Construction of low dissipative high-order well-balanced filter schemes for non-equilibrium flows
- Center for Turbulence Research, Stanford University, Stanford, CA 94305 (United States)
- NASA Ames Research Center, Moffett Field, CA 94035 (United States)
- Lawrence Livermore National Laboratory, Livermore, CA 94551 (United States)
- Division of Applied Mathematics, Brown University, Providence, RI 02912 (United States)
The goal of this paper is to generalize the well-balanced approach for non-equilibrium flow studied by Wang et al. (2009) to a class of low dissipative high-order shock-capturing filter schemes and to explore more advantages of well-balanced schemes in reacting flows. More general 1D and 2D reacting flow models and new examples of shock turbulence interactions are provided to demonstrate the advantage of well-balanced schemes. The class of filter schemes developed by Yee et al. (1999) , Sjoegreen and Yee (2004) and Yee and Sjoegreen (2007) consist of two steps, a full time step of spatially high-order non-dissipative base scheme and an adaptive non-linear filter containing shock-capturing dissipation. A good property of the filter scheme is that the base scheme and the filter are stand-alone modules in designing. Therefore, the idea of designing a well-balanced filter scheme is straightforward, i.e. choosing a well-balanced base scheme with a well-balanced filter (both with high-order accuracy). A typical class of these schemes shown in this paper is the high-order central difference schemes/predictor-corrector (PC) schemes with a high-order well-balanced WENO filter. The new filter scheme with the well-balanced property will gather the features of both filter methods and well-balanced properties: it can preserve certain steady-state solutions exactly; it is able to capture small perturbations, e.g. turbulence fluctuations; and it adaptively controls numerical dissipation. Thus it shows high accuracy, efficiency and stability in shock/turbulence interactions. Numerical examples containing 1D and 2D smooth problems, 1D stationary contact discontinuity problem and 1D turbulence/shock interactions are included to verify the improved accuracy, in addition to the well-balanced behavior.
- OSTI ID:
- 21499746
- Journal Information:
- Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 11 Vol. 230; ISSN JCTPAH; ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
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