Weighted Non-linear Compact Schemes for the Direct Numerical Simulation of Compressible, Turbulent Flows

Journal Article · Tue Jan 21 04:00:00 EST 2014 · Journal of Scientific Computing

DOI:https://doi.org/10.1007/s10915-014-9818-0· OSTI ID:1342896

Ghosh, Debojyoti; Baeder, James D.

A new class of compact-reconstruction weighted essentially non-oscillatory (CRWENO) schemes were introduced (Ghosh and Baeder in SIAM J Sci Comput 34(3): A1678–A1706, 2012) with high spectral resolution and essentially non-oscillatory behavior across discontinuities. The CRWENO schemes use solution-dependent weights to combine lower-order compact interpolation schemes and yield a high-order compact scheme for smooth solutions and a non-oscillatory compact scheme near discontinuities. The new schemes result in lower absolute errors, and improved resolution of discontinuities and smaller length scales, compared to the weighted essentially non-oscillatory (WENO) scheme of the same order of convergence. Several improvements to the smoothness-dependent weights, proposed in the literature in the context of the WENO schemes, address the drawbacks of the original formulation. This paper explores these improvements in the context of the CRWENO schemes and compares the different formulations of the non-linear weights for flow problems with small length scales as well as discontinuities. Simplified one- and two-dimensional inviscid flow problems are solved to demonstrate the numerical properties of the CRWENO schemes and its different formulations. Canonical turbulent flow problems—the decay of isotropic turbulence and the shock-turbulence interaction—are solved to assess the performance of the schemes for the direct numerical simulation of compressible, turbulent flows

• Research Organization: Argonne National Lab. (ANL), Argonne, IL (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
• DOE Contract Number: AC02-06CH11357
• OSTI ID: 1342896
• Journal Information: Journal of Scientific Computing, Journal Name: Journal of Scientific Computing Journal Issue: 1 Vol. 61; ISSN 0885-7474
• Publisher: Springer
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
CRWENO schemes
Compact schemes
Compressible flows
Direct numerical simulation
High resolution schemes