High-Order Semi-Lagrangian Monte Carlo Simulations of Turbulent Mixing

This work presents simulations of the probability density function (PDF) of species undergoing turbulent mixing. A new algorithm, the Monte Carlo semi-Lagrangian discontinuous spectral element method (DSEM-SL), is used. The algorithm is based on classic spectral element methods, with the addition of a set of samples of Lagrangian particles at each of the spectral element Gauss quadrature points. At each time step, the particles are advected with a mean velocity and a stochastic diffusion velocity; their properties are then interpolated back onto the quadrature points, where the particles are re-initialized. This provides an inherent load-balancing by keeping constant the number of particles in each element. The diffusive Wiener increment is independent between samples of particles, but the same for all particles in a sample, thus preserving the smoothness of the species’ fields. The Monte Carlo DSEM-SL code is used to simulate the PDF of species mixing in a turbulent shear layer, with velocity and length scales relevant to hydrogen micromix combustors. Verification with an existing Lagrangian PDF code is performed, and the two approaches’ computational efficiencies are compared.