High-order meshless solver for compressible fluid flow and global stability analysis using polyharmonic spline radial basis functions

Abstract

This study presents a high-order meshless global stability analysis of compressible flow within a Taylor Couette apparatus using Polyharmonic Spline Radial Basis Functions (PHS-RBF) appended with polynomials as interpolation functions. Analyzing the flow within the Taylor Couette apparatus is fundamental in fluid dynamics, providing critical insights into flow instabilities and transition phenomena that impact the understanding of rotating fluid systems and their practical applications. Our methodology involves a two-step computational approach. First, a meshless solver is developed for solving compressible fluid flow equations. The base flow profiles are computed from this solver. This base flow solution is then utilized as input for a developed stability code that performs the global stability analysis. The PHS-RBF method offers several advantages, including high accuracy and flexibility in handling complex geometries without a structured grid, making it particularly suited for this type of analysis. This approach also ensures that the spatial discretization of the perturbed and linearized Navier-Stokes equations is highly accurate and stable. The stability analysis results reveal the critical Reynolds and Mach numbers at which instabilities arise, offering deeper insights into the transition mechanisms in compressible flow within the Taylor Couette apparatus. This work demonstrates the effectiveness of the meshless method for high-order stability analysis and opens up new possibilities for studying flow instabilities in complex fluid systems without the limitations imposed by traditional mesh-based methods. The insights gained from this research can be directly applied to improving the design and analysis of rotating fluid systems, enhancing their efficiency and stability in various engineering applications.