Scalar conservation and boundedness in simulations of compressible flow

Pramod K. Subbareddy; Anand Kartha; Graham V. Candler

doi:10.1016/j.jcp.2017.08.001

Scalar conservation and boundedness in simulations of compressible flow

Pramod K. Subbareddy, Anand Kartha, Graham V. Candler

Aerospace Engineering and Mechanics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

With the proper combination of high-order, low-dissipation numerical methods, physics-based subgrid-scale models, and boundary conditions it is becoming possible to simulate many combustion flows at relevant conditions. However, non-premixed flows are a particular challenge because the thickness of the fuel/oxidizer interface scales inversely with Reynolds number. Sharp interfaces can also be present in the initial or boundary conditions. When higher-order numerical methods are used, there are often aphysical undershoots and overshoots in the scalar variables (e.g. passive scalars, species mass fractions or progress variable). These numerical issues are especially prominent when low-dissipation methods are used, since sharp jumps in flow variables are not always coincident with regions of strong variation in the scalar fields: consequently, special detection mechanisms and dissipative fluxes are needed. Most numerical methods diffuse the interface, resulting in artificial mixing and spurious reactions. In this paper, we propose a numerical method that mitigates this issue. We present methods for passive and active scalars, and demonstrate their effectiveness with several examples.

Original language	English (US)
Pages (from-to)	827-846
Number of pages	20
Journal	Journal of Computational Physics
Volume	348
DOIs	https://doi.org/10.1016/j.jcp.2017.08.001
State	Published - Nov 1 2017

Bibliographical note

Funding Information:
We would like to acknowledge discussions with Paul Dimotakis and coworkers at the California Institute of Technology. This work was sponsored by Air Force Office of Scientific Research under grant numbers FA9550-12-1-0461 and FA9550-12-1-0064 and Department of Energy/National Nuclear Security Administration Award number DE-NA0002382. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the funding agencies or the U.S. Government.

Funding Information:
We would like to acknowledge discussions with Paul Dimotakis and coworkers at the California Institute of Technology. This work was sponsored by Air Force Office of Scientific Research under grant numbers FA9550-12-1-0461 and FA9550-12-1-0064 and Department of Energy/ National Nuclear Security Administration Award number DE-NA0002382 . The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the funding agencies or the U.S. Government.

Publisher Copyright:
© 2017 Elsevier Inc.

Keywords

Boundedness
Compressible flow
Multispecies
Numerical methods
Reacting flow
Scalar excursions

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10.1016/j.jcp.2017.08.001

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title = "Scalar conservation and boundedness in simulations of compressible flow",

abstract = "With the proper combination of high-order, low-dissipation numerical methods, physics-based subgrid-scale models, and boundary conditions it is becoming possible to simulate many combustion flows at relevant conditions. However, non-premixed flows are a particular challenge because the thickness of the fuel/oxidizer interface scales inversely with Reynolds number. Sharp interfaces can also be present in the initial or boundary conditions. When higher-order numerical methods are used, there are often aphysical undershoots and overshoots in the scalar variables (e.g. passive scalars, species mass fractions or progress variable). These numerical issues are especially prominent when low-dissipation methods are used, since sharp jumps in flow variables are not always coincident with regions of strong variation in the scalar fields: consequently, special detection mechanisms and dissipative fluxes are needed. Most numerical methods diffuse the interface, resulting in artificial mixing and spurious reactions. In this paper, we propose a numerical method that mitigates this issue. We present methods for passive and active scalars, and demonstrate their effectiveness with several examples.",

keywords = "Boundedness, Compressible flow, Multispecies, Numerical methods, Reacting flow, Scalar excursions",

author = "Subbareddy, {Pramod K.} and Anand Kartha and Candler, {Graham V.}",

note = "Funding Information: We would like to acknowledge discussions with Paul Dimotakis and coworkers at the California Institute of Technology. This work was sponsored by Air Force Office of Scientific Research under grant numbers FA9550-12-1-0461 and FA9550-12-1-0064 and Department of Energy/National Nuclear Security Administration Award number DE-NA0002382. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the funding agencies or the U.S. Government. Funding Information: We would like to acknowledge discussions with Paul Dimotakis and coworkers at the California Institute of Technology. This work was sponsored by Air Force Office of Scientific Research under grant numbers FA9550-12-1-0461 and FA9550-12-1-0064 and Department of Energy/ National Nuclear Security Administration Award number DE-NA0002382 . The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the funding agencies or the U.S. Government. Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

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doi = "10.1016/j.jcp.2017.08.001",

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AU - Kartha, Anand

AU - Candler, Graham V.

N1 - Funding Information: We would like to acknowledge discussions with Paul Dimotakis and coworkers at the California Institute of Technology. This work was sponsored by Air Force Office of Scientific Research under grant numbers FA9550-12-1-0461 and FA9550-12-1-0064 and Department of Energy/National Nuclear Security Administration Award number DE-NA0002382. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the funding agencies or the U.S. Government. Funding Information: We would like to acknowledge discussions with Paul Dimotakis and coworkers at the California Institute of Technology. This work was sponsored by Air Force Office of Scientific Research under grant numbers FA9550-12-1-0461 and FA9550-12-1-0064 and Department of Energy/ National Nuclear Security Administration Award number DE-NA0002382 . The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the funding agencies or the U.S. Government. Publisher Copyright: © 2017 Elsevier Inc.

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N2 - With the proper combination of high-order, low-dissipation numerical methods, physics-based subgrid-scale models, and boundary conditions it is becoming possible to simulate many combustion flows at relevant conditions. However, non-premixed flows are a particular challenge because the thickness of the fuel/oxidizer interface scales inversely with Reynolds number. Sharp interfaces can also be present in the initial or boundary conditions. When higher-order numerical methods are used, there are often aphysical undershoots and overshoots in the scalar variables (e.g. passive scalars, species mass fractions or progress variable). These numerical issues are especially prominent when low-dissipation methods are used, since sharp jumps in flow variables are not always coincident with regions of strong variation in the scalar fields: consequently, special detection mechanisms and dissipative fluxes are needed. Most numerical methods diffuse the interface, resulting in artificial mixing and spurious reactions. In this paper, we propose a numerical method that mitigates this issue. We present methods for passive and active scalars, and demonstrate their effectiveness with several examples.

AB - With the proper combination of high-order, low-dissipation numerical methods, physics-based subgrid-scale models, and boundary conditions it is becoming possible to simulate many combustion flows at relevant conditions. However, non-premixed flows are a particular challenge because the thickness of the fuel/oxidizer interface scales inversely with Reynolds number. Sharp interfaces can also be present in the initial or boundary conditions. When higher-order numerical methods are used, there are often aphysical undershoots and overshoots in the scalar variables (e.g. passive scalars, species mass fractions or progress variable). These numerical issues are especially prominent when low-dissipation methods are used, since sharp jumps in flow variables are not always coincident with regions of strong variation in the scalar fields: consequently, special detection mechanisms and dissipative fluxes are needed. Most numerical methods diffuse the interface, resulting in artificial mixing and spurious reactions. In this paper, we propose a numerical method that mitigates this issue. We present methods for passive and active scalars, and demonstrate their effectiveness with several examples.

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KW - Reacting flow

KW - Scalar excursions

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JO - Journal of Computational Physics

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SN - 0021-9991

ER -

Scalar conservation and boundedness in simulations of compressible flow

Abstract

Bibliographical note

Keywords

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