Hybrid High-order Eulerian-Lagrangian methods for simulations of particle-laden flow with shocks
نویسندگان
چکیده
The development of a Hybrid high order Eulerian-Lagrangian algorithm to simulate shock wave interactions with particles is discussed. The Hybrid high order WENO/central finite difference scheme is assessed in three-dimensional simulations, as well as the effective use of the high order polynomials and regularization techniques in the approximation to the singular source term in the advection equation. The mathematical model is based on a coupled system, consisting of a non-linear hyperbolic conservation laws with a source term that accounts the influence of the particles on the flow and kinematic equations, which govern the fluid flow and particle motion, respectively. The continuum conservation equations solve the carrier flow with a Hybrid scheme that uses the weighted essentially non-oscillatory (WENO) method for shock capturing, and a more computationally efficient high order scheme, including a central finite difference or spectral methods in regions where the solution is smooth. Numerical experiments illustrate the accuracy and efficiency of the Hybrid code compared with the pure WENO. Initial efforts have been made towards the development of a Hybrid WENO-spectral particle-source-in-cell (PSIC) algorithm. Specifically, a new regularization of the singular source term through polynomial approximations that couples particles and fluid have shown regularize discontinuities while converging at higher error away from discontinuity.
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