An ALE‐based finite element strategy for modeling compressible two‐phase flows

• Published in: International journal for numerical methods in fluids 2022-12, Vol.94 (12), p.2040-2086
• Main Authors: Potghan, Nilesh, Jog, Chandrashekhar S.
• Format: Article
• Language: English
• Subjects: ALE; Compressible fluids; compressible two‐phase flow; Computation; dummy‐node technique; Finite element method; Fluid dynamics; Fluid flow; Fluids; Interpolation; Mathematical models; Pressure field; Surface tension
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.5134

In this work, we develop a numerical strategy for solving two‐phase immiscible compressible fluid flows in a general arbitrary Lagrangian–Eulerian framework. The interpolation functions for the field variables are chosen so as to produce a stable numerical formulation. We model one of the fluids in a Lagrangian setting and use a conforming mesh moving with it which circumvents the need of solving an additional diffusion equation to track or construct the interface. The discontinuity in the pressure field across the interface is accurately modeled using the dummy‐node technique. This technique yields a sharp and accurate representation of the interface and in turn a correct computation of the surface tension forces. We present a variational form of the governing equations including the surface tension effect and their exact linearization. Various benchmark examples are presented to illustrate the good performance and good coarse‐mesh accuracy of the proposed scheme. We present an ALE‐based finite element strategy for modeling compressible immiscible two‐phase flows. The appropriate choice of the interpolation functions ensures the stability of numerical strategy. We present the variational formulation based on the complete set of Navier–Stokes equations for a compressible fluid, including the surface tension effect, and their exact linearization. The use of Lagrangian setting for Fluid 1 helps to represent the interface and compute the surface tension force accurately. The discontinuity in the pressure field across the interface is accounted for by using a dummy‐node technique. The robustness and good coarse‐mesh accuracy of the algorithm is demonstrated by means of numerous examples.