Computational Approaches to Compressible Micropolar Fluid Flow in Moving Parallel Plate Configurations

In this paper, we consider the unsteady flow of a compressible micropolar fluid between two moving, thermally isolated parallel plates. The fluid is characterized as viscous and thermally conductive, with polytropic thermodynamic properties. Although the mathematical model is inherently three-dimensional, we assume that the variables depend on only a single spatial dimension, reducing the problem to a one-dimensional formulation. The non-homogeneous boundary conditions representing the movement of the plates lead to moving domain boundaries. The model is formulated in mass Lagrangian coordinates, which leads to a time-invariant domain. This work focuses on numerical simulations of the fluid flow for different configurations. Two computational approaches are used and compared. The first is based on the finite difference method and the second is based on the Faedo–Galerkin method. To apply the Faedo–Galerkin method, the boundary conditions must first be homogenized and the model equations reformulated. On the other hand, in the finite difference method, the non-homogeneous boundary conditions are implemented directly, which reduces the computational complexity of the numerical scheme. In the performed numerical experiments, it was observed that, for the same accuracy, the Faedo–Galerkin method was approximately 40 times more computationally expensive compared to the finite difference method. However, on a dense numerical grid, the finite difference method required a very small time step, which could lead to an accumulation of round-off errors. On the other hand, the Faedo–Galerkin method showed the convergence of the solutions as the number of expansion terms increased, despite the higher computational cost. Comparisons of the obtained results show good agreement between the two approaches, which confirms the consistency and validity of the numerical solutions.