Development and Verification of a Two-Dimensional Euler Solver for Airfoil Flow Using a Structured Finite Volume Method

Abstract

This work presents the development and verification of a two-dimensional compressible flow solver for airfoil analysis based on the inviscid Euler equations. The solver is implemented in Python as a structured finite volume method on a body-fitted C-type mesh and is designed to replicate the numerical formulation of a legacy Fortran code while introducing modern array-based computational techniques. The governing equations are discretized using a central difference flux scheme with artificial dissipation for numerical stability. Time integration is performed using a multistage explicit Runge–Kutta method with local time stepping. Boundary conditions are applied through a combination of solid wall constraints, far-field conditions, and ghost-cell updates to maintain consistent stencil operations. A key aspect of this work is the re-architecture of the solver using NumPy-based vectorization and precomputed geometric metrics, including face normals and cell volumes. These design choices significantly reduce computational overhead while preserving numerical equivalence with the original formulation. A layered verification strategy is employed, beginning with exact geometric validation on uniform grids and progressing to full solver integration on a NACA 0012 airfoil mesh. Results demonstrate stable convergence and physically consistent flow solutions across subsonic and transonic regimes. Pressure coefficient distributions and Mach contour plots confirm expected aerodynamic behavior, including symmetry in zero angle cases and lift generation under nonzero angle of attack. The implementation establishes a validated computational framework that can serve as a foundation for further extensions, including viscous modeling and convergence acceleration techniques.