A fully coupled high‐order discontinuous Galerkin method for diffusion flames in a low‐Mach number framework

Abstract

We present a fully coupled solver based on the discontinuous Galerkin method for steady‐state diffusion flames using the low‐Mach approximation of the governing equations with a one‐step kinetic model. The nonlinear equation system is solved with a Newton–Dogleg method and initial estimates for flame calculations are obtained from a flame‐sheet model. Details on the spatial discretization and the nonlinear solver are presented. The method is tested with reactive and nonreactive benchmark cases. Convergence studies are presented, and we show that the expected convergence rates are obtained. The solver for the low‐Mach equations is used for calculating a differentially heated cavity configuration, which is validated against benchmark solutions. Additionally, a two‐dimensional counter diffusion flame is calculated, and the results are compared with the self‐similar one dimensional solution of said configuration.

An extended discontinuous Galerkin shock tracking method

“…The BoSSS code has found successful applications in a range of challenging scenarios. These applications include simulations of incompressible flows with active particles, 39 compressible inviscid and viscous flows with moving immersed boundaries, 22 extension for shock-capturing in high Mach number flows, 23 diffusion flames in low Mach number flows, 40 incompressible multiphase flows, 41 viscoelastic fluid flows 42 and helical flows, 43,44 are not supported. All XDG shock tracking test cases discussed in this work (Section 7) can be reproduced by downloading the publicly available repository 2 and starting the respective jupyter notebooks from the directory ./examples/ShockFitting.…”