Ensuring ∑ₛYₛ = 1 in transport of species mass fractions

Creators: Baumgart, Alexandra; Blanquart, Guillaume¹

1. California Institute of Technology

Abstract

Reacting flow simulations often require the transport of several species mass fractions. Unfortunately, the solutions of the discretized species equations do not always meet key physical constraints: namely, each mass fraction must be bounded between 0 and 1, and the sum of mass fractions must be equal to 1. First order linear schemes such as upwind meet these constraints, but are very dissipative. High order linear schemes (e.g., QUICK [1]) ensure the sum of mass fractions equals 1, but are not bounded. Nonlinear schemes such as weighted essentially non-oscillatory (WENO) schemes are often preferred for their high order accuracy and non-oscillatory property. However, the sum of mass fractions is not guaranteed to equal 1.

A variety of approaches have been used to address this challenge [2], [3], [4], [5]. In detailed chemistry simulations, often out of the N species equations are transported, with the last inert species being computed to maintain a sum equal to 1 [2]. Alternatively, the mass fractions may be renormalized after computing the reconstruction at the faces [3]. Algorithms have been derived to satisfy both physical constraints [4], [5], although the conditions are scheme-dependent and do not extend easily to multiple dimensions. Here, we propose a simple method for preserving the sum of mass fractions without penalizing the inert species.

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Acknowledgement

This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Department of Energy Computational Science Graduate Fellowship under Award Number DE-SC0021110. This work used Stampede3 at TACC through allocation MCH230009 from the Advanced Cyberinfrastructure Coordination Ecosystem: Services & Support (ACCESS) program, which is supported by National Science Foundation grants #2138259, #2138286, #2138307, #2137603, and #2138296.

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

Contributions

Alexandra Baumgart: Writing – original draft, Visualization, Validation, Software, Resources, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. Guillaume Blanquart: Writing – review & editing, Supervision, Methodology, Funding acquisition, Conceptualization.

Data Availability

Data will be made available on request.

Conflict of Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Resource type: Journal Article
Publisher: Elsevier
Published in: Journal of Computational Physics, 513, 113199, ISSN: 0021-9991.
Languages: English

Ensuring ∑ₛYₛ = 1 in transport of species mass fractions