An Implicit Multigrid Method for Turbulent Combustion

An implicit multigrid scheme for solving the Navier–Stokes, turbulence, species, and variance transport equations describing turbulent combustion is presented. Turbulence chemistry interaction is included by use of presumed probability density functions (pdf). To avoid stiffness problems associated with chemically reacting flows, time integration is performed by an implicit LU-SGS algorithm. This requires the formation of a source term Jacobian. The complete, analytically derived Jacobian, including assumed pdf modeling, is given in the present paper. Thus, the high numerical stability of the original algorithm is maintained. Convergence acceleration is accomplished by a nonlinear multigrid method. Strongly nonlinear source terms in species, turbulence, and variance conservation equations usually keep multigrid methods from converging. It is shown that freezing of coarse grid source terms including spatial derivatives and restriction damping in regions of high chemical activity may remedy this problem. Two finite-rate chemistry test cases with methane and hydrogen combustion at supersonic speed demonstrate a strong reduction in required CPU time.