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

• Published in: Combustion theory and modelling Vol. 23; no. 4; pp. 592 - 625
• Main Authors: Emmett, Matthew, Motheau, Emmanuel, Zhang, Weiqun, Minion, Michael, Bell, John B.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 04.07.2019; Taylor & Francis Ltd
• Subjects: Adaptive algorithms; Algorithms; AMR; Compressibility; Computer simulation; Dimethyl ether; DNS; Finite element method; flame simulations; Fluid dynamics; Fluid flow; Grid refinement (mathematics); high-order numerical methods; Mathematical analysis; MATHEMATICS AND COMPUTING; Navier-Stokes equations; Reaction kinetics; spectral deferred corrections; Two dimensional jets; WENO schemes
• ISSN: 1364-7830; 1741-3559
• DOI: 10.1080/13647830.2019.1566574

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.