Publications

2026

• 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
• Path-following methods for phase-field simulation of quasi-static crack propagation
  
  • Loiseau Flavien
  • Lazarus Véronique
  , 2026. 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 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 identify several path-following methods that are both constitutive model-independent and problem-independent, while remaining straightforward to implement. To achieve this, we focus on partitioned path-following methods based on the displacement field, which decouple the path-following control equation from the rest of the system, providing an easier integration into staggered solvers. In addition, we also introduce a new path-following method which limit the maximum strain increment outside the cracked regions. Second, through three crack propagation problems of increasing complexity, we assess the equilibrium path predictions of the variational phase-field model by comparison with the associated sharp crack model. 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.
• 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, The, 2026. 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