Showing papers by "Mark H. Carpenter published in 2009"
TL;DR: A systematic approach is presented that enables ''energy stable'' modifications for existing WENO schemes of any order and develops new weight functions and derive constraints on their parameters, which provide consistency, much faster convergence of the high-order ESWenO schemes to their underlying linear schemes for smooth solutions with arbitrary number of vanishing derivatives, and better resolution near strong discontinuities than the conventional counterparts.
147 citations
TL;DR: A new third-order Energy Stable Weighted Essentially Non-Oscillatory (ESWENO) finite difference scheme for scalar and vector hyperbolic equations with piecewise continuous initial conditions is developed and is proven to be linearly stable in the energy norm for both continuous and discontinuous solutions.
117 citations
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TL;DR: Block-to-block interface interpolation operators are constructed for several common high-order finite difference discretizations that maintain the strict stability, accuracy, and conservation properties of the base scheme even when nonconforming grids or dissimilar operators are used in adjoining blocks.
Abstract: Block-to-block interface interpolation operators are constructed for several common high-order finite difference discretizations. In contrast to conventional interpolation operators, these new interpolation operators maintain the strict stability, accuracy and conservation of the base scheme even when nonconforming grids or dissimilar operators are used in adjoining blocks. The stability properties of the new operators are verified using eigenvalue analysis, and the accuracy properties are verified using numerical simulations of the Euler equations in two spatial dimensions.
97 citations
22 Jun 2009
TL;DR: In this paper, a roughness-based transition control for a low-speed swept airfoil model with a chord Reynolds number of 7.15 million has been proposed, with the goal of evaluating this methodology in the context of transition prediction for a known configuration for which roughness based crossflow transition control has been demonstrated under flight conditions and analyzing the mechanism of transition delay via the introduction of discrete roughness elements.
Abstract: A combination of parabolized stability equations and secondary instability theory has been applied to a low-speed swept airfoil model with a chord Reynolds number of 7.15 million, with the goals of (i) evaluating this methodology in the context of transition prediction for a known configuration for which roughness based crossflow transition control has been demonstrated under flight conditions and (ii) of analyzing the mechanism of transition delay via the introduction of discrete roughness elements (DRE). Roughness based transition control involves controlled seeding of suitable, subdominant crossflow modes, so as to weaken the growth of naturally occurring, linearly more unstable crossflow modes. Therefore, a synthesis of receptivity, linear and nonlinear growth of stationary crossflow disturbances, and the ensuing development of high frequency secondary instabilities is desirable to understand the experimentally observed transition behavior. With further validation, such higher fidelity prediction methodology could be utilized to assess the potential for crossflow transition control at even higher Reynolds numbers, where experimental data is currently unavailable.
18 citations
05 Jan 2009
TL;DR: In this article, a systematic approach is presented that enables energy stable modifications for existing WENO schemes of any order, and a one-parameter family of fifth-order upwind-biased ESWENO scheme up to eighth order are presented in the appendix.
Abstract: A third-order Energy Stable Weighted Essentially Non-Oscillatory (ESWENO) finite difference scheme developed by Yamaleev and Carpenter was proven to be stable in the energy norm for both continuous and discontinuous solutions of systems of linear hyperbolic equations. Herein, a systematic approach is presented that enables 'energy stable' modifications for existing WENO schemes of any order. The technique is demonstrated by developing a one-parameter family of fifth-order upwind-biased ESWENO schemes; ESWENO schemes up to eighth order are presented in the appendix. New weight functions are also developed that provide (1) formal consistency, (2) much faster convergence for smooth solutions with an arbitrary number of vanishing derivatives, and (3) improved resolution near strong discontinuities.
6 citations