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Designing adaptive low-dissipative high order schemes for long-time integrations
KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.
2004 (English)In: Turbulent flow computation, Kluwer Academic Publishers, 2004, 141-198 p.Chapter in book (Refereed)
Abstract [en]

A general framework for the design of adaptive low-dissipative high order schmes is presented. It encompasses a rather complete treatment of the numerical approach based on four integrated design criteria: (1) For stability considerations, condition the governing equations before the application of the appropriate numerical scheme whenever it is possible. (2) For consistency, compatible schemes that possess stability properties, including physical and numerical boundary condition treatments, similar to those of the discrete analogue of the continuum are preferred. (3) For the minimization of numerical dissipation contamination, efficient and adaptive numerical dissipation control to further improve nonlinear stability and accuracy should be used. (4) For practical considerations, the numerical approach should be efficient and applicable to general geometries, and an efficient and reliable dynamic grid adaptation should be used if necessary. These design criteria are, in general, very useful to a wide spectrum of flow simulations. However, the demand on the overall numerical approach for nonlinear stability and accuracy is much more stringent for long-time integration of complex multiscale viscous shock/shear/turbulence/acoustics interactions and numerical combustion. Robust classical numerical methods for less complex flow physics are not suitable or practical for such applications. The present approach is designed expressly to address such flow problems, especially unsteady flows. The minimization of employing very fine grids to overcome the production of spurious numerical solutions and/or instability due to under-resolved grids is also sought [79, 17]. The incremental studies to illustrate the performance of the approach are summarized. Extensive testing and full implementation of the approach is forthcoming. The results shown so far are very encouraging.

Place, publisher, year, edition, pages
Kluwer Academic Publishers, 2004. 141-198 p.
, Fluid Mechanics and its Applications, ISSN 09265112
Keyword [en]
Adaptive numerical dissipation/Filer controls, Entropy splitting, High order finite difference methods, Integration-by-parts, Linear and nonlinear filters, Linear and nonlinear instabilities, Low-dissipative schemes, Multi-resolution wavelets, Skew-symmetric form, Summation-by-parts, Wavelets
National Category
Computational Mathematics
URN: urn:nbn:se:kth:diva-156909ScopusID: 2-s2.0-84859878285ISBN: 1402005237ISBN: 9781402005237OAI: diva2:770623

QC 20141211

Available from: 2014-12-11 Created: 2014-12-04 Last updated: 2014-12-11Bibliographically approved

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Sjögreen, Björn
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