A Fourth-Order Adaptive Mesh Refinement Algorithm for the Multicomponent, Reacting Compressible Navier-Stokes Equations

TL;DR

This paper introduces a fourth-order adaptive mesh refinement algorithm for multicomponent reacting compressible Navier-Stokes equations, combining high-order spatial discretization with multi-level spectral deferred corrections for accurate, efficient simulations of complex reacting flows.

Contribution

It develops a novel fourth-order in space and time adaptive mesh refinement scheme with spectral deferred corrections for reacting Navier-Stokes equations, enabling high-accuracy simulations of complex flows.

Findings

Demonstrates convergence on test cases including nonreacting and reacting flows.

Shows accurate simulation of dimethyl ether jet and turbulent hydrogen jet.

Maintains fourth-order accuracy at coarse-fine boundaries.

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.