeled by parabolic PDEs [61]. The historic part of this chapter is partially based on [159].

In many engineering problems, including building modeling, the relevant information lies at the surface of a domain. In addition, only a few point-wise evaluations may be needed. Thus, classical numerical approaches would require a whole domain computation, which requires a considerable amount of information (and computation effort). The idea of us...

MathSciNet review of our manuscript.

A review of our manuscript on MathSciNet.

Review of our manuscript on MathSciNet.

A review of our manuscript on MathSciNet.

Some of the most important geometric integrators for both ordinary and partial differential equations are reviewed and illustrated with examples in mechanics. The class of Hamiltonian differential systems is recalled and its symplectic structure is highlighted. The associated natural geometric integrators, known as symplectic integrators, are then...

Reference solution for a small solitonic gas obtained with the spectral method.

This work is devoted to proposing a hybrid numerical–analytical method to address the problem of heat and moisture transfer in porous soils. Several numerical and analytical models have been used to study heat and moisture transfer. The complexity of the coupled transfer in soils is such that analytical solutions exist only for limited problems, wh...

This book intends to stimulate research in simulation of diffusion problems in building physics, by first providing an overview of mathematical models and numerical techniques such as the finite difference and finite-element methods traditionally used in building simulation tools. Then, nonconventional methods such as reduced order models, boundary...

This paper presents an extensive review of heat and mass transfer correlations in the framework of sorption machines operating based on the falling film technology, in which ammonia-water and lithium bromide-water are used as the working fluid pairs. Heat and mass transfer correlations are summarized as well as the application range and geometrical...

In this article, we present a model of heat transfer occurring through a liquid film flowing down a vertical wall. This new model is formally derived using the method of asymptotic expansions by introducing appropriately chosen dimensionless variables. In our study the small parameter, known as the film parameter, is chosen as the ratio of the flow...

This manuscript is devoted to the modelling of water waves in the deep water regime with some emphasis on the underlying variational structures. The present article should be considered as a review of some existing models and modelling approaches even if new results are presented as well. Namely, we derive the deep water analogue of the celebrated...

A proper generalised decomposition for solving inverse heat conduction problems is proposed in this article as an innovative method offering important numerical savings. It is based on the solution of a parametric problem, considering the unknown parameter as a coordinate of the problem. Then, considering this solution, all sets of cost function ca...

Good building airtightness is of major importance to achieve energy efficient buildings. Poor workmanship may lead to unintended air transfer through the building envelope. The tradititional method to assess the impact of air leakage on the building heat loss is to add an infiltration heat loss to the existing conduction heat loss, without consider...

Detailed modelling of air leakage paths through complex building wall assemblies is a challenging task. It requires transient modelling of diffusion and advection phenomena through fluid and solid domains, including porous materials and air channels.
In this article, the development of a numerical model coupling heat air and moisture transfers (co...

In this short note, we present a multi-symplectic structure of the
Serre-Green-Naghdi (SGN) equations modelling nonlinear long surface waves in
shallow water. This multi-symplectic structure allow the use of efficient
finite difference or pseudo-spectral numerical schemes preserving exactly the
multi-symplectic form at the discrete level.

This paper proposes a reduced order model to simulate heat and moisture behaviour of material based on proper general decomposition (PGD). This innovative method is an a priori model reduction method. It proposes an alternative way for computing solutions of the problem by considering a separated representation of the solution. PGD offers an intere...

KEYWORDS: Model Order Reduction, HAM transfers, Proper Generalised Decomposition ABSTRACT: This paper proposes a reduced order model to simulate two-dimensional heat and moisture behaviour of material based on Proper General Decomposition (PGD). This innovative method is an a priori method. It proposes an alternative way for computing solutions of...

To meet the higher requirements of current and future building codes, understanding and controlling
air transfer through building envelopes is of importance. In this paper, the development of a simplified heat-airflow numerical model is presented and a first comparison with experimental data is performed. An experimental setup to visualize air path...

In this study, we discuss an approximate set of equations describing water
wave propagating in deep water. These generalized Klein-Gordon (gKG) equations
possess a variational formulation, as well as a canonical Hamiltonian and
multi-symplectic structures. Periodic travelling wave solutions are constructed
numerically to high accuracy and compared...

Geometric discretizations that preserve certain Hamiltonian structures at the discrete level has been proven to enhance the accuracy of numerical schemes. In particular, numerous symplectic and multi-symplectic schemes have been proposed to solve numerically the celebrated Korteweg-de Vries (KdV) equation. In this work, we show that geometrical sch...

Geometric discretizations that preserve certain Hamiltonian structures at the discrete level has been proven to enhance the accuracy of numerical schemes. In particular, numerous symplectic and multi-symplectic schemes have been proposed to solve numerically the celebrated Korteweg-de Vries (KdV) equation. In this
work, we show that geometrical sch...

In this paper we present a method of construction of invariant numerical schemes for partial differential equations. The resulting schemes preserve the Lie-symmetry group of the continuous equation and they are at least as accurate as the original scheme. The improvement of the numerical properties thanks to the Lie-symmetry preservation is illustr...

Lie-symmetry based integrators are constructed in order to preserve the local invariance properties of the equations. The geometrical methods leading to discretized equations for numerical computations involve many different concepts. Therefore they give rise to numerical schemes that vary in the accuracy, in the computational cost and in the imple...

We propose a new approach for moving frame construction that allows to make finite difference scheme invariant. This approach takes into account the order of accuracy and guarantees numerical properties of invariant schemes that overcome those of classical schemes. Benefits obtained with this process are illustrated with the Burgers equation.

Dans cette communication, nous présentons un procédé de construction de schémas numériques conservant les symétries de l'équation continue. Les performances de tels schémas sont illustrées sur deux exemples: l'équation de Burger's et l'équation de convection diffusion.

## Citations

... This approach necessitates the ability to separate high and low mode components of signal and then to chose or to design the damping/stabilizing operator through its symbol to obtain desired filtering properties. This leads to the usage of two different time schemes, one for each set of components; multi-grid as well as hierarchical-like methods including wavelets have been used in that direction, [13,53,54,55]. ...

... The governing equations of heat and mass transfer in building porous materials have been proposed in [1]. Since this early work of Luikov, several numerical models have been developed and recently reported in [2]. These tools enable to compute accurately the prediction of the physical phenomena as illustrated in [3]. ...

... [28]) are suited to discretize the flow of Hamiltonian equations, and as their name suggests, are designed to preserve the symplectic structure in the process. Qualitatively, this results in a better control on the conservation of the energy of the system ( [22]), even for simulations on large time intervals. Designed in the early eighties, they are now widely used in various applications, like conservative large scale molecular dynamics [25]. ...

Reference: Symplectic Groupoids for Poisson Integrators

... Numerical tools such as building simulation programs have been elaborated to predict energy efficiency and help building's design. An extensive review of such programs is proposed in [2,3]. ...

... Moreover, hybrid method of Chebyshev wavelet finite difference method is employed to solve the system of higher order boundary value problem [17]. Other works of proposed hybrid method can be seen in computation of the temperature and moisture in porous medium [18]. Numerical solution of hybrid method which couples between finite difference method and asymptotic interpolation has been proposed to solve the variable accelerated problem of third grade fluid in a rotating frame [19]. ...

... The most common absorption cooling systems working fluids are ammonia-water and water-lithium bromide. The ammonia-water is employed in applications including refrigeration systems with temperatures below 0°C [3,4]. The water-lithium bromide is used for air-conditioning applications due to the limitations of the water thermodynamic properties. ...

... Indeed, a large class of models for water waves inherits a Hamiltonian structure of infinite dimension. Thus a multisymplectic structure can be exhibited, for example, for Serre-type equations in deep water configuration [172], and for the Serre-Green-Naghdi equations in shallow water configuration [173]. Therefore multisymplectic schemes appear as natural structure preserving integrators applied to these models. ...

Reference: A review of some geometric integrators

... The governing equations of the full order model are then projected on to the lower dimensional subspace by choosing an appropriate test basis. Other linear basis construction methods include balanced truncation [4,5], reduced basis methods [6,7,8], rational interpolation [9], and proper generalized decomposition [10,11]. Linear basis ROMs have achieved considerable success in complex problems such as turbulent flows [12,13,14] and combustion instabilities [15,16]. ...

... The fundamental mechanisms of air/water vapour diffusion in rock and construction materials have been previously studied [14][15][16][17][18]. Bartelt-Hunt and Smith [19] mentioned that the transportation of organic vapour in the unsaturated vadose zone is important in understanding the distribution of organic contaminants in the subsurface environments and their exchange between the subsurface environment and the atmosphere. ...