Publications

2026

• Path-following methods for phase-field simulation of quasi-static crack propagation
  
  • Loiseau Flavien
  • Lazarus Véronique
  International Journal of Solids and Structures, Elsevier, 2026, 334, pp.113974. The variational approach to fracture, particularly through its regularization as a phase-field model, has become a widely used tool for simulating the quasi-static propagation of cracks in structures. However, classic incremental loading can induce unstable crack growth, violating the quasi-static assumption, and in some cases, leads to a loss of force balance, preventing self-consistency and the estimation of dissipated energy during snapback instabilities. To address this challenge, path-following methods are investigated. Their aim is to adjust the applied load so that it stays at the propagation threshold, thereby preserving the quasi-static assumption and ensuring equilibrium solutions. In this work, we apply and evaluate multiple path-following methods within the framework of variational phase-field fracture models, which are developed to regularize linear elastic variational sharp crack evolution problems. Our study pursues two objectives. First, we review several existing path-following methods, with a focus on partitioned strategies based on the displacement field, which decouple the path-following control equation from the rest of the system, facilitating easier integration with staggered solvers. In addition, we introduce a new path-following method whose particularity is to limit the maximum strain increment outside the cracked regions. Second, we use the Γ-convergence to the sharp crack model to evaluate these methods across three crack propagation problems of increasing complexity. The comparison demonstrates that the proposed path-following method offers a simple yet highly effective approach to capture the equilibrium path in phase-field fracture simulations. This method robustly maintains the quasi-static assumption, ensuring physically meaningful results. By enabling accurate estimation of the energy dissipated during snapback instabilities, it paves the way for the rational design of more resistant heterogeneous materials. (10.1016/j.ijsolstr.2026.113974)
  DOI : 10.1016/j.ijsolstr.2026.113974
• Comparison of Probabilistic Turbo Equalization Techniques in UWA Communication Systems
  
  • Khemir Melek
  • Arbi Tarak
  • Geller Benoit
  , 2026. <div><p>This paper provides a comprehensive comparison of probabilistic turbo equalization techniques for underwater acoustic (UWA) communications. We focus on two advanced methods: Expectation Propagation (EP)-based equalization and a Probabilistic Adaptive Technique (PAT) that leverages soft information, exchanged between the channel decoder and the equalizer through an enhanced optimization criterion. Unlike EP, which suffers from numerical instabilities and high computational cost due to matrix inversions, the PAT achieves low complexity by both selectively choosing the most relevant constellation points and by exploiting the sparsity of the UWA channel. We present simulations over synthetic time-varying channels and real underwater channels from the WATERMARK platform. Our results show that the PAT achieves better BER performance at lower computational complexity.</p></div>
• An all-topology two-fluid model for two-phase flows derived through Hamilton's Stationary Action Principle
  
  • Haegeman Ward
  • Orlando Giuseppe
  • Kokh Samuel
  • Massot Marc
  Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, 2026, 482 (2334), pp.20250835. We present a novel multi-fluid model for compressible two-phase flows. The model is derived through a newly developed Stationary Action Principle framework. It is fully closed and introduces a new interfacial quantity, the interfacial work. The closures for the interfacial quantities are provided by the variational principle. They are physically sound and well-defined for all types of flow topologies. The model is shown to be hyperbolic, symmetrizable, and admits an entropy conservation law. Its non-conservative products yield uniquely defined jump conditions which are provided. As such, it allows for the proper treatment of weak solutions. In the multi-dimensional setting, the model presents lift forces which are discussed. The model constitutes a sound basis for future numerical simulations. (10.1098/rspa.2025.0835)
  DOI : 10.1098/rspa.2025.0835
• A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms
  
  • Orlando Giuseppe
  • Haegeman Ward
  • Pelanti Marica
  • Massot Marc
  , 2026. We present a robust computational framework for the numerical solution of a hyperbolic 6-equation single-velocity two-phase system. The system's main interest is that, when combined with instantaneous mechanical relaxation, it recovers the solution of the 5-equation model of Kapila. Several numerical methods based on this strategy have been developed over the years. However, neither the 5- nor 6-equation model admits a complete set of jump conditions because they involve non-conservative products. Different discretizations of these terms in the 6-equation model exist. The precise impact of these discretizations on the numerical solutions of the 5-equation model, in particular for shocks, is still an open question to which this work provides new insights. We consider the phasic total energies as prognostic variables to naturally enforce discrete conservation of total energy and compare the accuracy and robustness of different discretizations for the hyperbolic operator. Namely, we discuss the construction of an HLLC approximate Riemann solver in relation to jump conditions. We then compare an HLLC wave-propagation scheme which includes the non-conservative terms, with Rusanov and HLLC solvers for the conservative part in combination with suitable approaches for the non-conservative terms. We show that some approaches for the discretization of non-conservative terms fit within the framework of path-conservative schemes for hyperbolic problems. We then analyze the use of various numerical strategies on several relevant test cases, showing both the impact of the theoretical shortcomings of the models as well as the importance of the choice of a robust framework for the global numerical strategy.
• Numerical relaxation techniques for mass transfer in three-phase liquid-vapor-gas flows
  
  • Pelanti Marica
  Computers and Fluids, Elsevier, 2026, 305, pp.106893. We describe liquid-vapor-gas flows by a hyperbolic single-velocity three-phase compressible flow model with instantaneous pressure relaxation that we studied in previous work. The model includes thermal relaxation terms to account for heat transfer, and chemical relaxation terms to describe mass transfer between the liquid and vapor phases. To numerically solve the model system we use a fractional step method where we alternate between the solution of the homogeneous system via finite volume HLLC-type schemes and the solution of systems of ordinary differential equations that take into account the relaxation source terms. In this work we propose a novel numerical procedure for chemical relaxation that can efficiently describe arbitrary-rate mass transfer, both slow finite-rate processes and stiff instantaneous ones. The main idea consists in describing the relaxation process by a system of ordinary differential equations that admits an analytical semi-exact exponential solution. This relaxation system is built by employing the relaxed models that can be derived analytically from the parent three-phase flow model in the limit of instantaneous mechanical and thermal relaxation processes, in order to guarantee the constraints of pressure and temperature equilibrium during phase transition. Some numerical experiments in one and two dimensions are presented to show the effectiveness of the proposed method. (10.1016/j.compfluid.2025.106893)
  DOI : 10.1016/j.compfluid.2025.106893
• Modelling of relative velocity, velocity fluctuations and their interactions for two-fluid models by Stationary Action Principle
  
  • Haegeman Ward
  • Orlando Giuseppe
  • Kokh Samuel
  • Massot Marc
  ESAIM: Proceedings and Surveys, EDP Sciences, 2026. The objective of this contribution is the derivation of a two-fluid model including a relative velocity between the two phases and velocity fluctuations, describing pseudo-turbulent effects, as internal variables based on Stationary Action Principle. The variational derivation, used to obtain the model, relies on the variation of a single trajectory related to the mass-weighted average velocity under the barotropic assumption. The model is hyperbolic, satisfies a second principle of thermodynamics, and admits either linearly degenerate or genuinely nonlinear characteristic fields. Moreover, the variational approach yields a fully closed model and its non-conservative products are uniquely defined for weak solutions in 1D, i.e. jump conditions can be derived. In the laminar case, when velocity fluctuations are negligible, we recover previously derived multi-fluid models which have been analyzed in several contributions. As such, the present framework allows for an original extension of the existing models to include velocity fluctuations of each phase for pseudo-turbulent flows, their coupling with the relative velocity between phases, as well as dissipative effects compatible with the thermodynamics of irreversible processes. Eventually, we provide a discussion of the limitations of the proposed model, especially regarding the extension to the open problem of non-barotropic flows.