Showing papers by "Mark H. Carpenter published in 2013"
TL;DR: A comparison technique is used to derive a new Entropy Stable Weighted Essentially Non-Oscillatory (SSWENO) finite difference method, appropriate for simulations of problems with shocks.
286 citations
TL;DR: In this article, the Lax-Wendroff theorem states that conservation law equations that are split into linear combinations of the divergence and product rule form and then discretized using any diagonal-norm skew-symmetric summation-by-parts spatial operator yield discrete operators that are conservative.
154 citations
24 Jun 2013
TL;DR: In this article, the authors provide a summary of selected research activities targeting the current gaps in high-fidelity transition prediction, specifically those related to the receptivity and laminar breakdown phases of crossflow induced transition in a subsonic swept-wing boundary layer.
Abstract: The economic and environmental benefits of laminar flow technology via reduced fuel burn of subsonic and supersonic aircraft cannot be realized without minimizing the uncertainty in drag prediction in general and transition prediction in particular. Transition research under NASA's Aeronautical Sciences Project seeks to develop a validated set of variable fidelity prediction tools with known strengths and limitations, so as to enable "sufficiently" accurate transition prediction and practical transition control for future vehicle concepts. This paper provides a summary of selected research activities targeting the current gaps in high-fidelity transition prediction, specifically those related to the receptivity and laminar breakdown phases of crossflow induced transition in a subsonic swept-wing boundary layer. The results of direct numerical simulations are used to obtain an enhanced understanding of the laminar breakdown region as well as to validate reduced order prediction methods.
20 citations
24 Jun 2013
TL;DR: In this article, a systematic approach is presented for developing entropy stable (SS) formulations of any order for the Navier-Stokes equations, which are valid for smooth as well as discontinuous flows provided sufficient dissipation is added at shocks and discontinuities.
Abstract: A systematic approach is presented for developing entropy stable (SS) formulations of any order for the Navier-Stokes equations. These SS formulations discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality. They are valid for smooth as well as discontinuous flows provided sufficient dissipation is added at shocks and discontinuities. Entropy stable formulations exist for all diagonal norm, summation-by-parts (SBP) operators, including all centered finite-difference operators, Legendre collocation finite-element operators, and certain finite-volume operators. Examples are presented using various entropy stable formulations that demonstrate the current state-of-the-art of these schemes.
16 citations
24 Jun 2013
10 citations
24 Jun 2013
TL;DR: In this article, a systematic approach is presented for developing entropy stable (SS) formulations of any order for the Navier-Stokes equations, which are valid for smooth as well as discontinuous flows provided sufficient dissipation is added at shocks and discontinuities.
Abstract: A systematic approach is presented for developing entropy stable (SS) formulations of any order for the Navier-Stokes equations. These SS formulations discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality. They are valid for smooth as well as discontinuous flows provided sufficient dissipation is added at shocks and discontinuities. Entropy stable formulations exist for all diagonal norm, summation-by-parts (SBP) operators, including all centered finite-difference operators, Legendre collocation finite-element operators, and certain finite-volume operators. Examples are presented using various entropy stable formulations that demonstrate the current state-of-the-art of these schemes.
8 citations