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ISSN Online: 2379-1748
ISBN Flash Drive: 978-1-56700-517-2
5-6th Thermal and Fluids Engineering Conference (TFEC)
A VARIATIONAL APPROACH TO DESIGN AN ALE SCHEME FOR N-FLUID FLOWS
Resumo
In some highly demanding fluid dynamics simulations, it appears necessary to simulate multi-fluid flows involving numerous constraints at the same time, such as (and non-limitatively): large numbers of fluids (typically 10 and above), both isentropic and strongly shocked compressible evolution, large heat sources, large deformations, transport over large distances, and highly variable or contrasted equation of state (EOS) stiffnesses.
Fulfilling such a challenge in a robust and tractable way demands that thermodynamic consistency of the numerical scheme be carefully ensured. This is addressed here over an arbitrarily evolving computational grid (ALE or Arbitrary Lagrangian−Eulerian approach) by a three-step mimicking derivation: i) to ensure a compatible (approximately symplectic) exchange between internal and kinetic energies under isentropic conditions, a variational least action principle is used to generate the proper pressure forces in the momentum equations; ii) to generate the conservative internal energy equation, a tally is performed to match the kinetic energy, and iii) artificial dissipation is added to ensure shock stability, but other physical terms could also be included (drag, heat exchange, etc.).
Varied multi-fluid test cases show satisfactory behavior, including the 2D, close-to-sonic, high volumefraction convergence of eight Gaussian packets of different stiffened-gas fluids in a background of perfect gas (under the sole pressure coupling).
Fulfilling such a challenge in a robust and tractable way demands that thermodynamic consistency of the numerical scheme be carefully ensured. This is addressed here over an arbitrarily evolving computational grid (ALE or Arbitrary Lagrangian−Eulerian approach) by a three-step mimicking derivation: i) to ensure a compatible (approximately symplectic) exchange between internal and kinetic energies under isentropic conditions, a variational least action principle is used to generate the proper pressure forces in the momentum equations; ii) to generate the conservative internal energy equation, a tally is performed to match the kinetic energy, and iii) artificial dissipation is added to ensure shock stability, but other physical terms could also be included (drag, heat exchange, etc.).
Varied multi-fluid test cases show satisfactory behavior, including the 2D, close-to-sonic, high volumefraction convergence of eight Gaussian packets of different stiffened-gas fluids in a background of perfect gas (under the sole pressure coupling).