arXiv subjects

Denys Dutykh

Publications and source records attributed to Denys Dutykh.

At least 73 records · Page 4Linked to original sources

arXiv2020

Derivation of an intermediate viscous Serre-Green-Naghdi equation

In this note we present the current status of the derivation of a viscous Serre-Green-Naghdi system. For this goal, the flow domain is separated into two regions. The upper region is governed by inviscid Euler equations, while the bottom region (the so-called boundary layer) is described by Navier-Stokes equations. We consider a particular regime linking the Reynolds number and the shallowness parameter. The computations presented in this note are performed in the fully nonlinear regime. The boundary layer flow reduces to a Prantdl-like equation. Further approximations seem to be needed to obtain a tractable model.

math.AP↗

arXiv2019

Nonlinear deformation and run-up of single tsunami waves of positive polarity: numerical simulations and analytical predictions

The estimate of individual wave run-up is especially important for tsunami warning and risk assessment as it allows to evaluate the inundation area. Here as a model of tsunami we use the long single wave of positive polarity. The period of such wave is rather long which makes it different from the famous Korteweg-de Vries soliton. This wave nonlinearly deforms during its propagation in the ocean, what results in a steep wave front formation. Situations, when waves approach the coast with a steep front are often observed during large tsunamis, e.g. 2004 Indian Ocean and 2011 15 Tohoku tsunamis. Here we study the nonlinear deformation and run-up of long single waves of positive polarity in the conjoined water basin, which consists of the constant depth section and a plane beach. The work is performed numerically and analytically in the framework of the nonlinear shallow water theory. Analytically, wave propagation along the constant depth section and its run-up on a beach are considered independently without taking into account wave interaction with the toe of the bottom slope. The propagation along the bottom of constant depth is described by Riemann wave, while the wave 20 run-up on a plane beach is calculated using rigorous analytical solutions of the nonlinear shallow water theory following the Carrier-Greenspan approach. Numerically, we use the finite volume method with the second order UNO2 reconstruction in space and the third order Runge-Kutta scheme with locally adaptive time steps. During wave propagation along the constant depth section, the wave becomes asymmetric with a steep wave front. Shown, that the maximum run-up height depends on the front steepness of the incoming wave approaching the toe of the bottom slope. The corresponding formula for maximum 25 run-up height, which takes into account the wave front steepness, is proposed.

physics.flu-dyn↗

arXiv2019

Dispersive effects during long wave run-up on a plane beach

Dispersive effects during long wave run-up on a plane beach are studied. We take an advantage of experimental data collection of different wave types (single pulses, sinusoidal waves, bi-harmonic waves, and frequency modulated wave trains) and simulate their run-up using two models: (i) non-dispersive nonlinear shallow water theory and (ii) dispersive Boussinesq type model based on the modified Peregrine system. It is shown, that for long positive pulses, dispersive effects are not so important and nonlinear shallow water theory can be used. However, for periodic sinusoidal and bi-harmonic pulses of the same period, the dispersive effects result in significant wave transformation during its propagation, but do not have a strong impact on its maximal run-up height. Overall, for maximum wave run-up height, we could not find a preference of dispersive model against the nondispersive one, and, therefore, suggest using nonlinear shallow water model for long wave run-up height estimation.

physics.ao-ph↗

arXiv2019

Experimental and numerical study of the propagation of focused wave groups in the nearshore zone

The propagation of focused wave groups in intermediate water depth and the shoaling zone is experimentally and numerically considered in this paper. The experiments are carried out in a two-dimensional wave flume and wave trains derived from Pierson-Moskowitz and JONSWAP spectrum are generated. The peak frequency does not change during the wave train propagation for Pierson-Moskowitz waves; however, a downshift of this peak is observed for JONSWAP waves. An energy partitioning is performed in order to track the spatial evolution of energy. Four energy regions are defined for each spectrum type. A nonlinear energy transfer between different spectral regions as the wave train propagates is demonstrated and quantified. Numerical simulations are conducted using a modified Boussinesq model for long waves in shallow waters of varying depth. Experimental results are in satisfactory agreement with numerical predictions, especially in the case of wave trains derived from JONSWAP spectrum.

physics.flu-dyn↗

arXiv2019

Interpreting Distortions in Dimensionality Reduction by Superimposing Neighbourhood Graphs

To perform visual data exploration, many dimensionality reduction methods have been developed. These tools allow data analysts to represent multidimensional data in a 2D or 3D space, while preserving as much relevant information as possible. Yet, they cannot preserve all structures simultaneously and they induce some unavoidable distortions. Hence, many criteria have been introduced to evaluate a map's overall quality, mostly based on the preservation of neighbourhoods. Such global indicators are currently used to compare several maps, which helps to choose the most appropriate mapping method and its hyperparameters. However, those aggregated indicators tend to hide the local repartition of distortions. Thereby, they need to be supplemented by local evaluation to ensure correct interpretation of maps. In this paper, we describe a new method, called MING, for `Map Interpretation using Neighbourhood Graphs'. It offers a graphical interpretation of pairs of map quality indicators, as well as local evaluation of the distortions. This is done by displaying on the map the nearest neighbours graphs computed in the data space and in the embedding. Shared and unshared edges exhibit reliable and unreliable neighbourhood information conveyed by the mapping. By this mean, analysts may determine whether proximity (or remoteness) of points on the map faithfully represents similarity (or dissimilarity) of original data, within the meaning of a chosen map quality criteria. We apply this approach to two pairs of widespread indicators: precision/recall and trustworthiness/continuity, chosen for their wide use in the community, which will allow an easy handling by users.

cs.CV↗

arXiv2019

An efficient numerical method for a long-term simulation of heat and mass transfer: the case of an insulated rammed earth wall

Innovative numerical scheme studied in this work enables to overcome two main limitations of Building Performance Simulation (BPS) programs as high computational cost and the choice of a very fine numerical grid. The method, called Super-Time-Stepping (STS), is novel to the state-of-the-art of building simulations, but has already proved to be sufficiently efficient in recent studies from anisotropic heat conduction in astrophysics (Meyer et al. 2014). The given research is focused on employment of this adopted numerical method to model drying of a rammed earth wall with an additional insulation layer. The results show considerable advantage of the STS method compared to standard Euler explicit scheme. It is possible to choose at least 100 times bigger time-steps to maintain high accuracy and to cut computational cost by more than 92% in the same time.

cs.CE↗

arXiv2019

Dispersive and non-dispersive nonlinear long wave transformations: Numerical and experimental results

The description of gravity waves propagating on the water surface is considered from a historical point of view, with specific emphasis on the development of a theoretical framework and equations of motion for long waves in shallow water. This provides the foundation for a subsequent discussion about tsunami wave propagation and run-up on a sloping beach, and in particular the role of wave dispersion for this problem. Wave tank experiments show that wave dispersion can play a significant role for the propagation and wave transformation of wave signals that include some higher frequency components. However, the maximum run-up height is less sensitive to dispersive effects, suggesting that run-up height can be adequately calculated by use of non-dispersive model equations.

physics.flu-dyn↗

arXiv2019

Hamiltonian regularisation of shallow water equations with uneven bottom

The regularisation of nonlinear hyperbolic conservation laws has been a problem of great importance for achieving uniqueness of weak solutions and also for accurate numerical simulations. In a recent work, the first two authors proposed a so-called Hamiltonian regularisation for nonlinear shallow water and isentropic Euler equations. The characteristic property of this method is that the regularisation of solutions is achieved without adding any artificial dissipation or ispersion. The regularised system possesses a Hamiltonian structure and, thus, formally preserves the corresponding energy functional. In the present article we generalise this approach to shallow water waves over general, possibly time-dependent, bottoms. The proposed system is solved numerically with continuous Galerkin method and its solutions are compared with the analogous solutions of the classical shallow water and dispersive Serre-Green-Naghdi equations. The numerical results confirm the absence of dispersive and dissipative effects in presence of bathymetry variations.

physics.flu-dyn↗

arXiv2019

On the comparison of three numerical methods applied to building simulation: finite-differences, RC circuit approximation and a spectral method

Predictions of physical phenomena in buildings are carried out by using physical models formulated as a mathematical problem and solved by means of numerical methods, aiming at evaluating, for instance, the building thermal or hygrothermal performance by calculating distributions and fluxes of heat and moisture transfer. Therefore, the choice of the numerical method is crucial since it is a compromise among (i) the solution accuracy, (ii) the computational cost to obtain the solution and (iii) the complexity of the method implementation. An efficient numerical method enables to compute an accurate solution with a minimum computational run time (CPU). On that account, this article brings an investigation on the performance of three numerical methods. The first one is the standard and widely used finite-difference approach, while the second one is the so-called RC approach, which is a particular method brought to the building physics area by means of an analogy of electric circuits. The third numerical method is the spectral one, which has been recently proposed to solve nonlinear diffusive problems in building physics. The three methods are evaluated in terms of accuracy on the assessment of the dependent variable (temperature or vapor pressure) or of density of fluxes for three different cases: i) heat diffusion through a concrete slab, ii) moisture diffusion through an aerated concrete slab and iii) heat diffusion using measured temperatures as boundary conditions. Results highlight the spectral approach as the most accurate method. The RC based model with a few number of resistances does not provide accurate results for temperature and vapor pressure distributions neither to flux densities nor conduction loads.

cs.CE↗

arXiv2019

Evaluation of the reliability of building energy performance models for parameter estimation

The fidelity of a model relies both on its accuracy to predict the physical phenomena and its capability to estimate unknown parameters using observations. This article focuses on this second aspect by analyzing the reliability of two mathematical models proposed in the literature for the simulation of heat losses through building walls. The first one, named DuFort-Frankel (DF), is the classical heat diffusion equation combined with the DuFort-Frankel numerical scheme. The second is the so-called RC lumped approach, based on a simple ordinary differential equation to compute the temperature within the wall. The reliability is evaluated following a two stages method. First, samples of observations are generated using a pseudo-spectral numerical model for the heat diffusion equation with known input parameters. The results are then modified by adding a noise to simulate experimental measurements. Then, for each sample of observation, the parameter estimation problem is solved using one of the two mathematical models. The reliability is assessed based on the accuracy of the approach to recover the unknown parameter. Three case studies are considered for the estimation of (i) the heat capacity, (ii) the thermal conductivity or (iii) the heat transfer coefficient at the interface between the wall and the ambient air. For all cases, the DF mathematical model has a very satisfactory reliability to estimate the unknown parameters without any bias. However, the RC model lacks of fidelity and reliability. The error on the estimated parameter can reach 40% for the heat capacity, 80% for the thermal conductivity and 450% for the heat transfer coefficient.

cs.CE↗

arXiv2019

On some model equations for pulsatile flow in viscoelastic vessels

Considered here is the derivation of partial differential equations arising in pulsatile flow in pipes with viscoelastic walls. The equations are asymptotic models describing the propagation of long-crested pulses in pipes with cylindrical symmetry. Additional effects due to viscous stresses in bio-fluids are also taken into account. The effects of viscoelasticity of the vessels on the propagation of solitary and periodic waves in a vessel of constant radius are being explored numerically.

physics.flu-dyn↗

arXiv2019

On the multi-symplectic structure of Boussinesq-type systems. II: Geometric discretization

In this paper we consider the numerical approximation of systems of Boussinesq-type to model surface wave propagation. Some theoretical properties of these systems (multi-symplectic and Hamiltonian formulations, well-posedness and existence of solitary-wave solutions) were previously analyzed by the authors in Part I. As a second part of the study, considered here is the construction of geometric schemes for the numerical integration. By using the method of lines, the geometric properties, based on the multi-symplectic and Hamiltonian structures, of different strategies for the spatial and time discretizations are discussed and illustrated.

math.NA↗

arXiv2019

Effects of vorticity on the travelling waves of some shallow water two-component systems

In the present study we consider three two-component (integrable and non-integrable) systems which describe the propagation of shallow water waves on a constant shear current. Namely, we consider the two-component Camassa-Holm equations, the Zakharov-Ito system and the Kaup--Boussinesq equations all including constant vorticity effects. We analyze both solitary and periodic-type travelling waves using the simple and geometrically intuitive phase space analysis. We get the pulse-type solitary wave solutions and the front solitary wave solutions. For the Zakharov-Ito system we underline the occurrence of the pulse and anti-pulse solutions. The front wave solutions decay algebraically in the far field. For the Kaup-Boussinesq system, interesting analytical multi-pulsed travelling wave solutions are found.

physics.class-ph↗

arXiv2019

A new model for simulating heat, air and moisture transport in porous building materials

This work presents a detailed mathematical model combined with an innovative efficient numerical model to predict heat, air and moisture transfer through porous building materials. The model considers the transient effects of air transport and its impact on the heat and moisture transfer. The achievement of the mathematical model is detailed in the continuity of Luikov's work. A system composed of two advection-diffusion differential equations plus one exclusively diffusion equation is derived. The main issue to take into account the transient air transfer arises in the very small characteristic time of the transfer, implying very fine discretisation. To circumvent these difficulties, the numerical model is based on the Du Fort-Frankel explicit and unconditionally stable scheme for the exclusively diffusion equation. It is combined with a two-step Runge-Kutta scheme in time with the Scharfetter-Gummel numerical scheme in space for the coupled advection-diffusion equations. At the end, the numerical model enables to relax the stability condition, and, therefore, to save important computational efforts. A validation case is considered to evaluate the efficiency of the model for a nonlinear problem. Results highlight a very accurate solution computed about 16 times faster than standard approaches. After this numerical validation, the reliability of the mathematical model is evaluated by comparing the numerical predictions to experimental observations. The latter is measured within a multi-layered wall submitted to a sudden increase of vapor pressure on the inner side and driven climate boundary conditions on the outer side. A very satisfactory agreement is noted between the numerical predictions and experimental observations indicating an overall good reliability of the proposed model.

physics.app-ph↗

arXiv2019

On time relaxed schemes and formulations for dispersive wave equations

The numerical simulation of nonlinear dispersive waves is a central research topic of many investigations in the nonlinear wave community. Simple and robust solvers are needed for numerical studies of water waves as well. The main difficulties arise in the numerical approximation of high order derivatives and in severe stability restrictions on the time step, when explicit schemes are used. In this study we propose new relaxed system formulations which approximate the initial dispersive wave equation. However, the resulting relaxed system involves first order derivatives only and it is written in the form of an evolution problem. Thus, many standard methods can be applied to solve the relaxed problem numerically. In this article we illustrate the application of the new relaxed scheme on the classical Korteweg-de Vries equation as a prototype of stiff dispersive PDEs.

physics.class-ph↗

arXiv2019

An efficient numerical model for liquid water uptake in porous material and its parameter estimation

The goal of this study is to propose an efficient numerical model for the predictions of capillary adsorption phenomena in a porous material. The Scharfetter-Gummel numerical scheme is proposed to solve an advection-diffusion equation with gravity flux. Its advantages such as accuracy, relaxed stability condition, and reduced computational cost are discussed along with the study of linear and nonlinear cases. The reliability of the numerical model is evaluated by comparing the numerical predictions with experimental observations of liquid uptake in bricks. A parameter estimation problem is solved to adjust the uncertain coefficients of moisture diffusivity and hydraulic conductivity.

cs.CE↗

arXiv2019

An innovative method to determine optimum insulation thickness based on non-uniform adaptive moving grid

It is well known that thermal insulation is a leading strategy for reducing energy consumption associated to heating or cooling processes in buildings. Nevertheless, building insulation can generate high expenditures so that the selection of an optimum insulation thickness requires a detailed energy simulation as well as an economic analysis. In this way, the present study proposes an innovative non-uniform adaptive method to determine the optimal insulation thickness of external walls. First, the method is compared with a reference solution to properly understand the features of the method, which can provide high accuracy with less spatial nodes. Then, the adaptive method is used to simulate the transient heat conduction through the building envelope of buildings located in Brazil, where there is a large potential of energy reduction. Simulations have been efficiently carried out for different wall and roof configurations, showing that the innovative method efficiently provides a gain of 25% on the computer run time.

cs.CE↗

arXiv2019

On the Reducibility and the Lenticular Sets of Zeroes of Almost Newman Lacunary Polynomials

The class B of lacunary polynomials f(x) := -1 + x + x^n + x^{m_1} + x^{m_2} + ... + x^{m_s}, where s >= 0, m_1 - n >= n - 1, m_{q+1} - m_{q} >= n - 1 for 1 <= q < s, n >= 3 is studied. A polynomial having its coefficients in {0, 1} except its constant coefficient equal to -1 is called an almost Newman polynomial. A general theorem of factorization of the almost Newman polynomials of the class B is obtained. Such polynomials possess lenticular roots in the open unit disk off the unit circle in the small angular sector π/18 <= arg z <= π/18 and their nonreciprocal parts are always irreducible. The existence of lenticuli of roots is a peculiarity of the class B. By comparison with the Odlyzko - Poonen Conjecture and its variant Conjecture, an `Asymptotic Reducibility Conjecture' is formulated aiming at establishing the proportion of irreducible polynomials in this class. This proportion is conjectured to be 3/4 and estimated using Monte-Carlo methods. The numerical approximate value ~ 0.756 is obtained. The results extend those on trinomials (Selmer) and quadrinomials (Ljunggren, Mills, Finch and Jones).

math.NT↗