Unsteady Euler airfoil solutions using unstructured dynamic meshes

TLDR

The paper presents two algorithms for solving the time‑dependent Euler equations and a dynamic mesh algorithm to analyze unsteady aerodynamics of oscillating airfoils. Both algorithms are developed on unstructured triangular grids; one employs a Runge–Kutta time‑stepping scheme with finite‑volume central differencing, while the other uses a modified Euler integration with an upwind‑biased Van Leer flux‑vector splitting discretization. Results demonstrate the capability of the solvers and dynamic mesh algorithm for unsteady Euler analysis of oscillating airfoils.

Abstract

Two algorithms for the solution of the time-dependent Euler equations are presented for unsteady aerodynamic analysis of oscillating airfoils. Both algorithms were developed for use on an unstructured grid made up of triangles. The first flow solver involves a Runge-Kutta time-stepping scheme with a finite-volume spatial discretization that reduces to central differencing on a rectangular mesh. The second flow solver involves a modified Euler time-integration scheme with an upwind-biased spatial discretization based on the flux-vector splitting of Van Leer. The paper presents descriptions of the Euler solvers and dynamic mesh algorithm along with results which assess the capability.