Thermodynamic-Metric Preconditioning for Entropy-Stable Implicit Simulation of Gas-Liquid Two-Fluid Networks

• Lucas Tavares

  Universidade Federal do Vale do São Francisco, Avenida José de Sá Maniçoba S/N, Centro, Petrolina, Brazil

  Author

• Bruno Azevedo

  Universidade Estadual de Santa Cruz, Rodovia Jorge Amado Km 16, Salobrinho, Ilhéus, Brazil

  Author

Gas-liquid multiphase transport in annular channels and networked conduits is often modeled by two-fluid balance laws whose numerical solution becomes challenging under stiff interfacial exchange, strong slip, and sparse operational constraints. In practical regimes, reliable computation requires more than accuracy: it requires positivity of phase masses and volume fractions, bounded thermodynamic states, and dissipation consistent with the second law. This paper develops a structure-preserving implicit simulation framework for one-dimensional two-fluid networks based on a thermodynamic metric that acts simultaneously as an entropy symmetrizer and as a preconditioner for Newton--Krylov solves. The central contribution is a preconditioning strategy defined in entropy-variable coordinates, where the Jacobian of the discretized residual is rendered close to symmetric in a weighted inner product and where stiff source couplings are balanced by metric-consistent scaling. A complementary constrained projection is introduced to enforce admissibility during nonlinear iterations without destroying differentiability, enabling stable sensitivity analysis through discrete adjoints. The method integrates network junction constraints through a Schur-complement coupling that preserves conservation while maintaining the entropy inequality at the fully discrete level. Numerical experiments on annular segments and branched networks demonstrate that the thermodynamic-metric preconditioner reduces Krylov iterations across wide operating envelopes and suppresses solver stagnation near phase-disappearance limits, while the admissibility projection eliminates nonphysical intermediate iterates that would otherwise destabilize implicit solves. The resulting approach targets robust, scalable simulation and gradient computation for multiphase networks under stiff closures and limited numerical damping.

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