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Xavier Raynaud

Publications and source records attributed to Xavier Raynaud.

17 recordsLinked to original sources
arXiv2026

Comprehensive parameter and electrochemical dataset for a 1 Ah graphite/LNMO battery cell for physical modelling as a blueprint for data reporting in battery research

While current technology has enabled their widespread use, further improvements are needed for stationary, portable, and mobile applications, for example by the development of novel cathode materials. Digitalization of battery development, combining both experimental and modelling efforts is extremely valuable in this development. This is addressed in the present paper, where the authors present a comprehensive dataset for a graphite/LNMO 1 Ah pouch cell, including material, design, and electrochemical data. The dataset, validated through the BattMo modelling framework, supports physical modelling and aims to benefit the battery modelling community by offering a comprehensive resource for future studies. Both the dataset and the accompanying software for numerical validation is openly available and processed in such a way that it can serve as blueprint for reporting of comparable research data.

cond-mat.mtrl-sci↗
arXiv2025

BattMo -- Battery Modelling Toolbox

This paper presents the Battery Modelling Toolbox (BattMo), a flexible finite volume continuum modelling framework in MATLAB\textsuperscript{\textregistered} (\citeproc{ref-MATLAB}{The MathWorks Inc., 2025}) for simulating the performance of electro-chemical cells. BattMo can quickly setup and solve models for a variety of battery chemistries, even considering 3D designs such as cylindrical and prismatic cells. The simulation input parameters, including the material parameters and geometric descriptions, are specified through JSON schemas. In this respect, we follow the guidelines of the Battery Interface Ontology (BattINFO) to support semantic interoperability in accordance with the FAIR principles (\citeproc{ref-fair}{Wilkinson et al., 2016}). The Doyle-Fuller-Newman (DFN) (\citeproc{ref-Doyle1993ModelingCell}{Doyle et al., 1993}) approach is used as a base model. We include fully coupled thermal simulations. It is possible to include degradation mechanisms such as SEI layer growth, and the use of composite material, such as a mixture of Silicon and graphite. The models are setup in a hierarchical way, for clarity and modularity. Each model corresponds to a computational graph, which introduces a set of variables (the nodes) and functional relationship (the edges). This design enables the flexibility for changing and designing new models. The solver in BattMo uses automatic differentiation and support adjoint computation. We can therefore compute the derivative of objective functions with respect to all parameters efficiently. Gradient-based optimization routines can be used to calibrate parameters from experimental data.

physics.comp-ph↗
arXiv2025

Modeling and Simulation of Coupled Biochemical and Two-Phase Compositional Flow in Underground Hydrogen Storage

Integrating microbial activity into underground hydrogen storage models is crucial for simulating long-term reservoir behavior. In this work, we present a coupled framework that incorporates bio-geochemical reactions and compositional flow models within the Matlab Reservoir Simulation Toolbox (MRST). Microbial growth and decay are modeled using a double Monod formulation, with populations influenced by hydrogen and carbon dioxide availability. First, a refined Equation of State (EoS) is employed to accurately capture hydrogen dissolution, thereby improving phase behavior and modeling of microbial activity. The model is then discretized using a cell-centered finite-volume method with implicit Euler time discretization. A fully coupled fully implicit strategy is considered. Our implementation builds upon MRST's compositional module by incorporating the S{\o}reide-Whitson EoS, microbial reaction kinetics, and specific effects such as bio-clogging and molecular diffusion. Through a series of 1D, 2D and 3D simulations, we analyze the effects of microbial-induced bio-geochemical transformations on underground hydrogen storage in porous media.These results highlight that accounting for bio-geochemical effects can substantially impact hydrogen loss, purity, and overall storage performance.

physics.comp-ph↗
arXiv2020

A semi-discrete scheme derived from variational principles for global conservative solutions of a Camassa-Holm system

We define a kinetic and a potential energy such that the principle of stationary action from Lagrangian mechanics yields a Camassa--Holm system (2CH) as the governing equations. After discretizing these energies, we use the same variational principle to derive a semi-discrete system of equations as an approximation of the 2CH system. The discretizaton is only available in Lagrangian coordinates and requires the inversion of a discrete Sturm--Liouville operator with time-varying coefficients. We show the existence of fundamental solutions for this operator at initial time with appropriate decay. By propagating the fundamental solutions in time, we define an equivalent semi-discrete system for which we prove that there exists unique global solutions. Finally, we show how the solutions of the semi-discrete system can be used to construct a sequence of functions converging to the conservative solution of the 2CH system.

math.AP↗
arXiv2017

Symmetries and multipeakon solutions for the modified two-component Camassa-Holm system

Compared with the two-component Camassa-Holm system, the modified two-component Camassa-Holm system introduces a regularized density which makes possible the existence of solutions of lower regularity, and in particular of multipeakon solutions. In this paper, we derive a new pointwise invariant for the modified two-component Camassa-Holm system. The derivation of the invariant uses directly the symmetry of the system, following the classical argument of Noether's theorem. The existence of the multipeakon solutions can be directly inferred from this pointwise invariant. This derivation shows the strong connection between symmetries and the existence of special solutions. The observation also holds for the scalar Camassa-Holm equation and, for comparison, we have also included the corresponding derivation. Finally, we compute explicitly the solutions obtained for the peakon-antipeakon case. We observe the existence of a periodic solution which has not been reported in the literature previously. This case shows the attractive effect that the introduction of an elastic potential can have on the solutions.

math.AP↗
arXiv2017

Combining the Modified Discrete Element Method with the Virtual Element Method for Fracturing of Porous Media

Simulation of fracturing processes in porous rocks can be divided into two main branches: (i) modeling the rock as a continuum which is enhanced with special features to account for fractures, or (ii) modeling the rock by a discrete (or discontinuous) approach that describes the material directly as a collection of separate blocks or particles, e.g., as in the discrete element method (DEM). In the modified discrete element (MDEM) method, the effective forces between virtual particles are modified in all regions, without failing elements, so that they reproduce the discretization of a first order finite element method (FEM) for linear elasticity. This provides an expression of the virtual forces in terms of general Hook's macro-parameters. Previously, MDEM has been formulated through an analogy with linear elements for FEM. We show the connection between MDEM and the virtual element method (VEM), which is a generalization of FEM to polyhedral grids. Unlike standard FEM, which computes strain-states in a reference space, MDEM and VEM compute stress-states directly in real space. This connection leads us to a new derivation of the MDEM method. Moreover, it gives the basis for coupling (M)DEM to domain with linear elasticity described by polyhedral grids, which makes it easier to apply realistic boundary conditions in hydraulic-fracturing simulations. This approach also makes it possible to combine fine-scale (M)DEM behavior near the fracturing region with linear elasticity on complex reservoir grids in the far-field region without regridding. To demonstrate the simulation of hydraulic fracturing, the coupled (M)DEM-VEM method is implemented using the Matlab Reservoir Simulation Toolbox (MRST) and linked to an industry-standard reservoir simulator.

math.NA↗
arXiv2016

Virtual Element Method for geomechanics on reservoir grids

In this paper we study the use of Virtual Element method for geomechanics. Our emphasis is on applications to reservoir simulations. The physical processes that form the reservoirs, such as sedimentation, erosion and faulting, lead to complex geometrical structures. A minimal representation, with respect to the physical parameters of the system, then naturally leads to general polyhedral grids. Numerical methods which can directly handle this representation will be highly favorable, in particular in the setting of advanced work-flows. The Virtual Element method is a promising candidate to solve the linear elasticity equations on such models. In this paper, we investigate some of the limits of the VEM method when used on reservoir models. First, we demonstrate that care must be taken to make the method robust for highly elongated cells, which is common in these applications, and show the importance of calculating forces in terms of traction on the boundary of the elements for elongated distorted cells. Second, we study the effect of triangulations on the surfaces of curved faces, which also naturally occur in subsurface models. We also demonstrate how a more stable regularization term for reservoir application can be derived.

math.NA↗
arXiv2014

A continuous interpolation between conservative and dissipative solutions for the two-component Camassa-Holm system

We introduce a novel solution concept, denoted $\alpha$-dissipative solutions, that provides a continuous interpolation between conservative and dissipative solutions of the Cauchy problem for the two-component Camassa-Holm system on the line with vanishing asymptotics. All the $\alpha$-dissipative solutions are global weak solutions of the same equation in Eulerian coordinates, yet they exhibit rather distinct behavior at wave breaking. The solutions are constructed after a transformation into Lagrangian variables, where the solution is carefully modified at wave breaking.

math.AP↗
arXiv2013

Periodic conservative solutions for the two-component Camassa-Holm system

We construct a global continuous semigroup of weak periodic conservative solutions to the two-component Camassa-Holm system, $u_t-u_{txx}+\kappa u_x+3uu_x-2u_xu_{xx}-uu_{xxx}+\eta\rho\rho_x=0$ and $\rho_t+(u\rho)_x=0$, for initial data $(u,\rho)|_{t=0}$ in $H^1_{\rm per}\times L^2_{\rm per}$. It is necessary to augment the system with an associated energy to identify the conservative solution. We study the stability of these periodic solutions by constructing a Lipschitz metric. Moreover, it is proved that if the density $\rho$ is bounded away from zero, the solution is smooth. Furthermore, it is shown that given a sequence $\rho_0^n$ of initial values for the densities that tend to zero, then the associated solutions $u^n$ will approach the global conservative weak solution of the Camassa-Holm equation. Finally it is established how the characteristics govern the smoothness of the solution.

math.AP↗
arXiv2013

Global dissipative solutions of the two-component Camassa-Holm system for initial data with nonvanishing asymptotics

We show existence of a global weak dissipative solution of the Cauchy problem for the two-component Camassa-Holm (2CH) system on the line with nonvanishing and distinct spatial asymptotics. The influence from the second component in the 2CH system on the regularity of the solution, and, in particular, the consequences for wave breaking, is discussed. Furthermore, the interplay between dissipative and conservative solutions is treated.

math.AP↗
arXiv2011

Convergent Numerical Schemes for the Compressible Hyperelastic Rod Wave Equation

We propose a fully discretised numerical scheme for the hyperelastic rod wave equation on the line. The convergence of the method is established. Moreover, the scheme can handle the blow-up of the derivative which naturally occurs for this equation. By using a time splitting integrator which preserves the invariants of the problem, we can also show that the scheme preserves the positivity of the energy density.

math.NA↗
arXiv2010

Lipschitz metric for the Camassa-Holm equation on the line

We study stability of solutions of the Cauchy problem on the line for the Camassa-Holm equation $u_t-u_{xxt}+3uu_x-2u_xu_{xx}-uu_{xxx}=0$ with initial data $u_0$. In particular, we derive a new Lipschitz metric $d_\D$ with the property that for two solutions $u$ and $v$ of the equation we have $d_\D(u(t),v(t))\le e^{Ct} d_\D(u_0,v_0)$. The relationship between this metric and the usual norms in $H^1$ and $L^\infty$ is clarified. The method extends to the generalized hyperelastic-rod equation $u_t-u_{xxt}+f(u)_x-f(u)_{xxx}+(g(u)+\frac12 f"(u)(u_x)^2)_x=0$ (for $f$ without inflection points).

math.AP↗
arXiv2010

Lipschitz metric for the periodic Camassa-Holm equation

We study stability of conservative solutions of the Cauchy problem for the periodic Camassa-Holm equation $u_t-u_{xxt}+\kappa u_x+3uu_x-2u_xu_{xx}-uu_{xxx}=0$ with initial data $u_0$. In particular, we derive a new Lipschitz metric $d_\D$ with the property that for two solutions $u$ and $v$ of the equation we have $d_\D(u(t),v(t))\le e^{Ct} d_\D(u_0,v_0)$. The relationship between this metric and usual norms in $H^1_{\rm per}$ and $L^\infty_{\rm per}$ is clarified.

math.AP↗
arXiv2009

Global semigroup of conservative solutions of the nonlinear variational wave equation

We prove the existence of a global semigroup for conservative solutions of the nonlinear variational wave equation $u_{tt}-c(u)(c(u)u_x)_x=0$. We allow for initial data $u|_{t=0}$ and $u_t|_{t=0}$ that contain measures. We assume that $0<κ^{-1}\le c(u) \le κ$. Solutions of this equation may experience concentration of the energy density $(u_t^2+c(u)^2u_x^2)dx$ into sets of measure zero. The solution is constructed by introducing new variables related to the characteristics, whereby singularities in the energy density become manageable. Furthermore, we prove that the energy may only focus on a set of times of zero measure or at points where $c'(u)$ vanishes. A new numerical method to construct conservative solutions is provided and illustrated on examples.

math.AP↗
arXiv2009

Lipschitz metric for the Hunter-Saxton equation

We study stability of solutions of the Cauchy problem for the Hunter-Saxton equation $u_t+uu_x=\frac14(\int_{-\infty}^xu_x^2 dx-\int_{x}^\infty u_x^2 dx)$ with initial data $u_0$. In particular, we derive a new Lipschitz metric $d_\D$ with the property that for two solutions $u$ and $v$ of the equation we have $d_\D(u(t),v(t))\le e^{Ct} d_\D(u_0,v_0)$.

math.AP↗
arXiv2009

Symmetric waves are traveling waves

We show that horizontally symmetric water waves are traveling waves. The result is valid for the Euler equations, and is based on a general principle that applies to a large class of nonlinear partial differential equations, including some of the most famous model equations for water waves. A detailed analysis is given for weak solutions of the Camassa-Holm equation. In addition, we establish the existence of nonsymmetric linear rotational waves for the Euler equations.

math.AP↗