TIME-ACCURATE EULER SIMULATIONS OF VORTEX CONVECTION

This paper presents a new family of time-accurate Euler solvers, which are high order accurate in both time and space for one dimensional problems, but only 2nd order accurate in time for multidimensional cases due to the application of Strang’s time-splitting method. We apply them to simulate the long-term 2 D convection of a vortex in a free-stream. Numerical results indicate a significant spatial accuracy improvement over traditional rotorcraft Computational Fluid Dynamics codes. On a typical mesh, with 4 points across the vortex core, the 5th order SHIFT scheme can convect the vortex with 20 percent decay in the peak-to-peak vertical velocity across the vortex core for approximately 90 core radii while a 3rd order TVD scheme will have the same decay after a convection of just 3 core radii. However, the temporal accuracy is still not satisfactory. Therefore, future work will concentrate on reducing the factorization errors for multidimensional cases.