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

Accurate monotonicity- and extrema-preserving methods through adaptive nonlinear hybridizations

“…More recently, the approach by Hill and Pullin of combining WENO methods selectively with centered differencing is similar to these methods [16]. Finally, Tang and Baeder [34] provide design principles for a piece-wise parabolic method with enhanced accuracy for use in vorticity-dominated flows.…”

High accuracy flow simulations: Advances and challenges for future needs in aeronautics

“…The field of high-order methods has seen a surge of research activity over the last decade, particularly due to its potential in applications such as LES [30][31][32][33][34], DNS [35][36][37], Computational Aero-Acoustics (CAA) [38,39], turbulent combustion [40] and vortex-dominated flows [41]. However, this field has not yet reached the level of maturity required to solve real flow problems on complicated geometries.…”

Adaptive Euler simulations of airfoil–vortex interaction

“…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. The resulting improved third-order accurate spatial discretization is called as Q6c, i.e.…”

“…The measured time histories of the surface pressure coefficient at three chordwise locations (2, 5, and 10% of the chord length) in Reference [20] are used to verify the reduced numerical diffusion contained in the direct numerical simulation by combining the two-step grid redistribution method of Reference [19] and the improved spatially third-order accurate Euler solver of Reference [14]. It is found in Figure 5 that compared with multiblock grid Navier-Stokes results in Reference [20] based on nearly 193 000 points, our adaptive Euler computation with only about 32 800 points gives much steeper slopes of the pressure and much larger peak values due to much less numerical diffusion inherent in the computation.…”

“…This can be observed in both the magnitude of the negative peak loading as well as the slope of the loading as the vortex passes underneath the airfoil. The combination of the grid redistribution method of Reference [19] and the improved Euler solver of Reference [14] significantly improves the result. In fact, the result from the direct Euler simulation using the modified TURNS methodology is almost identical to the one given by the perturbation method.…”