Characteristic-Based Flux Splitting to Solve Compressible Flow over an Airfoil

Instabilities of Stationary Inviscid Compressible Flow around an Airfoil

In this paper we numerically solve the stationary inviscid flow around an airfoil. Using the second-order explicit Runge–Kutta method in combination with the MUSCL scheme and the minmod limiter, we do not obtain a machine accurate solution. This has already been observed in literature and is explained by the non-differentiability of the minmod limiter. An analysis of the limiter shows that it i...

Airfoil design for compressible inviscid flow based on shape calculus

Aerodynamic design based on the Hadamard representation of shape gradients is considered. Using this approach, the gradient of an objective function with respect to a deformation of the shape can be computed as a boundary integral without any additional “mesh sensitivities” or volume quantities. The resulting very fast gradient evaluation procedure greatly supports a one-shot optimization strat...

The numerical simulation of compressible flow in a Shubin nozzle using schemes of Bean-Warming and flux vector splitting

Over the last ten years, robustness of schemes has raised an increasing interest among the CFD community. The objective of this article is to solve the quasi-one-dimensional compressible flow inside a “Shubin nozzle” and to investigate Bean-Warming and flux vector splitting methods for numerical solution of compressible flows. Two different conditions have been considered: first, there is a sup...

A Nonlinear Multiscale Viscosity Method to Solve Compressible Flow Problems

On Numerical Simulation of Airfoil Vibrations Induced by Compressible Flow∗

The subject of the paper is the numerical simulation of the interaction of twodimensional compressible viscous flow and a vibrating airfoil. The airfoil is considered as a solid body with two degrees of freedom, moving in the vertical direction and rotating around an elastic axis. The numerical simulation consists of the solution of the Navier-Stokes system by the space discontinuous Galerkin m...