Title: Adaptive clipping‐and‐redistribution algorithms for bounded and conservative high‐order interpolations applied to discontinuous and reactive flows

Abstract

A new adaptive clipping-and-redistribution method is presented which provides bounds-preservation for multidimensional interpolation in the context of high-order finite-volume discretizations with adaptive mesh refinement (AMR). The underlying finite-volume method (FVM) for the computational fluid dynamics applications is fourth-order accurate for smooth solutions and utilizes AMR for computational efficiency in solving multiscale problems involving turbulence and combustion. High-order interpolation between different AMR levels is required. However, this operation often leads to numerical issues because combustion species must have physical bounds preserved. The present study overcomes two major challenges in the development of the high-order interpolation method. First, the method needs to be bound-preserving near extrema or discontinuities to prevent the emergence of unphysical oscillations while maintaining fourth-order accuracy in smooth flows. Second, the method needs to satisfy the conservation requirement in multiple dimensions, particularly in the context of curvilinear coordinate transformations. Additionally, the method is designed to be localized and computationally inexpensive. The new interpolation scheme is demonstrated by solving reacting flows, which are extremely sensitive to unphysical overshoots in conserved quantities. The test problems are shock-induced H₂-O₂ combustion and a C₃H₈-air flame in a practical bluff-body combustor. Results show the method prevents new extrema near discontinuities while maintaining high-order accuracymore » in smooth regions. In particular, the method is extremely beneficial for combustion with stiff chemistry. With the proposed new method, even if flame fronts cross AMR interfaces or new grids are created in the vicinity of the flame, solution stability is retained.« less

Authors:

Overton‐Katz, Nathaniel  ^[1];

• Search DOE PAGES for author "Overton‐Katz, Nathaniel"
• Search DOE PAGES for ORCID "0000-0002-0846-0736"

Gao, Xinfeng ^[1]; Johansen, Hans  ^[2];

• Search DOE PAGES for author "Johansen, Hans"
• Search DOE PAGES for ORCID "0000-0002-9644-9982"

Guzik, Stephen M.  ^[1]

• Search DOE PAGES for author "Guzik, Stephen M."
• Search DOE PAGES for ORCID "0000-0001-9163-8787"

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+ Show Author Affiliations

1. Computational Fluid Dynamics and Propulsion Laboratory Colorado State University Fort Collins Colorado USA
2. Applied Numerical Algorithms Group Lawrence Berkeley National Laboratory Berkeley California USA

Publication Date:

Fri Dec 09 00:00:00 EST 2022

Research Org.:

Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Org.:

USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOD; National Science Foundation (NSF)

OSTI Identifier:

1902794

Alternate Identifier(s):

OSTI ID: 1924457; OSTI ID: 1983532

Grant/Contract Number:  

DE‐AC02‐05CH11231; AC02-05CH11231; FA9550-18-1-0057; 1723191

Resource Type:

Published Article

Journal Name:

International Journal for Numerical Methods in Fluids

Additional Journal Information:

Journal Name: International Journal for Numerical Methods in Fluids Journal Volume: 95 Journal Issue: 5; Journal ID: ISSN 0271-2091

Publisher:

Wiley Blackwell (John Wiley & Sons)

Country of Publication:

United Kingdom

Language:

English

Subject:

97 MATHEMATICS AND COMPUTING; adaptive clipping-and-redistribution; adaptive mesh refinement; computational combustion; high-order finite-volume method