Investigation of high-order upwinded differencing for vortex convection

Improving Godunov-type reconstructions for simulation of vortex-dominated flows

“…Although large accuracy improvement has been observed with the use of this fifth-order spatial discretization (e.g. [22][23][24][25]), there is still a large room left for further accuracy improvement [28]. In order to search for a more effective approach for improvement of the resolution capability of the Godunov-type schemes and thus reduction of their numerical diffusion, a systematic Fourier accuracy analysis is performed in this paper to investigate the spectral distribution of numerical errors inherent in a Godunov-type reconstruction, including both the reconstruction of the solution within each cell and the computation of the derivative terms of the reconstruction.…”

“…However, this third-order spatial discretization has been found too dissipative for simulation of vortex-dominated flows [1,3,22]. A fifth-order polynomial fit has been suggested to replace this more traditional third-order spatial discretization for better vortex preservation (e.g.…”

“…A fifth-order polynomial fit has been suggested to replace this more traditional third-order spatial discretization for better vortex preservation (e.g. [22][23][24][25]). In fact, this fifth-order polynomial fit has also been used in many monotone schemes (e.g.…”

Adaptive Euler simulations of airfoil–vortex interaction

“…Such a flow solver has been found very diffusive for simulation of vortex-dominated flows [6,7]. To improve the numerical accuracy over this spatial discretization, a more popular approach is to use a higher-order (e.g.…”

“…To improve the numerical accuracy over this spatial discretization, a more popular approach is to use a higher-order (e.g. fifth-order) polynomial fit of the interface values [5][6][7]. However, both Fourier accuracy analysis and the numerical result of a simple two-dimensional vortex convection case in References [13,14] have indicated that it would be much more effective for reduction of numerical diffusion by keeping the piecewise quadratic reconstruction of the solution but with the more accurate sixth-order compact difference computed slope and curvature.…”