A high-order numerical algorithm for DNS of low-Mach-number reactive flows with detailed chemistry and quasi-spectral accuracy. A novel and efficient algorithm is presented in this paper to deal with DNS of turbulent reacting flows under the low-Mach-number assumption, with detailed chemistry and a quasi-spectral accuracy. The temporal integration of the equations relies on an operating-split strategy, where chemical reactions are solved implicitly with a stiff solver and the convection-diffusion operators are solved with a Runge-Kutta-Chebyshev method. The spatial discretisation is performed with high-order compact schemes, and a FFT based constant-coefficient spectral solver is employed to solve a variable-coefficient Poisson equation. The numerical implementation takes advantage of the 2DECOMP & FFT libraries developed by [1], which are based on a pencil decomposition method of the domain and are proven to be computationally very efficient. An enhanced pressure-correction method is proposed to speed up the achievement of machine precision accuracy. It is demonstrated that a second-order accuracy is reached in time, while the spatial accuracy ranges from fourth-order to sixth-order depending on the set of imposed boundary conditions. The software developed to implement the present algorithm is called HOLOMAC, and its numerical efficiency opens the way to deal with DNS of reacting flows to understand complex turbulent and chemical phenomena in flames.

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  1. Scapin, Nicolò; Barba, Federico Dalla; Lupo, Giandomenico; Rosti, Marco Edorardo; Duwig, Christophe; Brandt, Luca: Finite-size evaporating droplets in weakly compressible homogeneous shear turbulence (2022)
  2. Abdelsamie, Abouelmagd; Lartigue, Ghislain; Frouzakis, Christos E.; Thévenin, Dominique: The Taylor-Green vortex as a benchmark for high-fidelity combustion simulations using low-Mach solvers (2021)
  3. Barba, Federico Dalla; Scapin, Nicoló; Demou, Andreas D.; Rosti, Marco E.; Picano, Francesco; Brandt, Luca: An interface capturing method for liquid-gas flows at low-Mach number (2021)
  4. Abide, Stéphane: Finite difference preconditioning for compact scheme discretizations of the Poisson equation with variable coefficients (2020)
  5. Bermúdez, A.; Busto, S.; Dumbser, M.; Ferrín, J. L.; Saavedra, L.; Vázquez-Cendón, M. E.: A staggered semi-implicit hybrid FV/FE projection method for weakly compressible flows (2020)
  6. Chung, Joseph D.; Zhang, Xiao; Kaplan, Carolyn R.; Oran, Elaine S.: The barely implicit correction algorithm for low-Mach-number flows. II: Application to reactive flows (2020)
  7. Lu, Xiaoyi; Pantano, Carlos: On mass conservation and solvability of the discretized variable-density zero-Mach Navier-Stokes equations (2020)
  8. Emmett, Matthew; Motheau, Emmanuel; Zhang, Weiqun; Minion, Michael; Bell, John B.: A fourth-order adaptive mesh refinement algorithm for the multicomponent, reacting compressible Navier-Stokes equations (2019)
  9. Hamon, François P.; Day, Marcus S.; Minion, Michael L.: Concurrent implicit spectral deferred correction scheme for low-Mach number combustion with detailed chemistry (2019)
  10. Hardy, Baptiste; De Wilde, Juray; Winckelmans, Grégoire: A penalization method for the simulation of weakly compressible reacting gas-particle flows with general boundary conditions (2019)
  11. Motheau, Emmanuel; Duarte, Max; Almgren, Ann; Bell, John B.: A hybrid adaptive low-Mach number/compressible method: Euler equations (2018)
  12. Nonaka, Andrew; Day, Marcus S.; Bell, John B.: A conservative, thermodynamically consistent numerical approach for low Mach number combustion. I: Single-level integration (2018)
  13. Su, Yunde; Kim, Seung Hyun: An improved consistent, conservative, non-oscillatory and high order finite difference scheme for variable density low Mach number turbulent flow simulation (2018)
  14. Motheau, E.; Abraham, J.: A high-order numerical algorithm for DNS of low-Mach-number reactive flows with detailed chemistry and quasi-spectral accuracy (2016)