Validation of an Output-Adaptive, Tetrahedral Cut-Cell Method for Sonic Boom Prediction

Abstract

A cut-cell approach to computational fluid dynamics that uses the median dual of a tetrahedral background grid is described. The discrete adjoint is also calculated for an adaptive method to control error in a specified output. The adaptive method is applied to sonic boom prediction by specifying an integral of offbody pressure signature as the output. These predicted signatures are compared to wind-tunnel measurements to validate the method for sonic boom prediction. Accurate midfield sonic boom pressure signatures are calculated with the Euler equations without the use of hybrid grid or signature propagation methods. Highly refined, shock-aligned anisotropic grids are produced by this method from coarse isotropic grids created without prior knowledge of shock locations. A heuristic reconstruction limiter provides stable flow and adjoint solution schemes while producing similar signatures to Barth-Jespersen and Venkatakrishnan limiters. The use of cut cells with an output-based adaptive scheme automates the volume grid generation task after a triangular mesh is generated for the cut surface.

Numerical Simulations of a Quiet SuperSonic Technology (QueSST) Aircraft Preliminary Design

“…9 to 11) and sonic boom predictions (Ref. 12), as well as internal flow applications such as s-ducts (Ref. 13).…”

Summary of the 2008 NASA Fundamental Aeronautics Program Sonic Boom Prediction Workshop

“…These reconstructed gradients are reduced with a continuously differentiable heuristic limiter that permits good iterative convergence. 42 Backward facing steps, e.g., blunt trailing edges, can create strong expansions in Euler flows. These strong expansions can create difficulties for approximate Riemann solvers.…”

Adjoint-based method for supersonic aircraft design using equivalent area distribution

“…This motivates the use of anisotropic output-based adaptation; indeed, several studies have shown that the adjoint-weighted residual method coupled with metric-based anisotropic adaptation can reduce the number of solution degrees of freedom an order of magnitude relative to isotropic adaptation. 5,6 While automated a posteriori grid adaptation is attractive for general flows, a priori adaptation can be more efficient if the locations of critical flow features are well known. A common example is refinement of the boundary layer in Reynolds-averaged Navier-Stokes simulations.…”