An adaptive ALE scheme for non-ideal compressible fluid dynamics over dynamic unstructured meshes

Abstract

This paper investigates the application of mesh adaptation techniques in the Non-Ideal Compressible Fluid Dynamic (NICFD) regime, a region near the vapor-liquid saturation curve where the flow behavior significantly departs from the ideal gas model, as indicated by a value of the fundamental derivative of gasdynamics less than one. A recent interpolation-free finite-volume adaptive scheme is exploited to modify the grid connectivity in a conservative way, and the governing equations for compressible inviscid flows are solved within the Arbitrary Lagrangian Eulerian framework by including special fictitious fluxes representing volume modifications due to mesh adaptation. The absence of interpolation of the solution to the new grid prevents spurious oscillations that may make the solution of the flow field in the NICFD regime more difficult and less robust. Non-ideal gas effects are taken into account by adopting the polytropic Peng-Robinson thermodynamic model. The numerical results focus on the problem of a piston moving in a tube filled with siloxane MD 4 M, a simple configuration which can be the core of experimental research activities aiming at investigating the thermodynamic behavior of NICFD flows. Several numerical tests involving different piston movements and initial states in 2D and 3D assess the capability of the proposed adaption technique to correctly capture compression and expansion waves, as well as the generation and propagation of shock waves, in the NICFD and in the non-classical regime.

An ALE residual distribution scheme for the unsteady Euler equations over triangular grids with local mesh adaptation

“…This can be consider a drawback of our method, but in this way, we can avoid to store the history of the grid modifications and the cumulative property of the swept area makes straightforward the treatment of consecutive topology changes involving the same edges. Once the mesh adaptation is ended, we compute the interface velocity for all grid nodes through (21) considering the whole swept area stored in ∆A i . Then, we compute the solution on the new grid by solving the non-linear system of equations…”

“…Following the second path, Guardone and co-workers [18,19] proposed a strategy to describe the local grid topology changes due to unstructured mesh adaptation as a series of fictitious collapses and expansions which can be treated within the underlying ALE formulation as continuous deformations, preserving mesh conservation and avoiding any interpolation. This strategy was also extended to three-dimensional grids [20] and non-ideal fluid flows [21]. Finally, still following the local path, also Barral and co-workers [15] proposed a three-dimensional adaptive ALE scheme for CFD simulations, which however guarantees conservativeness only if the volume domain does not change.…”

A pressure‐based method for weakly compressible two‐phase flows under a Baer–Nunziato type model with generic equations of state and pressure and velocity disequilibrium

“…A popular instance in this class is the Peng–Robinson 84 EOS, which is used in this work to model liquid and vapor CO$$$ {}_2 $$$ in Section 7.5. The expression of thermal and caloric EOSs for this model can be found in References 86 and 88.…”

Level-Set Mass-Conservative Front-Tracking Technique for Multistep Simulations of In-Flight Ice Accretion

“…In this work, the level-set formulation is originally combined with unstructured mesh adaptation techniques [23,24] to profit from the advantages of both IBMs and BFMs. The proposed robust strategy is able to obtain a body-fitted mesh compliant with complex geometries and even front collisions.…”