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 discretization 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 nonreacting 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.

References in corpus (2)

• A Survey of High Level Frameworks in Block-Structured Adaptive Mesh Refinement Packages
• A Validated Nonlinear Kelvin-Helmholtz Benchmark for Numerical Hydrodynamics

Cited by in corpus (4)

• Improved Coupling of Hydrodynamics and Nuclear Reactions via Spectral Deferred Corrections
• Convergence analysis of multi-level spectral deferred corrections
• A mesh-free framework for high-order direct numerical simulations of combustion in complex geometries
• Performance of explicit and IMEX MRI multirate methods on complex reactive flow problems within modern parallel adaptive structured grid frameworks