A novel Kalman filter based approach for multiscale reacting flow simulations

• We propose a novel approach for coupling fine- and coarse-grained solutions for coupling the density for reacting flows.
• The approach uses the Kalman filter to couple the fine-grained and coarse-grained solutions to the density.
• The combined solution results in the smoothing of the density profiles.
• This solution also capture the effects of heat release from fine-grained solutions.

A multi-scale approach for coupling a coarse-grained (CG) deterministic solution for a reacting flow with a fine-grained (FG) stochastic solution is proposed. The model includes a CG solution for the mass density and momentum and a FG solution for the temperature. A model for the turbulent transport in the FG solution is implemented using the linear-eddy model (LEM), which combines a deterministic implementation for reaction, diffusion and large-scale transport with a stochastic implementation for fine-scale transport. A common variable is obtained from these solutions based on a CG density field defined from continuity on the coarse scales and the spatial filtering of the density derived from the state equation in the FG solution. Kalman filtering is used to combine these two solutions. The resulting CG density is both smooth and steered by heat release from the FG solution. The algorithm is demonstrated on a 1D model combining continuity and the Burgers’ equation for the CG solution and the temperature equation with heat release for the FG solution. The results establish the feasibility of Kalman filtering in coupling deterministic CG solutions and stochastic FG solutions in reacting flow applications.