A fourth-order adaptive mesh refinement algorithm for the multicomponent, reacting compressible Navier–Stokes equations

Abstract

In this paper, we present a fourth-order in space and time block-structured adaptive mesh refinement algorithm for the compressible multicomponent reacting Navier–Stokes equations. The algorithm uses a finite-volume approach that incorporates a fourth-order discretisation of the convective terms. The time-stepping algorithm is based on a multi-level spectral deferred corrections method that enables explicit treatment of advection and diffusion coupled with an implicit treatment of reactions. The temporal scheme is embedded in a block-structured adaptive mesh refinement algorithm that includes subcycling in time with spectral deferred correction sweeps applied on levels. Here we present the details of the multi-level scheme paying particular attention to the treatment of coarse–fine boundaries required to maintain fourth-order accuracy in time. We then demonstrate the convergence properties of the algorithm on several test cases including both non-reacting and reacting flows. Finally we present simulations of a vitiated dimethyl ether jet in 2D and a turbulent hydrogen jet in 3D, both with detailed kinetics and transport.

Keywords:

• spectral deferred corrections
• high-order numerical methods
• AMR
• DNS
• WENO schemes
• flame simulations

Acknowledgments

Part of the simulations were performed using resources of the National Energy Research Scientific Computing Center (NERSC), a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Emmanuel Motheau  http://orcid.org/0000-0003-1968-1611

Additional information

Funding

The work here was supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under contract number DE-AC02005CH11231.