A meshless front tracking method for the Euler equations of fluid dynamics

A meshless front tracking method for the Euler equations of fluid dynamics

Witteveen, J.A.S.

Aerospace Engineering

Aerodynamics & Wind Energy

2009-06-01

A second order front tracking method is developed for solving the Euler equations of inviscid fluid dynamics numerically. Front tracking methods are usually limited to first order accuracy, since they are based on a piecewise constant approximation of the solution. Here the second order convergence is achieved by building a piecewise linear reconstruction of the piecewise constant front tracking solution in a post-processing step. The linearization is performed by decomposing the piecewise constant solution of the hyperbolic system into its wave components and by linearizing the wave solutions separately. In order to achieve a physically correct linearization, the front types of the previously developed improved front tracking method are employed. It is illustrated numerically for the one-dimensional unsteady interacting blast waves problem and a two-dimensional supersonic airfoil flow validation study that the proposed front tracking method can achieve second order convergence also in the presents of strong discontinuities.

front tracking
second order
meshless methods
Euler equations

http://resolver.tudelft.nl/uuid:f57d4dd7-fbdd-43d5-aa82-c1abd2a9cc14

Proceedings of the Computational Modelling and Advanced Simulations, CMAS 2009, 30 June-3 July, 2009, Bratislava, Slovakia

Institutional Repository

conference paper

(c) 2009 Witteveen, J.A.S.