AI Insight
This study derives the complete mathematical eigenstructure for two formulations of the Allaire five-equation model used to simulate flows with multiple fluids or phases. The authors demonstrate that performing variable reconstruction in characteristic space rather than physical space eliminates spurious pressure oscillations at material interfaces, with the fully conservative formulation using a thermodynamic jump term and the semi-conservative formulation employing a structural zero to maintain pressure equilibrium. Both formulations also reveal that shear waves decouple from thermodynamic and interface effects in compressible multiphase flows.
Why it matters
This work provides a rigorous mathematical foundation for accurately simulating flows involving multiple materials with different properties, such as gas-liquid interfaces in combustion engines, underwater explosions, or industrial mixing processes. The demonstrated elimination of numerical artifacts at material boundaries could improve the reliability of computational fluid dynamics simulations in aerospace, energy, and chemical engineering applications.
Understand the Science
⚠️ Preprint – Noch nicht peer-reviewed
Dieser Artikel wurde noch nicht von unabhängigen Experten begutachtet. Die Ergebnisse sind vorläufig und sollten mit Vorsicht interpretiert werden.
Abstract: Compressible multiphase and multicomponent solvers require accurate interface representation without spurious pressure oscillations. At material interfaces, pressure and velocity are continuous while density and the equation of state exhibit abrupt discontinuities. Standard approaches reconstruct primitive or characteristic variables to capture these properties, but do not clarify the failure mechanisms of conservative reconstruction or fully leverage the wave-decoupling advantages of characteristic decomposition. This work derives the complete eigenstructure of the Allaire five-equation model for two variable sets. In the fully conservative~(FC) formulation, $mathbf{U} = [alpha_1rho_1,,alpha_2rho_2,,rho u,,rho v,,rho E,,alpha_1]^T$, eigenvectors contain a thermodynamic jump term~$Psi$ that enforces $dp=0$ and $du=0$ at material contacts by compensating for compressibility mismatches. In the semi-conservative~(SC) formulation, $mathbf{V} = [alpha_1rho_1,,alpha_2rho_2,,rho u,,rho v,,p,,alpha_1]^T$, the volume-fraction eigenvector carries a structural zero in the pressure slot, enforcing equilibrium without thermodynamic correction. Explicit left and right eigenvectors are derived for one- and two-dimensional stiffened-gas flows. Both formulations satisfy Abgrall’s equilibrium condition when reconstruction is performed in characteristic space; reconstruction in physical space yields $mathcal{O}(1)$ pressure and velocity errors at interfaces regardless of the variable set. The eigenvector structure further reveals that the shear wave is decoupled from all thermodynamic and interface fields in both formulations, extending this result from single-species to compressible multiphase flows including gas-liquid configurations. One- and two-dimensional gas-gas and gas-liquid test cases confirm oscillation-free, accurate results.